%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP001-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 10:08:50 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 14 RR)
% Number of literals : 40 ( 39 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(a,b),X2) = multiply(a,multiply(b,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(a,multiply(b,X2)) = multiply(multiply(a,b),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(a,b),X2) = multiply(c,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(a,multiply(b,X2)) = multiply(c,X2),
inference(transitivity,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
multiply(a,multiply(b,b)) = multiply(c,b),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(c,b) = multiply(a,multiply(b,b)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,hypothesis,
multiply(X2,X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',squareness) ).
cnf(c11,plain,
multiply(b,b) = identity,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(a,multiply(b,b)) = multiply(a,identity),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
identity = multiply(X2,X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c14,plain,
multiply(X2,identity) = multiply(X2,multiply(X2,X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(X2,X2),X3) = multiply(X2,multiply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
multiply(X3,multiply(X3,X2)) = multiply(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(X3,X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c10]) ).
cnf(c18,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
multiply(multiply(X3,X3),X2) = X2,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
multiply(X3,multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
multiply(X2,multiply(X2,X2)) = X2,
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c14,c21]) ).
cnf(c23,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(a,multiply(b,b)) = a,
inference(transitivity,[status(thm)],[c12,c23]) ).
cnf(c25,plain,
multiply(c,b) = a,
inference(transitivity,[status(thm)],[c9,c24]) ).
cnf(c26,plain,
a = multiply(c,b),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(b,a) = multiply(b,multiply(c,b)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X2,multiply(X2,multiply(X3,multiply(X2,X3)))) = multiply(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c29,plain,
multiply(X3,multiply(X2,X3)) = multiply(X2,multiply(X2,multiply(X3,multiply(X2,X3)))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(X3,X2),multiply(X3,X2)) = multiply(X3,multiply(X2,multiply(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
multiply(X3,multiply(X2,multiply(X3,X2))) = multiply(multiply(X3,X2),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(multiply(X3,X2),multiply(X3,X2)) = identity,
inference(substitution,[status(thm)],[c10]) ).
cnf(c33,plain,
multiply(X3,multiply(X2,multiply(X3,X2))) = identity,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
multiply(X2,multiply(X3,multiply(X2,X3))) = identity,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X2,multiply(X2,multiply(X3,multiply(X2,X3)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X2,multiply(X2,multiply(X3,multiply(X2,X3)))) = X2,
inference(transitivity,[status(thm)],[c35,c22]) ).
cnf(c37,plain,
multiply(X3,multiply(X2,X3)) = X2,
inference(transitivity,[status(thm)],[c29,c36]) ).
cnf(c38,plain,
multiply(b,multiply(c,b)) = c,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(b,a) = c,
inference(transitivity,[status(thm)],[c27,c38]) ).
cnf(c40,plain,
$false,
inference(resolution,[status(thm)],[c1,c39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:12:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.43 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
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.43
% 0.09/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------