%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 10 RR)
% Number of literals : 23 ( 22 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; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(b,c) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_c_is_e) ).
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,
multiply(inverse(c),multiply(c,multiply(b,c))) = multiply(b,c),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(b,c) = multiply(inverse(c),multiply(c,multiply(b,c))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(c,b),X2) = multiply(c,multiply(b,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiply(c,multiply(b,X2)) = multiply(multiply(c,b),X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(c,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
multiply(multiply(c,b),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(c,b),X2) = X2,
inference(transitivity,[status(thm)],[c15,c7]) ).
cnf(c17,plain,
multiply(c,multiply(b,X2)) = X2,
inference(transitivity,[status(thm)],[c13,c16]) ).
cnf(c18,plain,
multiply(c,multiply(b,c)) = c,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(inverse(c),multiply(c,multiply(b,c))) = multiply(inverse(c),c),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(c),c) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c21,plain,
multiply(inverse(c),multiply(c,multiply(b,c))) = identity,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
multiply(b,c) = identity,
inference(transitivity,[status(thm)],[c11,c21]) ).
cnf(c23,plain,
$false,
inference(resolution,[status(thm)],[c1,c22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:13:29 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.42 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
% 0.12/0.42
% 0.12/0.42 % SZS status Unsatisfiable
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44
% 0.12/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------