%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:09:41 AM UTC 2026
% Result : Unsatisfiable 1.94s 0.66s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of clauses : 98 ( 98 unt; 0 nHn; 3 RR)
% Number of literals : 98 ( 97 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 209 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang2) ).
cnf(c2,axiom,
multiply(right_division(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
cnf(c3,plain,
multiply(right_division(X3,X2),X2) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = multiply(right_division(X3,X2),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
left_division(right_division(X3,X2),X3) = left_division(right_division(X3,X2),multiply(right_division(X3,X2),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
left_division(X2,multiply(X2,Y2)) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
cnf(c7,plain,
left_division(right_division(X3,X2),multiply(right_division(X3,X2),X2)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
left_division(right_division(X3,X2),X3) = X2,
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
left_division(right_division(multiply(X2,multiply(X4,X2)),multiply(multiply(multiply(X3,X2),X4),X2)),multiply(X2,multiply(X4,X2))) = multiply(multiply(multiply(X3,X2),X4),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(multiply(X4,X3),X2),X3) = left_division(right_division(multiply(X3,multiply(X2,X3)),multiply(multiply(multiply(X4,X3),X2),X3)),multiply(X3,multiply(X2,X3))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(multiply(X2,multiply(Y2,Z)),X2) = multiply(multiply(X2,Y2),multiply(Z,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang1) ).
cnf(c12,plain,
multiply(multiply(X4,multiply(X3,X2)),X4) = multiply(multiply(X4,X3),multiply(X2,X4)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(multiply(X4,X3),multiply(X2,X4)) = multiply(multiply(X4,multiply(X3,X2)),X4),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X3,X2) = multiply(X3,multiply(identity,X2)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(X3,X2),X3) = multiply(multiply(X3,multiply(identity,X2)),X3),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(multiply(X3,multiply(identity,X2)),X3) = multiply(multiply(X3,identity),multiply(X2,X3)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c19,axiom,
multiply(X2,identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c20,plain,
multiply(multiply(X3,identity),multiply(X2,X3)) = multiply(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(X3,multiply(identity,X2)),X3) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c17,c21]) ).
cnf(c23,plain,
multiply(multiply(X4,multiply(X3,X2)),X4) = multiply(X4,multiply(multiply(X3,X2),X4)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(X4,X3),multiply(X2,X4)) = multiply(X4,multiply(multiply(X3,X2),X4)),
inference(transitivity,[status(thm)],[c13,c23]) ).
cnf(c25,plain,
multiply(multiply(X4,left_inverse(X3)),multiply(multiply(X3,X2),X4)) = multiply(X4,multiply(multiply(left_inverse(X3),multiply(X3,X2)),X4)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,multiply(X2,X3)) = multiply(multiply(X3,X2),X3),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c27,plain,
right_division(multiply(X3,multiply(X2,X3)),X3) = right_division(multiply(multiply(X3,X2),X3),X3),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
right_division(multiply(X2,Y2),Y2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
cnf(c29,plain,
right_division(multiply(multiply(X3,X2),X3),X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
right_division(multiply(X3,multiply(X2,X3)),X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
right_division(multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))),left_inverse(X3)) = multiply(left_inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = right_division(multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))),left_inverse(X3)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(multiply(left_inverse(X3),X3),multiply(X2,left_inverse(X3))) = multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c34,plain,
multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))) = multiply(multiply(left_inverse(X3),X3),multiply(X2,left_inverse(X3))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
multiply(left_inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c36,plain,
multiply(multiply(left_inverse(X3),X3),multiply(X2,left_inverse(X3))) = multiply(identity,multiply(X2,left_inverse(X3))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(identity,multiply(X2,left_inverse(X3))) = multiply(X2,left_inverse(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c38,plain,
multiply(multiply(left_inverse(X3),X3),multiply(X2,left_inverse(X3))) = multiply(X2,left_inverse(X3)),
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))) = multiply(X2,left_inverse(X3)),
inference(transitivity,[status(thm)],[c34,c38]) ).
cnf(c40,plain,
right_division(multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))),left_inverse(X3)) = right_division(multiply(X2,left_inverse(X3)),left_inverse(X3)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
right_division(multiply(X2,left_inverse(X3)),left_inverse(X3)) = X2,
inference(substitution,[status(thm)],[c28]) ).
cnf(c42,plain,
right_division(multiply(left_inverse(X3),multiply(multiply(X3,X2),left_inverse(X3))),left_inverse(X3)) = X2,
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
multiply(left_inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c32,c42]) ).
cnf(c44,plain,
multiply(multiply(left_inverse(X3),multiply(X3,X2)),X4) = multiply(X2,X4),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X4,multiply(multiply(left_inverse(X3),multiply(X3,X2)),X4)) = multiply(X4,multiply(X2,X4)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(multiply(X4,left_inverse(X3)),multiply(multiply(X3,X2),X4)) = multiply(X4,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c25,c45]) ).
cnf(c47,plain,
multiply(X4,multiply(X2,X4)) = multiply(multiply(X4,left_inverse(X3)),multiply(multiply(X3,X2),X4)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
right_division(multiply(X4,multiply(X2,X4)),multiply(multiply(X3,X2),X4)) = right_division(multiply(multiply(X4,left_inverse(X3)),multiply(multiply(X3,X2),X4)),multiply(multiply(X3,X2),X4)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
right_division(multiply(multiply(X4,left_inverse(X3)),multiply(multiply(X3,X2),X4)),multiply(multiply(X3,X2),X4)) = multiply(X4,left_inverse(X3)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c50,plain,
right_division(multiply(X4,multiply(X2,X4)),multiply(multiply(X3,X2),X4)) = multiply(X4,left_inverse(X3)),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
right_division(multiply(X4,multiply(X3,X4)),multiply(multiply(multiply(X2,X4),X3),X4)) = multiply(X4,left_inverse(multiply(X2,X4))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
right_division(multiply(multiply(X3,left_inverse(X2)),X2),X2) = multiply(X3,left_inverse(X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c53,plain,
multiply(X3,left_inverse(X2)) = right_division(multiply(multiply(X3,left_inverse(X2)),X2),X2),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
right_division(multiply(X3,multiply(right_division(X2,X3),X3)),X3) = multiply(X3,right_division(X2,X3)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c55,plain,
multiply(X3,right_division(X2,X3)) = right_division(multiply(X3,multiply(right_division(X2,X3),X3)),X3),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(right_division(X2,X3),X3) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c57,plain,
multiply(X3,multiply(right_division(X2,X3),X3)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
right_division(multiply(X3,multiply(right_division(X2,X3),X3)),X3) = right_division(multiply(X3,X2),X3),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X3,right_division(X2,X3)) = right_division(multiply(X3,X2),X3),
inference(transitivity,[status(thm)],[c55,c58]) ).
cnf(c60,plain,
right_division(multiply(X3,X2),X3) = multiply(X3,right_division(X2,X3)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
left_division(X3,right_division(multiply(X3,X2),X3)) = left_division(X3,multiply(X3,right_division(X2,X3))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
left_division(X3,multiply(X3,right_division(X2,X3))) = right_division(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c63,plain,
left_division(X3,right_division(multiply(X3,X2),X3)) = right_division(X2,X3),
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
left_division(X2,right_division(multiply(X2,multiply(multiply(X3,left_inverse(X2)),X2)),X2)) = right_division(multiply(multiply(X3,left_inverse(X2)),X2),X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
right_division(multiply(multiply(X3,left_inverse(X2)),X2),X2) = left_division(X2,right_division(multiply(X2,multiply(multiply(X3,left_inverse(X2)),X2)),X2)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(multiply(X3,X2),multiply(left_inverse(X3),X3)) = multiply(X3,multiply(multiply(X2,left_inverse(X3)),X3)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c67,plain,
multiply(X3,multiply(multiply(X2,left_inverse(X3)),X3)) = multiply(multiply(X3,X2),multiply(left_inverse(X3),X3)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(multiply(X3,X2),multiply(left_inverse(X3),X3)) = multiply(multiply(X3,X2),identity),
inference(congruence,[status(thm)],[c35]) ).
cnf(c69,plain,
multiply(multiply(X3,X2),identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c70,plain,
multiply(multiply(X3,X2),multiply(left_inverse(X3),X3)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
multiply(X3,multiply(multiply(X2,left_inverse(X3)),X3)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c67,c70]) ).
cnf(c72,plain,
multiply(X2,multiply(multiply(X3,left_inverse(X2)),X2)) = multiply(X2,X3),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
right_division(multiply(X2,multiply(multiply(X3,left_inverse(X2)),X2)),X2) = right_division(multiply(X2,X3),X2),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
left_division(X2,right_division(multiply(X2,multiply(multiply(X3,left_inverse(X2)),X2)),X2)) = left_division(X2,right_division(multiply(X2,X3),X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
left_division(X2,right_division(multiply(X2,X3),X2)) = right_division(X3,X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c76,plain,
left_division(X2,right_division(multiply(X2,multiply(multiply(X3,left_inverse(X2)),X2)),X2)) = right_division(X3,X2),
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
right_division(multiply(multiply(X3,left_inverse(X2)),X2),X2) = right_division(X3,X2),
inference(transitivity,[status(thm)],[c65,c76]) ).
cnf(c78,plain,
multiply(X3,left_inverse(X2)) = right_division(X3,X2),
inference(transitivity,[status(thm)],[c53,c77]) ).
cnf(c79,plain,
multiply(X3,left_inverse(multiply(X2,X3))) = right_division(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(left_inverse(X2),multiply(X2,X3)) = X3,
inference(substitution,[status(thm)],[c43]) ).
cnf(c81,plain,
X3 = multiply(left_inverse(X2),multiply(X2,X3)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
right_division(X3,multiply(X2,X3)) = right_division(multiply(left_inverse(X2),multiply(X2,X3)),multiply(X2,X3)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
right_division(multiply(left_inverse(X2),multiply(X2,X3)),multiply(X2,X3)) = left_inverse(X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c84,plain,
right_division(X3,multiply(X2,X3)) = left_inverse(X2),
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
multiply(X3,left_inverse(multiply(X2,X3))) = left_inverse(X2),
inference(transitivity,[status(thm)],[c79,c84]) ).
cnf(c86,plain,
right_division(multiply(X4,multiply(X3,X4)),multiply(multiply(multiply(X2,X4),X3),X4)) = left_inverse(X2),
inference(transitivity,[status(thm)],[c51,c85]) ).
cnf(c87,plain,
right_division(multiply(X3,multiply(X2,X3)),multiply(multiply(multiply(X4,X3),X2),X3)) = left_inverse(X4),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
left_division(right_division(multiply(X3,multiply(X2,X3)),multiply(multiply(multiply(X4,X3),X2),X3)),multiply(X3,multiply(X2,X3))) = left_division(left_inverse(X4),multiply(X3,multiply(X2,X3))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(multiply(multiply(X4,X3),X2),X3) = left_division(left_inverse(X4),multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c10,c88]) ).
cnf(c90,plain,
left_division(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c91,plain,
multiply(X3,X2) = left_division(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
left_division(left_inverse(X3),multiply(left_inverse(X3),multiply(X3,X2))) = left_division(left_inverse(X3),X2),
inference(congruence,[status(thm)],[c43]) ).
cnf(c93,plain,
multiply(X3,X2) = left_division(left_inverse(X3),X2),
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
multiply(X4,multiply(X3,multiply(X2,X3))) = left_division(left_inverse(X4),multiply(X3,multiply(X2,X3))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
left_division(left_inverse(X4),multiply(X3,multiply(X2,X3))) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(multiply(multiply(X4,X3),X2),X3) = multiply(X4,multiply(X3,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c89,c95]) ).
cnf(c97,plain,
multiply(multiply(multiply(a,b),c),b) = multiply(a,multiply(b,multiply(c,b))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
$false,
inference(resolution,[status(thm)],[c1,c97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 27 09:38:19 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.94/0.66 Command-line arguments: --flatten --complete-subsets
% 1.94/0.66
% 1.94/0.66 % SZS status Unsatisfiable
% 1.94/0.66
% 1.94/0.67 % SZS output start CNFRefutation
% See solution above
% 2.29/0.74
% 2.29/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------