%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 09:35:19 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.43s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 3 RR)
% Number of literals : 50 ( 49 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 136 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c2,axiom,
multiply(Y,X,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
cnf(c3,plain,
multiply(X3,X2,X2) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = multiply(X3,X2,X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(multiply(X3,X2,X5),X4,X2) = multiply(multiply(X3,X2,X5),X4,multiply(X3,X2,X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
multiply(multiply(V,W,X2),Y2,multiply(V,W,Z)) = multiply(V,W,multiply(X2,Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c7,plain,
multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X4)) = multiply(X5,X4,multiply(X3,X2,X4)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(multiply(X5,X4,X3),X2,X4) = multiply(X5,X4,multiply(X3,X2,X4)),
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
multiply(multiply(multiply(X5,X4,X3),X3,X5),X2,X3) = multiply(multiply(X5,X4,X3),X3,multiply(X5,X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(X5,X4,X3),X3,multiply(X5,X2,X3)) = multiply(multiply(multiply(X5,X4,X3),X3,X5),X2,X3),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,Y2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_lemma) ).
cnf(c12,plain,
multiply(X3,X2,X3) = X3,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
X3 = multiply(X3,X2,X3),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(multiply(X5,X4,X3),X2,X5) = multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X5)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X5)) = multiply(X5,X4,multiply(X3,X2,X5)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c16,plain,
multiply(multiply(X5,X4,X3),X2,X5) = multiply(X5,X4,multiply(X3,X2,X5)),
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
multiply(multiply(X4,X3,X2),X2,X4) = multiply(X4,X3,multiply(X2,X2,X4)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,axiom,
multiply(X2,X2,Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
cnf(c19,plain,
multiply(X2,X2,X3) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X4,X3,multiply(X2,X2,X4)) = multiply(X4,X3,X2),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(X4,X3,X2),X2,X4) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c17,c20]) ).
cnf(c22,plain,
multiply(multiply(multiply(X5,X4,X3),X3,X5),X2,X3) = multiply(multiply(X5,X4,X3),X2,X3),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(multiply(X5,X4,X3),X3,multiply(X5,X2,X3)) = multiply(multiply(X5,X4,X3),X2,X3),
inference(transitivity,[status(thm)],[c10,c22]) ).
cnf(c24,plain,
multiply(multiply(X4,X3,X2),X2,multiply(X4,X4,X2)) = multiply(multiply(X4,X3,X2),X4,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(multiply(X4,X3,X2),X4,X2) = multiply(multiply(X4,X3,X2),X2,multiply(X4,X4,X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,X3,X2) = X3,
inference(substitution,[status(thm)],[c18]) ).
cnf(c27,plain,
multiply(multiply(X4,X3,X2),X2,multiply(X4,X4,X2)) = multiply(multiply(X4,X3,X2),X2,X4),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(multiply(X4,X3,X2),X2,multiply(X4,X4,X2)) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c27,c21]) ).
cnf(c29,plain,
multiply(multiply(X4,X3,X2),X4,X2) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
multiply(multiply(X2,inverse(X2),X3),X2,X3) = multiply(X2,inverse(X2),X3),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X2,inverse(X2),X3) = multiply(multiply(X2,inverse(X2),X3),X2,X3),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(multiply(multiply(X5,X4,X3),X3,X4),X2,X3) = multiply(multiply(X5,X4,X3),X3,multiply(X4,X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c33,plain,
multiply(multiply(X5,X4,X3),X3,multiply(X4,X2,X3)) = multiply(multiply(multiply(X5,X4,X3),X3,X4),X2,X3),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(multiply(X4,X3,X2),X2,X3) = multiply(X4,X3,multiply(X2,X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c35,plain,
multiply(X2,X2,X3) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c36,plain,
multiply(X4,X3,multiply(X2,X2,X3)) = multiply(X4,X3,X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(multiply(X4,X3,X2),X2,X3) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
multiply(multiply(multiply(X5,X4,X3),X3,X4),X2,X3) = multiply(multiply(X5,X4,X3),X2,X3),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(multiply(X5,X4,X3),X3,multiply(X4,X2,X3)) = multiply(multiply(X5,X4,X3),X2,X3),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
multiply(multiply(X2,inverse(X2),X3),X3,multiply(inverse(X2),X2,X3)) = multiply(multiply(X2,inverse(X2),X3),X2,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(multiply(X2,inverse(X2),X3),X2,X3) = multiply(multiply(X2,inverse(X2),X3),X3,multiply(inverse(X2),X2,X3)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,axiom,
multiply(inverse(Y2),Y2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(c43,plain,
multiply(inverse(X2),X2,X3) = X3,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(multiply(X2,inverse(X2),X3),X3,multiply(inverse(X2),X2,X3)) = multiply(multiply(X2,inverse(X2),X3),X3,X3),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(multiply(X2,inverse(X2),X3),X3,X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
multiply(multiply(X2,inverse(X2),X3),X3,multiply(inverse(X2),X2,X3)) = X3,
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
multiply(multiply(X2,inverse(X2),X3),X2,X3) = X3,
inference(transitivity,[status(thm)],[c41,c46]) ).
cnf(c48,plain,
multiply(X2,inverse(X2),X3) = X3,
inference(transitivity,[status(thm)],[c31,c47]) ).
cnf(c49,plain,
multiply(a,inverse(a),b) = b,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
$false,
inference(resolution,[status(thm)],[c1,c49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.25 % Computer : n018.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 21:05:10 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.43 Command-line arguments: --flatten --complete-subsets
% 0.25/0.43
% 0.25/0.43 % SZS status Unsatisfiable
% 0.25/0.43
% 0.25/0.44 % SZS output start CNFRefutation
% See solution above
% 0.32/0.47
% 0.32/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------