2 include "logic/equality.ma".
3 (* Inclusion of: ROB010-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : ROB010-1 : TPTP v3.1.1. Released v1.0.0. *)
6 (* Domain : Robbins Algebra *)
7 (* Problem : If -(a + -b) = c then -(c + -(b + a)) = a *)
8 (* Version : [Win90] (equality) axioms. *)
10 (* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
11 (* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
12 (* Source : [Win90] *)
13 (* Names : Lemma 3.3 [Win90] *)
15 (* Status : Unsatisfiable *)
16 (* Rating : 0.00 v2.0.0 *)
17 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *)
18 (* Number of atoms : 5 ( 5 equality) *)
19 (* Maximal clause size : 1 ( 1 average) *)
20 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
21 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
22 (* Number of variables : 7 ( 0 singleton) *)
23 (* Maximal term depth : 6 ( 3 average) *)
25 (* -------------------------------------------------------------------------- *)
26 (* ----Include axioms for Robbins algebra *)
27 (* Inclusion of: Axioms/ROB001-0.ax *)
28 (* -------------------------------------------------------------------------- *)
29 (* File : ROB001-0 : TPTP v3.1.1. Released v1.0.0. *)
30 (* Domain : Robbins algebra *)
31 (* Axioms : Robbins algebra axioms *)
32 (* Version : [Win90] (equality) axioms. *)
34 (* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
35 (* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
36 (* Source : [OTTER] *)
37 (* Names : Lemma 2.2 [Win90] *)
39 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
40 (* Number of literals : 3 ( 3 equality) *)
41 (* Maximal clause size : 1 ( 1 average) *)
42 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
43 (* Number of functors : 2 ( 0 constant; 1-2 arity) *)
44 (* Number of variables : 7 ( 0 singleton) *)
45 (* Maximal term depth : 6 ( 3 average) *)
47 (* -------------------------------------------------------------------------- *)
48 (* -------------------------------------------------------------------------- *)
49 (* -------------------------------------------------------------------------- *)
53 \forall add:\forall _:Univ.\forall _:Univ.Univ.
56 \forall negate:\forall _:Univ.Univ.
57 \forall H0:eq Univ (negate (add a (negate b))) c.
58 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
59 \forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
60 \forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add b a)))) a
63 autobatch paramodulation timeout=100;
67 (* -------------------------------------------------------------------------- *)