TPTP Problem File: GRP001-5.p
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%------------------------------------------------------------------------------
% File : GRP001-5 : TPTP v9.0.0. Released v1.0.0.
% Domain : Group Theory
% Problem : X^2 = identity => commutativity
% Version : [Cha70] axioms : Incomplete.
% English : If the square of every element is the identity, the system
% is commutative.
% Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% : [Lov69] Loveland (1969), Theorem-provers Combining Model Elimi
% : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% : [MRS72] Michie et al. (1972), G-deduction
% : [RR+72] Reboh et al. (1972), Study of automatic theorem provin
% : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [Cha70]
% Names : Example 4 [Luc68]
% : Example 1 [Lov69]
% : Example 2 [Cha70]
% : ROB2 [MRS72]
% : GROUP2 [RR+72]
% : Example 2 [CL73]
% : GROUP2 [WM76]
% : ROB2 [WM76]
% : EX2 [SPRFN]
% Status : Unsatisfiable
% Rating : 0.00 v2.2.0, 0.11 v2.1.0, 0.00 v2.0.0
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 4 RR)
% Number of literals : 13 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn)
% SPC : CNF_UNS_EPR_NEQ_HRN
% Comments : In this format it is essentially a monoid problem.
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cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(associativity1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(square_element,hypothesis,
product(X,X,identity) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c) ).
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