%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG023-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:34:47 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 12 ( 11 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
associator(x,x,y) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_alternative) ).
cnf(c2,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
cnf(c3,plain,
associator(X3,X3,X2) = add(multiply(multiply(X3,X3),X2),additive_inverse(multiply(X3,multiply(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(multiply(X2,X2),Y2) = multiply(X2,multiply(X2,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
cnf(c5,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
add(multiply(multiply(X3,X3),X2),additive_inverse(multiply(X3,multiply(X3,X2)))) = add(multiply(X3,multiply(X3,X2)),additive_inverse(multiply(X3,multiply(X3,X2)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
cnf(c8,plain,
add(multiply(X3,multiply(X3,X2)),additive_inverse(multiply(X3,multiply(X3,X2)))) = additive_identity,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
add(multiply(multiply(X3,X3),X2),additive_inverse(multiply(X3,multiply(X3,X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
associator(X3,X3,X2) = additive_identity,
inference(transitivity,[status(thm)],[c3,c9]) ).
cnf(c11,plain,
associator(x,x,y) = additive_identity,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
$false,
inference(resolution,[status(thm)],[c1,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG023-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 23:00:56 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --no-flatten-goal
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44
% 0.13/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------