2 include "logic/equality.ma".
3 (* Inclusion of: ROB013-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : ROB013-1 : 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 (* Source : [Win90] *)
12 (* Names : Lemma 3.5 [Win90] *)
13 (* Status : Unsatisfiable *)
14 (* Rating : 0.00 v2.0.0 *)
15 (* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *)
16 (* Number of atoms : 5 ( 5 equality) *)
17 (* Maximal clause size : 1 ( 1 average) *)
18 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
19 (* Number of functors : 5 ( 3 constant; 0-2 arity) *)
20 (* Number of variables : 7 ( 0 singleton) *)
21 (* Maximal term depth : 6 ( 3 average) *)
23 (* -------------------------------------------------------------------------- *)
24 (* ----Include axioms for Robbins algebra *)
25 (* Inclusion of: Axioms/ROB001-0.ax *)
26 (* -------------------------------------------------------------------------- *)
27 (* File : ROB001-0 : TPTP v3.1.1. Released v1.0.0. *)
28 (* Domain : Robbins algebra *)
29 (* Axioms : Robbins algebra axioms *)
30 (* Version : [Win90] (equality) axioms. *)
32 (* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
33 (* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
34 (* Source : [OTTER] *)
35 (* Names : Lemma 2.2 [Win90] *)
37 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
38 (* Number of literals : 3 ( 3 equality) *)
39 (* Maximal clause size : 1 ( 1 average) *)
40 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
41 (* Number of functors : 2 ( 0 constant; 1-2 arity) *)
42 (* Number of variables : 7 ( 0 singleton) *)
43 (* Maximal term depth : 6 ( 3 average) *)
45 (* -------------------------------------------------------------------------- *)
46 (* -------------------------------------------------------------------------- *)
47 (* -------------------------------------------------------------------------- *)
51 \forall add:\forall _:Univ.\forall _:Univ.Univ.
54 \forall negate:\forall _:Univ.Univ.
55 \forall H0:eq Univ (negate (add a b)) c.
56 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
57 \forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
58 \forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add (negate b) a)))) a
61 autobatch paramodulation timeout=100;
65 (* -------------------------------------------------------------------------- *)