%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO025-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 09:35:37 AM UTC 2026
% Result : Unsatisfiable 1.59s 0.67s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 7
% Syntax : Number of clauses : 205 ( 205 unt; 0 nHn; 4 RR)
% Number of literals : 205 ( 204 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 378 ( 105 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_identity) ).
cnf(c2,axiom,
pixley(X,Y,Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
cnf(c3,plain,
pixley(multiply(X2,inverse(X2)),n1,n1) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,inverse(X2)) = pixley(multiply(X2,inverse(X2)),n1,n1),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,add(Y2,Z)) = add(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(c6,plain,
multiply(X3,add(X2,inverse(X4))) = add(multiply(X2,X3),multiply(inverse(X4),X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(multiply(X4,inverse(X3)),multiply(X2,add(X4,inverse(X3)))) = add(multiply(X4,inverse(X3)),add(multiply(X4,X2),multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
pixley(X2,Y2,Z2) = add(multiply(X2,inverse(Y2)),add(multiply(X2,Z2),multiply(inverse(Y2),Z2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley_defn) ).
cnf(c9,plain,
pixley(X4,X3,X2) = add(multiply(X4,inverse(X3)),add(multiply(X4,X2),multiply(inverse(X3),X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
add(multiply(X4,inverse(X3)),add(multiply(X4,X2),multiply(inverse(X3),X2))) = pixley(X4,X3,X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
add(multiply(X4,inverse(X3)),multiply(X2,add(X4,inverse(X3)))) = pixley(X4,X3,X2),
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
add(multiply(multiply(X3,inverse(X3)),inverse(X2)),multiply(n1,add(multiply(X3,inverse(X3)),inverse(X2)))) = pixley(multiply(X3,inverse(X3)),X2,n1),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
pixley(multiply(X3,inverse(X3)),X2,n1) = add(multiply(multiply(X3,inverse(X3)),inverse(X2)),multiply(n1,add(multiply(X3,inverse(X3)),inverse(X2)))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(n1,add(multiply(X3,inverse(X3)),X2)) = add(multiply(multiply(X3,inverse(X3)),n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,axiom,
add(X2,inverse(X2)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c16,plain,
n1 = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X2,n1) = multiply(X2,add(X3,inverse(X3))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
add(multiply(X3,inverse(X3)),multiply(X2,n1)) = add(multiply(X3,inverse(X3)),multiply(X2,add(X3,inverse(X3)))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
add(multiply(X3,inverse(X3)),multiply(X2,add(X3,inverse(X3)))) = pixley(X3,X3,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c20,axiom,
pixley(X2,X2,Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
cnf(c21,plain,
pixley(X3,X3,X2) = X2,
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
add(multiply(X3,inverse(X3)),multiply(X2,add(X3,inverse(X3)))) = X2,
inference(transitivity,[status(thm)],[c19,c21]) ).
cnf(c23,plain,
add(multiply(X3,inverse(X3)),multiply(X2,n1)) = X2,
inference(transitivity,[status(thm)],[c18,c22]) ).
cnf(c24,plain,
add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)) = multiply(inverse(X3),n1),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(inverse(X3),n1) = add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
add(multiply(X2,inverse(X2)),multiply(add(X3,n1),n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c23]) ).
cnf(c27,plain,
add(X3,n1) = add(multiply(X2,inverse(X2)),multiply(add(X3,n1),n1)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
multiply(add(X2,Y2),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
cnf(c29,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
add(multiply(X2,inverse(X2)),multiply(add(X3,n1),n1)) = add(multiply(X2,inverse(X2)),n1),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c28]) ).
cnf(c32,plain,
n1 = multiply(add(X2,n1),n1),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
add(multiply(X2,inverse(X2)),n1) = add(multiply(X2,inverse(X2)),multiply(add(X3,n1),n1)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
add(multiply(X2,inverse(X2)),multiply(add(X3,n1),n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c23]) ).
cnf(c35,plain,
add(multiply(X2,inverse(X2)),n1) = add(X3,n1),
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
add(multiply(X2,inverse(X2)),multiply(add(X3,n1),n1)) = add(X4,n1),
inference(transitivity,[status(thm)],[c30,c35]) ).
cnf(c37,plain,
add(X2,n1) = add(X3,n1),
inference(transitivity,[status(thm)],[c27,c36]) ).
cnf(c38,plain,
add(X3,n1) = add(multiply(n1,inverse(add(X2,n1))),n1),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
add(X2,n1) = add(multiply(X3,n1),n1),
inference(substitution,[status(thm)],[c37]) ).
cnf(c40,plain,
add(add(X4,add(X3,n1)),add(X2,n1)) = add(add(X4,add(X3,n1)),add(multiply(X4,n1),n1)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(X4,add(X3,add(X2,X4))) = add(multiply(X3,X4),multiply(add(X2,X4),X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c42,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c28]) ).
cnf(c43,plain,
add(multiply(X3,X4),multiply(add(X2,X4),X4)) = add(multiply(X3,X4),X4),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(X4,add(X3,add(X2,X4))) = add(multiply(X3,X4),X4),
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
multiply(n1,add(X3,add(X2,n1))) = add(multiply(X3,n1),n1),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
add(multiply(X3,n1),n1) = multiply(n1,add(X3,add(X2,n1))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
add(add(X3,add(X2,n1)),add(multiply(X3,n1),n1)) = add(add(X3,add(X2,n1)),multiply(n1,add(X3,add(X2,n1)))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X4,add(add(X3,X4),X2)) = add(multiply(add(X3,X4),X4),multiply(X2,X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c49,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c28]) ).
cnf(c50,plain,
add(multiply(add(X3,X4),X4),multiply(X2,X4)) = add(X4,multiply(X2,X4)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(X4,add(add(X3,X4),X2)) = add(X4,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c48,c50]) ).
cnf(c52,plain,
multiply(X3,add(add(X2,X3),n1)) = add(X3,multiply(n1,X3)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
add(X3,multiply(n1,X3)) = multiply(X3,add(add(X2,X3),n1)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
add(X3,n1) = add(add(X2,X4),n1),
inference(substitution,[status(thm)],[c37]) ).
cnf(c55,plain,
add(add(X2,X4),n1) = add(X3,n1),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X4,add(add(X2,X4),n1)) = multiply(X4,add(X3,n1)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
add(X3,multiply(n1,X3)) = multiply(X3,add(X2,n1)),
inference(transitivity,[status(thm)],[c53,c56]) ).
cnf(c58,plain,
add(add(X3,add(X2,n1)),multiply(n1,add(X3,add(X2,n1)))) = multiply(add(X3,add(X2,n1)),add(X2,n1)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(add(X3,add(X2,n1)),add(X2,n1)) = add(X2,n1),
inference(substitution,[status(thm)],[c28]) ).
cnf(c60,plain,
add(add(X3,add(X2,n1)),multiply(n1,add(X3,add(X2,n1)))) = add(X2,n1),
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
add(add(X3,add(X2,n1)),add(multiply(X3,n1),n1)) = add(X2,n1),
inference(transitivity,[status(thm)],[c47,c60]) ).
cnf(c62,plain,
add(add(X4,add(X3,n1)),add(X2,n1)) = add(X3,n1),
inference(transitivity,[status(thm)],[c40,c61]) ).
cnf(c63,plain,
add(add(X2,add(X3,n1)),add(X4,n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
add(X4,n1) = add(add(X3,add(X4,n1)),add(X2,n1)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(n1,add(X4,n1)) = multiply(n1,add(add(X3,add(X4,n1)),add(X2,n1))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(n1,add(add(X3,add(X4,n1)),add(X2,n1))) = add(multiply(add(X3,add(X4,n1)),n1),n1),
inference(substitution,[status(thm)],[c44]) ).
cnf(c67,plain,
add(X3,n1) = add(multiply(add(X2,add(X4,n1)),n1),n1),
inference(substitution,[status(thm)],[c37]) ).
cnf(c68,plain,
add(multiply(add(X2,add(X4,n1)),n1),n1) = add(X3,n1),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(n1,add(add(X3,add(X5,n1)),add(X2,n1))) = add(X4,n1),
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
multiply(n1,add(X3,n1)) = add(X2,n1),
inference(transitivity,[status(thm)],[c65,c69]) ).
cnf(c71,plain,
multiply(n1,add(X2,n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
add(X3,n1) = multiply(n1,add(X2,n1)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
add(add(X4,n1),multiply(X3,add(X2,n1))) = add(multiply(n1,add(X2,n1)),multiply(X3,add(X2,n1))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(add(X2,n1),add(n1,X3)) = add(multiply(n1,add(X2,n1)),multiply(X3,add(X2,n1))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c75,plain,
add(multiply(n1,add(X2,n1)),multiply(X3,add(X2,n1))) = multiply(add(X2,n1),add(n1,X3)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
add(add(X4,n1),multiply(X3,add(X2,n1))) = multiply(add(X2,n1),add(n1,X3)),
inference(transitivity,[status(thm)],[c73,c75]) ).
cnf(c77,plain,
add(add(X3,n1),multiply(inverse(add(X2,n1)),add(X3,n1))) = multiply(add(X3,n1),add(n1,inverse(add(X2,n1)))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(add(X3,n1),add(n1,inverse(add(X2,n1)))) = add(add(X3,n1),multiply(inverse(add(X2,n1)),add(X3,n1))),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
add(add(X2,add(X3,n1)),add(X4,n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c62]) ).
cnf(c80,plain,
add(X3,n1) = add(add(X2,add(X3,n1)),add(X4,n1)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
inverse(add(X3,n1)) = inverse(add(add(X2,add(X3,n1)),add(X4,n1))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(inverse(add(X3,n1)),add(X4,n1)) = multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
add(add(X4,n1),multiply(inverse(add(X3,n1)),add(X4,n1))) = add(add(X4,n1),multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(X3,add(add(X2,X3),inverse(add(X2,X3)))) = add(X3,multiply(inverse(add(X2,X3)),X3)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c85,plain,
add(X3,multiply(inverse(add(X2,X3)),X3)) = multiply(X3,add(add(X2,X3),inverse(add(X2,X3)))),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
add(add(X2,X3),inverse(add(X2,X3))) = n1,
inference(substitution,[status(thm)],[c15]) ).
cnf(c87,plain,
multiply(X3,add(add(X2,X3),inverse(add(X2,X3)))) = multiply(X3,n1),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
add(X3,multiply(inverse(add(X2,X3)),X3)) = multiply(X3,n1),
inference(transitivity,[status(thm)],[c85,c87]) ).
cnf(c89,plain,
add(add(X4,n1),multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1))) = multiply(add(X4,n1),n1),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c28]) ).
cnf(c91,plain,
add(add(X4,n1),multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1))) = n1,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
add(add(X3,n1),multiply(inverse(add(X2,n1)),add(X3,n1))) = n1,
inference(transitivity,[status(thm)],[c83,c91]) ).
cnf(c93,plain,
multiply(add(X3,n1),add(n1,inverse(add(X2,n1)))) = n1,
inference(transitivity,[status(thm)],[c78,c92]) ).
cnf(c94,plain,
multiply(add(X2,n1),add(n1,inverse(add(X2,n1)))) = n1,
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
n1 = multiply(add(X2,n1),add(n1,inverse(add(X2,n1)))),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
add(multiply(n1,inverse(add(X2,n1))),n1) = add(multiply(n1,inverse(add(X2,n1))),multiply(add(X2,n1),add(n1,inverse(add(X2,n1))))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
add(multiply(n1,inverse(add(X2,n1))),multiply(add(X2,n1),add(n1,inverse(add(X2,n1))))) = pixley(n1,add(X2,n1),add(X2,n1)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c98,plain,
pixley(n1,add(X2,n1),add(X2,n1)) = n1,
inference(substitution,[status(thm)],[c2]) ).
cnf(c99,plain,
add(multiply(n1,inverse(add(X2,n1))),multiply(add(X2,n1),add(n1,inverse(add(X2,n1))))) = n1,
inference(transitivity,[status(thm)],[c97,c98]) ).
cnf(c100,plain,
add(multiply(n1,inverse(add(X2,n1))),n1) = n1,
inference(transitivity,[status(thm)],[c96,c99]) ).
cnf(c101,plain,
add(X2,n1) = n1,
inference(transitivity,[status(thm)],[c38,c100]) ).
cnf(c102,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(multiply(inverse(X3),n1),n1) = multiply(multiply(inverse(X3),n1),add(X2,n1)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
add(multiply(inverse(X3),n1),multiply(n1,multiply(inverse(X3),n1))) = multiply(multiply(inverse(X3),n1),add(X2,n1)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c105,plain,
multiply(multiply(inverse(X3),n1),add(X2,n1)) = add(multiply(inverse(X3),n1),multiply(n1,multiply(inverse(X3),n1))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c107,plain,
multiply(inverse(X3),n1) = multiply(inverse(X3),add(X2,n1)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(n1,multiply(inverse(X3),n1)) = multiply(n1,multiply(inverse(X3),add(X2,n1))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c28]) ).
cnf(c110,plain,
n1 = multiply(add(X2,n1),n1),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(n1,multiply(inverse(X3),add(X2,n1))) = multiply(multiply(add(X2,n1),n1),multiply(inverse(X3),add(X2,n1))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
n1 = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c113,plain,
multiply(X3,n1) = multiply(X3,add(X2,inverse(X2))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(multiply(X3,n1),multiply(inverse(X2),X3)) = multiply(multiply(X3,add(X2,inverse(X2))),multiply(inverse(X2),X3)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(X4,add(X3,X2)) = add(multiply(X3,X4),multiply(X2,X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c116,plain,
multiply(multiply(X4,add(X3,X2)),multiply(X2,X4)) = multiply(add(multiply(X3,X4),multiply(X2,X4)),multiply(X2,X4)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(add(multiply(X3,X4),multiply(X2,X4)),multiply(X2,X4)) = multiply(X2,X4),
inference(substitution,[status(thm)],[c28]) ).
cnf(c118,plain,
multiply(multiply(X4,add(X3,X2)),multiply(X2,X4)) = multiply(X2,X4),
inference(transitivity,[status(thm)],[c116,c117]) ).
cnf(c119,plain,
multiply(multiply(X3,add(X2,inverse(X2))),multiply(inverse(X2),X3)) = multiply(inverse(X2),X3),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(multiply(X3,n1),multiply(inverse(X2),X3)) = multiply(inverse(X2),X3),
inference(transitivity,[status(thm)],[c114,c119]) ).
cnf(c121,plain,
multiply(multiply(add(X2,n1),n1),multiply(inverse(X3),add(X2,n1))) = multiply(inverse(X3),add(X2,n1)),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(n1,multiply(inverse(X3),add(X2,n1))) = multiply(inverse(X3),add(X2,n1)),
inference(transitivity,[status(thm)],[c111,c121]) ).
cnf(c123,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),n1),
inference(congruence,[status(thm)],[c101]) ).
cnf(c124,plain,
multiply(n1,multiply(inverse(X3),add(X2,n1))) = multiply(inverse(X3),n1),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
multiply(n1,multiply(inverse(X2),n1)) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c108,c124]) ).
cnf(c126,plain,
add(multiply(inverse(X2),n1),multiply(n1,multiply(inverse(X2),n1))) = add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(n1,add(inverse(X2),inverse(X2))) = add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c128,plain,
add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
add(X2,n1) = add(n1,n1),
inference(substitution,[status(thm)],[c37]) ).
cnf(c130,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),add(n1,n1)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))) = multiply(inverse(X2),add(n1,n1)),
inference(substitution,[status(thm)],[c120]) ).
cnf(c132,plain,
multiply(inverse(X2),add(n1,n1)) = multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
n1 = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c134,plain,
multiply(n1,inverse(X2)) = multiply(add(X2,inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(add(X2,inverse(X2)),inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c136,plain,
multiply(n1,inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
inverse(X2) = multiply(n1,inverse(X2)),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
add(inverse(X3),multiply(X2,inverse(X3))) = add(multiply(n1,inverse(X3)),multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(inverse(X3),add(n1,X2)) = add(multiply(n1,inverse(X3)),multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c140,plain,
add(multiply(n1,inverse(X3)),multiply(X2,inverse(X3))) = multiply(inverse(X3),add(n1,X2)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
add(inverse(X3),multiply(X2,inverse(X3))) = multiply(inverse(X3),add(n1,X2)),
inference(transitivity,[status(thm)],[c138,c140]) ).
cnf(c142,plain,
add(inverse(X2),multiply(n1,inverse(X2))) = multiply(inverse(X2),add(n1,n1)),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(inverse(X2),add(n1,n1)) = add(inverse(X2),multiply(n1,inverse(X2))),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
add(inverse(X2),multiply(n1,inverse(X2))) = add(inverse(X2),inverse(X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c145,plain,
multiply(inverse(X2),add(n1,n1)) = add(inverse(X2),inverse(X2)),
inference(transitivity,[status(thm)],[c143,c144]) ).
cnf(c146,plain,
multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))) = multiply(multiply(add(n1,n1),n1),add(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(add(n1,n1),n1) = n1,
inference(substitution,[status(thm)],[c28]) ).
cnf(c148,plain,
multiply(multiply(add(n1,n1),n1),add(inverse(X2),inverse(X2))) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(transitivity,[status(thm)],[c146,c148]) ).
cnf(c150,plain,
multiply(inverse(X2),add(n1,n1)) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(transitivity,[status(thm)],[c132,c149]) ).
cnf(c151,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(n1,add(inverse(X3),inverse(X3))),
inference(transitivity,[status(thm)],[c130,c150]) ).
cnf(c152,plain,
multiply(n1,add(inverse(X3),inverse(X3))) = multiply(inverse(X3),add(X2,n1)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
add(X2,n1) = add(n1,n1),
inference(substitution,[status(thm)],[c37]) ).
cnf(c154,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),add(n1,n1)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(inverse(X3),add(X2,n1)) = add(inverse(X3),inverse(X3)),
inference(transitivity,[status(thm)],[c154,c145]) ).
cnf(c156,plain,
multiply(n1,add(inverse(X2),inverse(X2))) = add(inverse(X2),inverse(X2)),
inference(transitivity,[status(thm)],[c152,c155]) ).
cnf(c157,plain,
add(inverse(X3),inverse(X3)) = multiply(inverse(X3),add(X2,n1)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c158,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),n1),
inference(congruence,[status(thm)],[c101]) ).
cnf(c159,plain,
add(inverse(X2),inverse(X2)) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c157,c158]) ).
cnf(c160,plain,
multiply(n1,add(inverse(X2),inverse(X2))) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c156,c159]) ).
cnf(c161,plain,
add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c128,c160]) ).
cnf(c162,plain,
add(multiply(inverse(X2),n1),multiply(n1,multiply(inverse(X2),n1))) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c126,c161]) ).
cnf(c163,plain,
multiply(multiply(inverse(X3),n1),add(X2,n1)) = multiply(inverse(X3),n1),
inference(transitivity,[status(thm)],[c105,c162]) ).
cnf(c164,plain,
multiply(multiply(inverse(X2),n1),n1) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c103,c163]) ).
cnf(c165,plain,
add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)) = add(multiply(X2,inverse(X2)),multiply(inverse(X3),n1)),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
add(multiply(X2,inverse(X2)),multiply(inverse(X3),n1)) = inverse(X3),
inference(substitution,[status(thm)],[c23]) ).
cnf(c167,plain,
add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)) = inverse(X3),
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
multiply(inverse(X2),n1) = inverse(X2),
inference(transitivity,[status(thm)],[c25,c167]) ).
cnf(c169,plain,
inverse(X2) = multiply(inverse(X2),n1),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
add(multiply(X3,inverse(X3)),inverse(X2)) = add(multiply(X3,inverse(X3)),multiply(inverse(X2),n1)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
add(multiply(X3,inverse(X3)),multiply(inverse(X2),n1)) = inverse(X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c172,plain,
add(multiply(X3,inverse(X3)),inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
add(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))) = inverse(multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
inverse(multiply(X2,inverse(X2))) = add(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
add(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))) = n1,
inference(substitution,[status(thm)],[c15]) ).
cnf(c176,plain,
inverse(multiply(X2,inverse(X2))) = n1,
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
n1 = inverse(multiply(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(multiply(X2,inverse(X2)),n1) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
add(multiply(multiply(X3,inverse(X3)),n1),multiply(X2,n1)) = add(multiply(multiply(X3,inverse(X3)),inverse(multiply(X3,inverse(X3)))),multiply(X2,n1)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
add(multiply(multiply(X3,inverse(X3)),inverse(multiply(X3,inverse(X3)))),multiply(X2,n1)) = X2,
inference(substitution,[status(thm)],[c23]) ).
cnf(c181,plain,
add(multiply(multiply(X3,inverse(X3)),n1),multiply(X2,n1)) = X2,
inference(transitivity,[status(thm)],[c179,c180]) ).
cnf(c182,plain,
multiply(n1,add(multiply(X3,inverse(X3)),X2)) = X2,
inference(transitivity,[status(thm)],[c14,c181]) ).
cnf(c183,plain,
multiply(n1,add(multiply(X3,inverse(X3)),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
add(multiply(multiply(X3,inverse(X3)),inverse(X2)),multiply(n1,add(multiply(X3,inverse(X3)),inverse(X2)))) = add(multiply(multiply(X3,inverse(X3)),inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
inverse(X2) = multiply(n1,inverse(X2)),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c186,plain,
add(multiply(X3,inverse(X2)),inverse(X2)) = add(multiply(X3,inverse(X2)),multiply(n1,inverse(X2))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(inverse(X2),add(X3,n1)) = add(multiply(X3,inverse(X2)),multiply(n1,inverse(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c188,plain,
add(multiply(X3,inverse(X2)),multiply(n1,inverse(X2))) = multiply(inverse(X2),add(X3,n1)),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
add(multiply(X3,inverse(X2)),inverse(X2)) = multiply(inverse(X2),add(X3,n1)),
inference(transitivity,[status(thm)],[c186,c188]) ).
cnf(c190,plain,
add(multiply(multiply(X3,inverse(X3)),inverse(X2)),inverse(X2)) = multiply(inverse(X2),add(multiply(X3,inverse(X3)),n1)),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
add(multiply(X2,inverse(X2)),n1) = n1,
inference(substitution,[status(thm)],[c101]) ).
cnf(c192,plain,
multiply(inverse(X2),add(multiply(X3,inverse(X3)),n1)) = multiply(inverse(X2),n1),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(inverse(X2),add(multiply(X3,inverse(X3)),n1)) = inverse(X2),
inference(transitivity,[status(thm)],[c192,c168]) ).
cnf(c194,plain,
add(multiply(multiply(X3,inverse(X3)),inverse(X2)),inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c190,c193]) ).
cnf(c195,plain,
add(multiply(multiply(X3,inverse(X3)),inverse(X2)),multiply(n1,add(multiply(X3,inverse(X3)),inverse(X2)))) = inverse(X2),
inference(transitivity,[status(thm)],[c184,c194]) ).
cnf(c196,plain,
pixley(multiply(X3,inverse(X3)),X2,n1) = inverse(X2),
inference(transitivity,[status(thm)],[c13,c195]) ).
cnf(c197,plain,
pixley(multiply(X2,inverse(X2)),n1,n1) = inverse(n1),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(X2,inverse(X2)) = inverse(n1),
inference(transitivity,[status(thm)],[c4,c197]) ).
cnf(c199,plain,
pixley(multiply(X2,inverse(X2)),n1,n1) = inverse(n1),
inference(substitution,[status(thm)],[c196]) ).
cnf(c200,plain,
inverse(n1) = pixley(multiply(X2,inverse(X2)),n1,n1),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
pixley(multiply(X2,inverse(X2)),n1,n1) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c202,plain,
inverse(n1) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c200,c201]) ).
cnf(c203,plain,
multiply(X2,inverse(X2)) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c198,c202]) ).
cnf(c204,plain,
multiply(b,inverse(b)) = multiply(a,inverse(a)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c205,plain,
$false,
inference(resolution,[status(thm)],[c1,c204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO025-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.28 % Computer : n019.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Mon Sep 28 21:04:47 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.29 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/0.67 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.59/0.67
% 1.59/0.67 % SZS status Unsatisfiable
% 1.59/0.67
% 1.59/0.69 % SZS output start CNFRefutation
% See solution above
% 3.52/0.87
% 3.52/0.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------