%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:09 AM UTC 2026
% Result : Unsatisfiable 111.19s 14.48s
% Output : CNFRefutation 111.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 10
% Syntax : Number of clauses : 193 ( 193 unt; 0 nHn; 43 RR)
% Number of literals : 193 ( 192 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 342 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_substitution) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,equalish(inverse(a),inverse(b)),true) = equalish(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
equalish(inverse(a),inverse(b)) = ifeq(true,true,equalish(inverse(a),inverse(b)),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true) = ifeq(true,true,equalish(inverse(a),inverse(b)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
ifeq(true,true,equalish(inverse(a),inverse(b)),true) = ifeq(true,true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,product(X2,identity,X2),true) = product(X2,identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
product(X2,identity,X2) = ifeq(true,true,product(X2,identity,X2),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,product(X2,inverse(X2),identity),true) = product(X2,inverse(X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
product(X2,inverse(X2),identity) = ifeq(true,true,product(X2,inverse(X2),identity),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,equalish(multiply(X2,inverse(X2)),identity),true) = equalish(multiply(X2,inverse(X2)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
equalish(multiply(X2,inverse(X2)),identity) = ifeq(true,true,equalish(multiply(X2,inverse(X2)),identity),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,product(inverse(inverse(X2)),X3,multiply(X2,X3)),true) = product(inverse(inverse(X2)),X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
product(inverse(inverse(X3)),X2,multiply(X3,X2)) = ifeq(true,true,product(inverse(inverse(X3)),X2,multiply(X3,X2)),true),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true) = product(inverse(X3),multiply(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
product(inverse(X3),multiply(X3,X2),X2) = ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
cnf(c18,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true) = ifeq(product(X3,X2,multiply(X3,X2)),true,product(inverse(X3),multiply(X3,X2),X2),true),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,product(inverse(X3),X4,X2),true) = product(inverse(X3),X4,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
product(inverse(X4),X2,X3) = ifeq(true,true,product(inverse(X4),X2,X3),true),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq(product(X4,X3,X2),true,product(inverse(X4),X2,X3),true) = ifeq(product(X4,X3,X2),true,ifeq(true,true,product(inverse(X4),X2,X3),true),true),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
product(inverse(X2),X2,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c25,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq(true,true,product(inverse(X4),X2,X3),true) = ifeq(product(inverse(X4),X4,identity),true,product(inverse(X4),X2,X3),true),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(inverse(X4),X2,X3),true),true) = ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X4),X4,identity),true,product(inverse(X4),X2,X3),true),true),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,ifeq(product(X5,X4,identity),true,product(X5,X2,X3),true),true),true) = ifeq(product(X4,X3,X2),true,ifeq(product(X5,X4,identity),true,product(X5,X2,X3),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true) = ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
product(identity,X2,X2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
true = product(identity,X2,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = ifeq(product(identity,X4,X4),true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,axiom,
ifeq(product(U,Z,W),true,ifeq(product(Y2,Z,V),true,ifeq(product(X2,Y2,U),true,product(X2,V,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(c34,plain,
ifeq(product(identity,X4,X4),true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = true,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = true,
inference(transitivity,[status(thm)],[c32,c34]) ).
cnf(c36,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true) = true,
inference(transitivity,[status(thm)],[c29,c35]) ).
cnf(c37,plain,
ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X4),X4,identity),true,product(inverse(X4),X2,X3),true),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(inverse(X4),X2,X3),true),true) = true,
inference(transitivity,[status(thm)],[c27,c37]) ).
cnf(c39,plain,
ifeq(product(X4,X3,X2),true,product(inverse(X4),X2,X3),true) = true,
inference(transitivity,[status(thm)],[c23,c38]) ).
cnf(c40,plain,
ifeq(product(X3,X2,multiply(X3,X2)),true,product(inverse(X3),multiply(X3,X2),X2),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true) = true,
inference(transitivity,[status(thm)],[c20,c40]) ).
cnf(c42,plain,
product(inverse(X3),multiply(X3,X2),X2) = true,
inference(transitivity,[status(thm)],[c16,c41]) ).
cnf(c43,plain,
true = product(inverse(X3),multiply(X3,X2),X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(true,true,product(inverse(inverse(X3)),X2,multiply(X3,X2)),true) = ifeq(product(inverse(X3),multiply(X3,X2),X2),true,product(inverse(inverse(X3)),X2,multiply(X3,X2)),true),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq(product(inverse(X3),multiply(X3,X2),X2),true,product(inverse(inverse(X3)),X2,multiply(X3,X2)),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c46,plain,
ifeq(true,true,product(inverse(inverse(X3)),X2,multiply(X3,X2)),true) = true,
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
product(inverse(inverse(X3)),X2,multiply(X3,X2)) = true,
inference(transitivity,[status(thm)],[c14,c46]) ).
cnf(c48,plain,
product(inverse(inverse(X2)),inverse(X2),multiply(X2,inverse(X2))) = true,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
true = product(inverse(inverse(X2)),inverse(X2),multiply(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(true,true,equalish(multiply(X2,inverse(X2)),identity),true) = ifeq(product(inverse(inverse(X2)),inverse(X2),multiply(X2,inverse(X2))),true,equalish(multiply(X2,inverse(X2)),identity),true),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq(true,true,ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),true) = ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true) = ifeq(true,true,ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),true),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c54,plain,
ifeq(true,true,ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),true) = ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
ifeq(product(X2,Y2,W2),true,ifeq(product(X2,Y2,Z2),true,equalish(Z2,W2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
cnf(c56,plain,
ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),true) = true,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(true,true,ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true),true) = true,
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
ifeq(product(inverse(X3),X3,X2),true,equalish(X2,identity),true) = true,
inference(transitivity,[status(thm)],[c52,c57]) ).
cnf(c59,plain,
ifeq(product(inverse(inverse(X2)),inverse(X2),multiply(X2,inverse(X2))),true,equalish(multiply(X2,inverse(X2)),identity),true) = true,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(true,true,equalish(multiply(X2,inverse(X2)),identity),true) = true,
inference(transitivity,[status(thm)],[c50,c59]) ).
cnf(c61,plain,
equalish(multiply(X2,inverse(X2)),identity) = true,
inference(transitivity,[status(thm)],[c12,c60]) ).
cnf(c62,plain,
true = equalish(multiply(X2,inverse(X2)),identity),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq(true,true,product(X2,inverse(X2),identity),true) = ifeq(equalish(multiply(X2,inverse(X2)),identity),true,product(X2,inverse(X2),identity),true),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
ifeq(true,true,product(X4,X3,X2),true) = product(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c65,plain,
product(X4,X3,X2) = ifeq(true,true,product(X4,X3,X2),true),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
ifeq(equalish(multiply(X4,X3),X2),true,product(X4,X3,X2),true) = ifeq(equalish(multiply(X4,X3),X2),true,ifeq(true,true,product(X4,X3,X2),true),true),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c68,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq(true,true,product(X4,X3,X2),true) = ifeq(product(X4,X3,multiply(X4,X3)),true,product(X4,X3,X2),true),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
ifeq(equalish(multiply(X4,X3),X2),true,ifeq(true,true,product(X4,X3,X2),true),true) = ifeq(equalish(multiply(X4,X3),X2),true,ifeq(product(X4,X3,multiply(X4,X3)),true,product(X4,X3,X2),true),true),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,axiom,
ifeq(equalish(X2,Y2),true,ifeq(product(W2,Z2,X2),true,product(W2,Z2,Y2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
cnf(c72,plain,
ifeq(equalish(multiply(X4,X3),X2),true,ifeq(product(X4,X3,multiply(X4,X3)),true,product(X4,X3,X2),true),true) = true,
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(equalish(multiply(X4,X3),X2),true,ifeq(true,true,product(X4,X3,X2),true),true) = true,
inference(transitivity,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
ifeq(equalish(multiply(X4,X3),X2),true,product(X4,X3,X2),true) = true,
inference(transitivity,[status(thm)],[c66,c73]) ).
cnf(c75,plain,
ifeq(equalish(multiply(X2,inverse(X2)),identity),true,product(X2,inverse(X2),identity),true) = true,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,product(X2,inverse(X2),identity),true) = true,
inference(transitivity,[status(thm)],[c63,c75]) ).
cnf(c77,plain,
product(X2,inverse(X2),identity) = true,
inference(transitivity,[status(thm)],[c10,c76]) ).
cnf(c78,plain,
true = product(X2,inverse(X2),identity),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
ifeq(true,true,product(X2,identity,X2),true) = ifeq(product(X2,inverse(X2),identity),true,product(X2,identity,X2),true),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
ifeq(true,true,ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),true) = ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true) = ifeq(true,true,ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),true),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c83,plain,
ifeq(true,true,ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),true) = ifeq(product(inverse(X2),X2,identity),true,ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),true),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(product(inverse(X2),X2,identity),true,ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c85,plain,
ifeq(true,true,ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true),true) = true,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
ifeq(product(X3,inverse(X2),identity),true,product(X3,identity,X2),true) = true,
inference(transitivity,[status(thm)],[c81,c85]) ).
cnf(c87,plain,
ifeq(product(X2,inverse(X2),identity),true,product(X2,identity,X2),true) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
ifeq(true,true,product(X2,identity,X2),true) = true,
inference(transitivity,[status(thm)],[c79,c87]) ).
cnf(c89,plain,
product(X2,identity,X2) = true,
inference(transitivity,[status(thm)],[c8,c88]) ).
cnf(c90,plain,
product(inverse(b),identity,inverse(b)) = true,
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
true = product(inverse(b),identity,inverse(b)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
ifeq(true,true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true) = ifeq(product(inverse(b),identity,inverse(b)),true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
ifeq(true,true,product(inverse(b),identity,inverse(a)),true) = product(inverse(b),identity,inverse(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
product(inverse(b),identity,inverse(a)) = ifeq(true,true,product(inverse(b),identity,inverse(a)),true),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),X2,X2),true) = product(multiply(inverse(b),inverse(inverse(a))),X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c96,plain,
product(multiply(inverse(b),inverse(inverse(a))),X2,X2) = ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),X2,X2),true),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true) = product(multiply(inverse(b),inverse(inverse(a))),identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c98,plain,
product(multiply(inverse(b),inverse(inverse(a))),identity,identity) = ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(true,true,product(inverse(inverse(a)),identity,b),true) = product(inverse(inverse(a)),identity,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
product(inverse(inverse(a)),identity,b) = ifeq(true,true,product(inverse(inverse(a)),identity,b),true),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
ifeq(true,true,product(inverse(inverse(X2)),identity,X2),true) = product(inverse(inverse(X2)),identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c102,plain,
product(inverse(inverse(X2)),identity,X2) = ifeq(true,true,product(inverse(inverse(X2)),identity,X2),true),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
product(inverse(inverse(X2)),inverse(X2),identity) = true,
inference(substitution,[status(thm)],[c24]) ).
cnf(c104,plain,
true = product(inverse(inverse(X2)),inverse(X2),identity),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
ifeq(true,true,product(inverse(inverse(X2)),identity,X2),true) = ifeq(product(inverse(inverse(X2)),inverse(X2),identity),true,product(inverse(inverse(X2)),identity,X2),true),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(product(inverse(inverse(X2)),inverse(X2),identity),true,product(inverse(inverse(X2)),identity,X2),true) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c107,plain,
ifeq(true,true,product(inverse(inverse(X2)),identity,X2),true) = true,
inference(transitivity,[status(thm)],[c105,c106]) ).
cnf(c108,plain,
product(inverse(inverse(X2)),identity,X2) = true,
inference(transitivity,[status(thm)],[c102,c107]) ).
cnf(c109,plain,
product(inverse(inverse(a)),identity,a) = true,
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
true = product(inverse(inverse(a)),identity,a),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
ifeq(true,true,product(inverse(inverse(a)),identity,b),true) = ifeq(product(inverse(inverse(a)),identity,a),true,product(inverse(inverse(a)),identity,b),true),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
ifeq(true,true,ifeq(product(X3,X2,a),true,product(X3,X2,b),true),true) = ifeq(product(X3,X2,a),true,product(X3,X2,b),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c113,plain,
ifeq(product(X3,X2,a),true,product(X3,X2,b),true) = ifeq(true,true,ifeq(product(X3,X2,a),true,product(X3,X2,b),true),true),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,axiom,
equalish(a,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c115,plain,
true = equalish(a,b),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
ifeq(true,true,ifeq(product(X3,X2,a),true,product(X3,X2,b),true),true) = ifeq(equalish(a,b),true,ifeq(product(X3,X2,a),true,product(X3,X2,b),true),true),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
ifeq(equalish(a,b),true,ifeq(product(X3,X2,a),true,product(X3,X2,b),true),true) = true,
inference(substitution,[status(thm)],[c71]) ).
cnf(c118,plain,
ifeq(true,true,ifeq(product(X3,X2,a),true,product(X3,X2,b),true),true) = true,
inference(transitivity,[status(thm)],[c116,c117]) ).
cnf(c119,plain,
ifeq(product(X3,X2,a),true,product(X3,X2,b),true) = true,
inference(transitivity,[status(thm)],[c113,c118]) ).
cnf(c120,plain,
ifeq(product(inverse(inverse(a)),identity,a),true,product(inverse(inverse(a)),identity,b),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
ifeq(true,true,product(inverse(inverse(a)),identity,b),true) = true,
inference(transitivity,[status(thm)],[c111,c120]) ).
cnf(c122,plain,
product(inverse(inverse(a)),identity,b) = true,
inference(transitivity,[status(thm)],[c100,c121]) ).
cnf(c123,plain,
true = product(inverse(inverse(a)),identity,b),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true) = ifeq(product(inverse(inverse(a)),identity,b),true,product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true) = product(multiply(inverse(X2),X4),X3,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c126,plain,
product(multiply(inverse(X2),X4),X3,identity) = ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
ifeq(product(X4,X3,X2),true,product(multiply(inverse(X2),X4),X3,identity),true) = ifeq(product(X4,X3,X2),true,ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),true),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
product(inverse(X2),X3,multiply(inverse(X2),X3)) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c129,plain,
true = product(inverse(X2),X3,multiply(inverse(X2),X3)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true) = ifeq(product(inverse(X2),X4,multiply(inverse(X2),X4)),true,product(multiply(inverse(X2),X4),X3,identity),true),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),true) = ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X2),X4,multiply(inverse(X2),X4)),true,product(multiply(inverse(X2),X4),X3,identity),true),true),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c133,plain,
ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true) = ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c136,plain,
ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,axiom,
ifeq(product(Y2,Z2,V2),true,ifeq(product(X2,V2,W2),true,ifeq(product(X2,Y2,U2),true,product(U2,Z2,W2),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(c139,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true) = true,
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true) = true,
inference(transitivity,[status(thm)],[c137,c139]) ).
cnf(c141,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = true,
inference(transitivity,[status(thm)],[c134,c140]) ).
cnf(c142,plain,
ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X2),X4,multiply(inverse(X2),X4)),true,product(multiply(inverse(X2),X4),X3,identity),true),true) = true,
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),true) = true,
inference(transitivity,[status(thm)],[c131,c142]) ).
cnf(c144,plain,
ifeq(product(X4,X3,X2),true,product(multiply(inverse(X2),X4),X3,identity),true) = true,
inference(transitivity,[status(thm)],[c127,c143]) ).
cnf(c145,plain,
ifeq(product(inverse(inverse(a)),identity,b),true,product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true) = true,
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true) = true,
inference(transitivity,[status(thm)],[c124,c145]) ).
cnf(c147,plain,
product(multiply(inverse(b),inverse(inverse(a))),identity,identity) = true,
inference(transitivity,[status(thm)],[c98,c146]) ).
cnf(c148,plain,
true = product(multiply(inverse(b),inverse(inverse(a))),identity,identity),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),X2,X2),true) = ifeq(product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true,product(multiply(inverse(b),inverse(inverse(a))),X2,X2),true),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
ifeq(true,true,ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),true) = ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c151,plain,
ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true) = ifeq(true,true,ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),true),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
true = product(identity,X2,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c153,plain,
ifeq(true,true,ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),true) = ifeq(product(identity,X2,X2),true,ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),true),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
ifeq(product(identity,X2,X2),true,ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c155,plain,
ifeq(true,true,ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true),true) = true,
inference(transitivity,[status(thm)],[c153,c154]) ).
cnf(c156,plain,
ifeq(product(X3,identity,identity),true,product(X3,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c151,c155]) ).
cnf(c157,plain,
ifeq(product(multiply(inverse(b),inverse(inverse(a))),identity,identity),true,product(multiply(inverse(b),inverse(inverse(a))),X2,X2),true) = true,
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
ifeq(true,true,product(multiply(inverse(b),inverse(inverse(a))),X2,X2),true) = true,
inference(transitivity,[status(thm)],[c149,c157]) ).
cnf(c159,plain,
product(multiply(inverse(b),inverse(inverse(a))),X2,X2) = true,
inference(transitivity,[status(thm)],[c96,c158]) ).
cnf(c160,plain,
product(multiply(inverse(b),inverse(inverse(a))),inverse(a),inverse(a)) = true,
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
true = product(multiply(inverse(b),inverse(inverse(a))),inverse(a),inverse(a)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
ifeq(true,true,product(inverse(b),identity,inverse(a)),true) = ifeq(product(multiply(inverse(b),inverse(inverse(a))),inverse(a),inverse(a)),true,product(inverse(b),identity,inverse(a)),true),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
ifeq(true,true,product(X3,identity,X2),true) = product(X3,identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c164,plain,
product(X3,identity,X2) = ifeq(true,true,product(X3,identity,X2),true),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,product(X4,identity,X2),true) = ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,ifeq(true,true,product(X4,identity,X2),true),true),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
product(X3,inverse(X2),multiply(X3,inverse(X2))) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c167,plain,
true = product(X3,inverse(X2),multiply(X3,inverse(X2))),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
ifeq(true,true,product(X4,identity,X2),true) = ifeq(product(X4,inverse(X3),multiply(X4,inverse(X3))),true,product(X4,identity,X2),true),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,ifeq(true,true,product(X4,identity,X2),true),true) = ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,ifeq(product(X4,inverse(X3),multiply(X4,inverse(X3))),true,product(X4,identity,X2),true),true),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(true,true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true) = ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c171,plain,
ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true) = ifeq(true,true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true) = ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),true),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c174,plain,
ifeq(true,true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true) = ifeq(product(inverse(X4),X4,identity),true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X4),X4,identity),true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),true),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X4),X4,identity),true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c33]) ).
cnf(c177,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c175,c176]) ).
cnf(c178,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,inverse(X4),X5),true,product(X2,identity,X3),true),true) = true,
inference(transitivity,[status(thm)],[c172,c177]) ).
cnf(c179,plain,
ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,ifeq(product(X4,inverse(X3),multiply(X4,inverse(X3))),true,product(X4,identity,X2),true),true) = true,
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,ifeq(true,true,product(X4,identity,X2),true),true) = true,
inference(transitivity,[status(thm)],[c169,c179]) ).
cnf(c181,plain,
ifeq(product(multiply(X4,inverse(X3)),X3,X2),true,product(X4,identity,X2),true) = true,
inference(transitivity,[status(thm)],[c165,c180]) ).
cnf(c182,plain,
ifeq(product(multiply(inverse(b),inverse(inverse(a))),inverse(a),inverse(a)),true,product(inverse(b),identity,inverse(a)),true) = true,
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
ifeq(true,true,product(inverse(b),identity,inverse(a)),true) = true,
inference(transitivity,[status(thm)],[c162,c182]) ).
cnf(c184,plain,
product(inverse(b),identity,inverse(a)) = true,
inference(transitivity,[status(thm)],[c94,c183]) ).
cnf(c185,plain,
true = product(inverse(b),identity,inverse(a)),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(true,true,equalish(inverse(a),inverse(b)),true) = ifeq(product(inverse(b),identity,inverse(a)),true,equalish(inverse(a),inverse(b)),true),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(product(inverse(b),identity,inverse(b)),true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true) = ifeq(product(inverse(b),identity,inverse(b)),true,ifeq(product(inverse(b),identity,inverse(a)),true,equalish(inverse(a),inverse(b)),true),true),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
ifeq(product(inverse(b),identity,inverse(b)),true,ifeq(product(inverse(b),identity,inverse(a)),true,equalish(inverse(a),inverse(b)),true),true) = true,
inference(substitution,[status(thm)],[c55]) ).
cnf(c189,plain,
ifeq(product(inverse(b),identity,inverse(b)),true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true) = true,
inference(transitivity,[status(thm)],[c187,c188]) ).
cnf(c190,plain,
ifeq(true,true,ifeq(true,true,equalish(inverse(a),inverse(b)),true),true) = true,
inference(transitivity,[status(thm)],[c92,c189]) ).
cnf(c191,plain,
ifeq(true,true,equalish(inverse(a),inverse(b)),true) = true,
inference(transitivity,[status(thm)],[c6,c190]) ).
cnf(c192,plain,
equalish(inverse(a),inverse(b)) = true,
inference(transitivity,[status(thm)],[c4,c191]) ).
cnf(c193,plain,
$false,
inference(resolution,[status(thm)],[c1,c192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:19:44 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 111.19/14.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 111.19/14.48
% 111.19/14.48 % SZS status Unsatisfiable
% 111.19/14.48
% 111.19/14.49 % SZS output start CNFRefutation
% See solution above
% 111.99/14.60
% 111.99/14.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------