%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.09s 0.25s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of clauses : 94 ( 94 unt; 0 nHn; 31 RR)
% Number of literals : 94 ( 93 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 166 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_single_axiom) ).
cnf(c2,axiom,
multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(c,d,e),f,multiply(c,d,g)) = multiply(c,d,multiply(e,f,g)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) = inverse(multiply(c,d,multiply(e,f,g))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
multiply(X2,Y2,inverse(Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(c7,plain,
multiply(X2,X3,inverse(X3)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
X2 = multiply(X2,X3,inverse(X3)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X3,inverse(X3),X2) = multiply(X3,inverse(X3),multiply(X2,X3,inverse(X3))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(Y2,X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
cnf(c11,plain,
multiply(X3,X2,X2) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
X2 = multiply(X3,X2,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(X2,X5,multiply(X3,X2,X4)) = multiply(multiply(X3,X2,X2),X5,multiply(X3,X2,X4)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(multiply(X5,X4,X4),X3,multiply(X5,X4,X2)) = multiply(X5,X4,multiply(X4,X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
multiply(X4,X3,multiply(X5,X4,X2)) = multiply(X5,X4,multiply(X4,X3,X2)),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
multiply(X4,X3,multiply(X2,X4,X3)) = multiply(X2,X4,multiply(X4,X3,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X3,X2,X2) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c18,plain,
multiply(X2,X4,multiply(X4,X3,X3)) = multiply(X2,X4,X3),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X4,X3,multiply(X2,X4,X3)) = multiply(X2,X4,X3),
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
multiply(X3,inverse(X3),multiply(X2,X3,inverse(X3))) = multiply(X2,X3,inverse(X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(X2,X3,inverse(X3)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c22,plain,
multiply(X3,inverse(X3),multiply(X2,X3,inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(X3,inverse(X3),X2) = X2,
inference(transitivity,[status(thm)],[c9,c22]) ).
cnf(c24,plain,
multiply(a,inverse(a),b) = b,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,X2,X2) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c27,plain,
X2 = multiply(X3,X2,X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(multiply(X5,X4,X3),X2,X4) = multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X4)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X4)) = multiply(X5,X4,multiply(X3,X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
multiply(multiply(X5,X4,X3),X2,X4) = multiply(X5,X4,multiply(X3,X2,X4)),
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
multiply(multiply(X4,X3,inverse(X3)),X2,X3) = multiply(X4,X3,multiply(inverse(X3),X2,X3)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X4,X3,multiply(inverse(X3),X2,X3)) = multiply(multiply(X4,X3,inverse(X3)),X2,X3),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X3,X2,inverse(X2)) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c34,plain,
multiply(multiply(X4,X3,inverse(X3)),X2,X3) = multiply(X4,X2,X3),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X4,X3,multiply(inverse(X3),X2,X3)) = multiply(X4,X2,X3),
inference(transitivity,[status(thm)],[c32,c34]) ).
cnf(c36,plain,
multiply(X4,X2,multiply(inverse(X2),X3,X2)) = multiply(X4,X3,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(X4,X3,X2) = multiply(X4,X2,multiply(inverse(X2),X3,X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X2,X3,X3) = X3,
inference(substitution,[status(thm)],[c10]) ).
cnf(c39,plain,
X3 = multiply(X2,X3,X3),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(inverse(X3),X2,X3) = multiply(inverse(X3),X2,multiply(X2,X3,X3)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(X2,X3,multiply(inverse(X3),X2,X3)) = multiply(inverse(X3),X2,multiply(X2,X3,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c42,plain,
multiply(inverse(X3),X2,multiply(X2,X3,X3)) = multiply(X2,X3,multiply(inverse(X3),X2,X3)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,X3,multiply(inverse(X3),X2,X3)) = multiply(X2,X2,X3),
inference(substitution,[status(thm)],[c35]) ).
cnf(c44,axiom,
multiply(X2,X2,Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
cnf(c45,plain,
multiply(X2,X2,X3) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X2,X3,multiply(inverse(X3),X2,X3)) = X2,
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
multiply(inverse(X3),X2,multiply(X2,X3,X3)) = X2,
inference(transitivity,[status(thm)],[c42,c46]) ).
cnf(c48,plain,
multiply(inverse(X3),X2,X3) = X2,
inference(transitivity,[status(thm)],[c40,c47]) ).
cnf(c49,plain,
multiply(inverse(X2),X3,X2) = X3,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(X4,X2,multiply(inverse(X2),X3,X2)) = multiply(X4,X2,X3),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(X4,X3,X2) = multiply(X4,X2,X3),
inference(transitivity,[status(thm)],[c37,c50]) ).
cnf(c52,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(d,multiply(g,f,e),c) = multiply(d,c,multiply(g,f,e)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c54,plain,
multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(d,c,multiply(g,f,e)),inverse(multiply(c,d,multiply(e,f,g)))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(g,f,e) = multiply(g,e,f),
inference(substitution,[status(thm)],[c51]) ).
cnf(c56,plain,
multiply(d,c,multiply(g,f,e)) = multiply(d,c,multiply(g,e,f)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(b,multiply(d,c,multiply(g,f,e)),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(d,c,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(X3,X4,X2) = multiply(X3,X2,X4),
inference(substitution,[status(thm)],[c51]) ).
cnf(c59,plain,
multiply(X3,X2,X4) = multiply(X3,X4,X2),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
X2 = multiply(X3,inverse(X3),X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c61,plain,
multiply(X3,X4,X2) = multiply(X3,X4,multiply(X4,inverse(X4),X2)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(X3,X2,inverse(X3)) = multiply(X3,inverse(X3),X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c63,plain,
multiply(X3,inverse(X3),X2) = multiply(X3,X2,inverse(X3)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X3,X4,multiply(X4,inverse(X4),X2)) = multiply(X3,X4,multiply(X4,X2,inverse(X4))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(X3,X2,multiply(X4,X3,inverse(X3))) = multiply(X4,X3,multiply(X3,X2,inverse(X3))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c66,plain,
multiply(X4,X3,multiply(X3,X2,inverse(X3))) = multiply(X3,X2,multiply(X4,X3,inverse(X3))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(X3,X2,inverse(X2)) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c68,plain,
multiply(X3,X2,multiply(X4,X3,inverse(X3))) = multiply(X3,X2,X4),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(X4,X3,multiply(X3,X2,inverse(X3))) = multiply(X3,X2,X4),
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
multiply(X3,X4,multiply(X4,X2,inverse(X4))) = multiply(X4,X2,X3),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(X4,X2,X3) = multiply(X4,X3,X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c72,plain,
multiply(X3,X4,multiply(X4,X2,inverse(X4))) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
multiply(X3,X4,multiply(X4,inverse(X4),X2)) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c64,c72]) ).
cnf(c74,plain,
multiply(X3,X4,X2) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c61,c73]) ).
cnf(c75,plain,
multiply(X3,X2,X4) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c59,c74]) ).
cnf(c76,plain,
multiply(c,multiply(g,e,f),d) = multiply(d,c,multiply(g,e,f)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(d,c,multiply(g,e,f)) = multiply(c,multiply(g,e,f),d),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(b,multiply(d,c,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(c,multiply(g,e,f),d),inverse(multiply(c,d,multiply(e,f,g)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(c,multiply(g,e,f),d) = multiply(c,d,multiply(g,e,f)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c80,plain,
multiply(b,multiply(c,multiply(g,e,f),d),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(c,d,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(e,f,g) = multiply(g,e,f),
inference(substitution,[status(thm)],[c75]) ).
cnf(c82,plain,
multiply(g,e,f) = multiply(e,f,g),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(c,d,multiply(g,e,f)) = multiply(c,d,multiply(e,f,g)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(b,multiply(c,d,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(substitution,[status(thm)],[c6]) ).
cnf(c86,plain,
multiply(b,multiply(c,d,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
multiply(b,multiply(c,multiply(g,e,f),d),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(transitivity,[status(thm)],[c80,c86]) ).
cnf(c88,plain,
multiply(b,multiply(d,c,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(transitivity,[status(thm)],[c78,c87]) ).
cnf(c89,plain,
multiply(b,multiply(d,c,multiply(g,f,e)),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(transitivity,[status(thm)],[c57,c88]) ).
cnf(c90,plain,
multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(transitivity,[status(thm)],[c54,c89]) ).
cnf(c91,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b,
inference(transitivity,[status(thm)],[c52,c90]) ).
cnf(c92,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b,
inference(transitivity,[status(thm)],[c25,c91]) ).
cnf(c93,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = b,
inference(transitivity,[status(thm)],[c5,c92]) ).
cnf(c94,plain,
$false,
inference(resolution,[status(thm)],[c1,c93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n011.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Mon Sep 28 21:04:45 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 Command-line arguments: --no-flatten-goal
% 0.09/0.25
% 0.09/0.25 % SZS status Unsatisfiable
% 0.09/0.25
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.57/0.30
% 0.57/0.30 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------