%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:09:42 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.44s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 5 RR)
% Number of literals : 16 ( 15 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang1) ).
cnf(c2,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(multiply(X2,X3),X2) = multiply(multiply(X2,X3),multiply(identity,X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang4) ).
cnf(c6,plain,
multiply(X3,multiply(multiply(X2,identity),X3)) = multiply(multiply(X3,X2),multiply(identity,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(multiply(X3,X2),multiply(identity,X3)) = multiply(X3,multiply(multiply(X2,identity),X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(X2,identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
multiply(multiply(X2,identity),X3) = multiply(X2,X3),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,multiply(multiply(X2,identity),X3)) = multiply(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(multiply(X3,X2),multiply(identity,X3)) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c4,c11]) ).
cnf(c13,plain,
multiply(multiply(a,multiply(b,c)),a) = multiply(a,multiply(multiply(b,c),a)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(a,multiply(multiply(b,c),a)) = multiply(multiply(a,b),multiply(c,a)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
multiply(multiply(a,multiply(b,c)),a) = multiply(multiply(a,b),multiply(c,a)),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
$false,
inference(resolution,[status(thm)],[c1,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sun Sep 27 09:38:04 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.44 Command-line arguments: --no-flatten-goal
% 0.03/0.44
% 0.03/0.44 % SZS status Unsatisfiable
% 0.03/0.44
% 0.03/0.44 % SZS output start CNFRefutation
% See solution above
% 0.03/0.45
% 0.03/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------