%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:08:52 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 18 RR)
% Number of literals : 47 ( 46 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c13,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c17,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c19,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c15,c19]) ).
cnf(c21,plain,
multiply(d,identity) = d,
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
d = multiply(d,identity),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c24,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c26,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
multiply(c,inverse(c)) = identity,
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
identity = multiply(c,inverse(c)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(d,identity) = multiply(d,multiply(c,inverse(c))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(d,c),X2) = multiply(d,multiply(c,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
multiply(d,multiply(c,X2)) = multiply(multiply(d,c),X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
multiply(b,c) = multiply(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
multiply(d,c) = multiply(b,c),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(multiply(d,c),X2) = multiply(multiply(b,c),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(multiply(b,c),X2) = multiply(b,multiply(c,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
multiply(multiply(d,c),X2) = multiply(b,multiply(c,X2)),
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
multiply(d,multiply(c,X2)) = multiply(b,multiply(c,X2)),
inference(transitivity,[status(thm)],[c31,c36]) ).
cnf(c38,plain,
multiply(d,multiply(c,inverse(c))) = multiply(b,multiply(c,inverse(c))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(c,inverse(c)) = identity,
inference(substitution,[status(thm)],[c26]) ).
cnf(c40,plain,
multiply(b,multiply(c,inverse(c))) = multiply(b,identity),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(b,identity) = b,
inference(substitution,[status(thm)],[c20]) ).
cnf(c42,plain,
multiply(b,multiply(c,inverse(c))) = b,
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
multiply(d,multiply(c,inverse(c))) = b,
inference(transitivity,[status(thm)],[c38,c42]) ).
cnf(c44,plain,
multiply(d,identity) = b,
inference(transitivity,[status(thm)],[c29,c43]) ).
cnf(c45,plain,
d = b,
inference(transitivity,[status(thm)],[c22,c44]) ).
cnf(c46,plain,
b = d,
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
$false,
inference(resolution,[status(thm)],[c1,c46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:16:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.10/0.44
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45
% 0.10/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------