%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.30s 0.39s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 54 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
inverse(inverse(a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(c2,axiom,
multiply(X,Y,inverse(Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(c3,plain,
multiply(X2,X3,inverse(X3)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = multiply(X2,X3,inverse(X3)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X3,inverse(X3),X2) = multiply(X3,inverse(X3),multiply(X2,X3,inverse(X3))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
multiply(Y2,X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_1) ).
cnf(c7,plain,
multiply(X3,X2,X2) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
X2 = multiply(X3,X2,X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X2,X5,multiply(X3,X2,X4)) = multiply(multiply(X3,X2,X2),X5,multiply(X3,X2,X4)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(multiply(V,W,X2),Y2,multiply(V,W,Z)) = multiply(V,W,multiply(X2,Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c11,plain,
multiply(multiply(X5,X4,X4),X3,multiply(X5,X4,X2)) = multiply(X5,X4,multiply(X4,X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X4,X3,multiply(X5,X4,X2)) = multiply(X5,X4,multiply(X4,X3,X2)),
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
multiply(X4,X3,multiply(X2,X4,X3)) = multiply(X2,X4,multiply(X4,X3,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X3,X2,X2) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c15,plain,
multiply(X2,X4,multiply(X4,X3,X3)) = multiply(X2,X4,X3),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X4,X3,multiply(X2,X4,X3)) = multiply(X2,X4,X3),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
multiply(X3,inverse(X3),multiply(X2,X3,inverse(X3))) = multiply(X2,X3,inverse(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,X3,inverse(X3)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
multiply(X3,inverse(X3),multiply(X2,X3,inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
multiply(X3,inverse(X3),X2) = X2,
inference(transitivity,[status(thm)],[c5,c19]) ).
cnf(c21,plain,
multiply(X2,inverse(X2),inverse(inverse(X2))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(inverse(X2)) = multiply(X2,inverse(X2),inverse(inverse(X2))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X2,inverse(X2),inverse(inverse(X2))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
inverse(inverse(a)) = a,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
$false,
inference(resolution,[status(thm)],[c1,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 % Computer : n008.cluster.edu
% 0.19/0.29 % Model : x86_64 x86_64
% 0.19/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.29 % Memory : 8046.5625MB
% 0.19/0.29 % OS : Linux 6.8.0-71-generic
% 0.19/0.29 % CPULimit : 300
% 0.19/0.29 % WCLimit : 300
% 0.19/0.29 % DateTime : Mon Sep 28 21:03:24 UTC 2026
% 0.19/0.30 % CPUTime :
% 0.19/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.39 Command-line arguments: --no-flatten-goal
% 0.30/0.39
% 0.30/0.39 % SZS status Unsatisfiable
% 0.30/0.39
% 0.30/0.40 % SZS output start CNFRefutation
% See solution above
% 0.30/0.42
% 0.30/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------