%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:35:38 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.35s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 4 RR)
% Number of literals : 85 ( 84 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 188 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_inverse) ).
cnf(c2,axiom,
multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c3,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(multiply(X3,X2),multiply(inverse(X3),X2)) = add(multiply(X3,X2),multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
add(multiply(X3,X2),multiply(X2,inverse(X3))) = add(multiply(X2,X3),multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
add(multiply(X2,Y2),multiply(X2,inverse(Y2))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
cnf(c10,plain,
add(multiply(X2,X3),multiply(X2,inverse(X3))) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
add(multiply(X3,X2),multiply(X2,inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
add(multiply(X3,X2),multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c5,c11]) ).
cnf(c13,plain,
add(multiply(X2,add(X3,inverse(X3))),multiply(inverse(X2),add(X3,inverse(X3)))) = add(X3,inverse(X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
add(X3,inverse(X3)) = add(multiply(X2,add(X3,inverse(X3))),multiply(inverse(X2),add(X3,inverse(X3)))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
add(add(X2,Y2),Z) = add(X2,add(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(c16,plain,
add(add(X3,X2),inverse(X3)) = add(X3,add(X2,inverse(X3))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
add(X3,add(X2,inverse(X3))) = add(add(X3,X2),inverse(X3)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
add(inverse(X3),multiply(X3,X2)) = add(inverse(X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c22,plain,
add(multiply(X3,X4),X2) = add(X2,multiply(X3,X4)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
add(X3,multiply(X4,X2)) = add(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
add(X4,add(X3,multiply(X4,X2))) = add(X4,add(multiply(X4,X2),X3)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
add(add(X4,multiply(X4,X2)),X3) = add(X4,add(multiply(X4,X2),X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c26,plain,
add(X4,add(multiply(X4,X2),X3)) = add(add(X4,multiply(X4,X2)),X3),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
add(X3,multiply(X3,X2)) = add(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
multiply(X2,add(Y2,add(X2,Z2))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
cnf(c31,plain,
multiply(X3,add(X2,add(X3,X4))) = X3,
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
X4 = multiply(X4,add(X3,add(X4,X2))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X4,X5) = multiply(X4,multiply(X5,add(X3,add(X5,X2)))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
add(X5,multiply(X4,X5)) = add(X5,multiply(X4,multiply(X5,add(X3,add(X5,X2))))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
add(X2,multiply(Y2,multiply(X2,Z2))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
cnf(c36,plain,
add(X5,multiply(X4,multiply(X5,add(X3,add(X5,X2))))) = X5,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c29,c37]) ).
cnf(c39,plain,
add(add(X4,multiply(X4,X2)),X3) = add(X4,X3),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
add(X4,add(multiply(X4,X2),X3)) = add(X4,X3),
inference(transitivity,[status(thm)],[c26,c39]) ).
cnf(c41,plain,
add(X4,add(X3,multiply(X4,X2))) = add(X4,X3),
inference(transitivity,[status(thm)],[c24,c40]) ).
cnf(c42,plain,
add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))) = add(inverse(X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
add(inverse(X3),multiply(X2,X3)) = add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(X3,inverse(X2)) = multiply(inverse(X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
multiply(inverse(X2),X3) = multiply(X3,inverse(X2)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
add(multiply(X3,X2),multiply(inverse(X2),X3)) = add(multiply(X3,X2),multiply(X3,inverse(X2))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
add(multiply(X3,X2),multiply(X3,inverse(X2))) = X3,
inference(substitution,[status(thm)],[c9]) ).
cnf(c48,plain,
add(multiply(X3,X2),multiply(inverse(X2),X3)) = X3,
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
add(multiply(X2,X3),multiply(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))) = add(inverse(X3),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c52,plain,
add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
add(inverse(X3),multiply(X2,X3)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c43,c52]) ).
cnf(c54,plain,
add(inverse(X3),multiply(X3,X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c20,c53]) ).
cnf(c55,plain,
add(inverse(X3),multiply(X3,add(X3,X2))) = add(add(X3,X2),inverse(X3)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
add(add(X3,X2),inverse(X3)) = add(inverse(X3),multiply(X3,add(X3,X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c58,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
add(X4,multiply(X3,multiply(X4,X2))) = X4,
inference(substitution,[status(thm)],[c35]) ).
cnf(c61,plain,
X4 = add(X4,multiply(X3,multiply(X4,X2))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
add(X4,X5) = add(X4,add(X5,multiply(X3,multiply(X5,X2)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X5,add(X4,X5)) = multiply(X5,add(X4,add(X5,multiply(X3,multiply(X5,X2))))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X5,add(X4,add(X5,multiply(X3,multiply(X5,X2))))) = X5,
inference(substitution,[status(thm)],[c30]) ).
cnf(c65,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
add(inverse(X3),multiply(X3,add(X3,X2))) = add(inverse(X3),X3),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
add(inverse(X2),X2) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c69,plain,
add(inverse(X3),multiply(X3,add(X3,X2))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
add(add(X3,X2),inverse(X3)) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c56,c69]) ).
cnf(c71,plain,
add(X3,add(X2,inverse(X3))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c17,c70]) ).
cnf(c72,plain,
add(X2,add(X3,inverse(X2))) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
add(X2,inverse(X2)) = add(X2,add(X3,inverse(X2))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(X3,add(X2,inverse(X2))) = multiply(X3,add(X2,add(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(X3,add(X2,add(X3,inverse(X2)))) = X3,
inference(substitution,[status(thm)],[c30]) ).
cnf(c76,plain,
multiply(X3,add(X2,inverse(X2))) = X3,
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
multiply(X2,add(X3,inverse(X3))) = X2,
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
add(multiply(X2,add(X3,inverse(X3))),multiply(inverse(X2),add(X3,inverse(X3)))) = add(X2,multiply(inverse(X2),add(X3,inverse(X3)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(inverse(X2),add(X3,inverse(X3))) = inverse(X2),
inference(substitution,[status(thm)],[c76]) ).
cnf(c80,plain,
add(X2,multiply(inverse(X2),add(X3,inverse(X3)))) = add(X2,inverse(X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
add(multiply(X2,add(X3,inverse(X3))),multiply(inverse(X2),add(X3,inverse(X3)))) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c78,c80]) ).
cnf(c82,plain,
add(X3,inverse(X3)) = add(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c14,c81]) ).
cnf(c83,plain,
add(a,inverse(a)) = add(b,inverse(b)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
add(b,inverse(b)) = add(a,inverse(a)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
$false,
inference(resolution,[status(thm)],[c1,c84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n016.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:09:48 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.35 Command-line arguments: --no-flatten-goal
% 0.22/0.35
% 0.22/0.35 % SZS status Unsatisfiable
% 0.22/0.35
% 0.22/0.36 % SZS output start CNFRefutation
% See solution above
% 0.22/0.38
% 0.22/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------