%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 10:11:35 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 2 RR)
% Number of literals : 63 ( 62 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 148 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(c3,plain,
ld(X3,mult(X3,mult(mult(ld(X3,X2),X),X3))) = mult(mult(ld(X3,X2),X),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(mult(ld(X3,X2),X),X3) = ld(X3,mult(X3,mult(mult(ld(X3,X2),X),X3))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(mult(A2,B2),mult(C,A2)) = mult(A2,mult(mult(B2,C),A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(c6,plain,
mult(mult(X3,ld(X3,X2)),mult(X,X3)) = mult(X3,mult(mult(ld(X3,X2),X),X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(X3,mult(mult(ld(X3,X2),X),X3)) = mult(mult(X3,ld(X3,X2)),mult(X,X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(c9,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(mult(X3,ld(X3,X2)),mult(X,X3)) = mult(X2,mult(X,X3)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
mult(X3,mult(mult(ld(X3,X2),X),X3)) = mult(X2,mult(X,X3)),
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
ld(X3,mult(X3,mult(mult(ld(X3,X2),X),X3))) = ld(X3,mult(X2,mult(X,X3))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(mult(ld(X3,X2),X),X3) = ld(X3,mult(X2,mult(X,X3))),
inference(transitivity,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
ld(X3,mult(X2,mult(X,X3))) = mult(mult(ld(X3,X2),X),X3),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
rd(ld(X3,mult(X2,mult(X,X3))),X3) = rd(mult(mult(ld(X3,X2),X),X3),X3),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(c17,plain,
rd(mult(mult(ld(X3,X2),X),X3),X3) = mult(ld(X3,X2),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
rd(ld(X3,mult(X2,mult(X,X3))),X3) = mult(ld(X3,X2),X),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
rd(ld(X2,mult(X2,mult(X,X2))),X2) = mult(ld(X2,X2),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
mult(ld(X2,X2),X) = rd(ld(X2,mult(X2,mult(X,X2))),X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
ld(X2,mult(X2,mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
rd(ld(X2,mult(X2,mult(X,X2))),X2) = rd(mult(X,X2),X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c16]) ).
cnf(c24,plain,
rd(ld(X2,mult(X2,mult(X,X2))),X2) = X,
inference(transitivity,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
mult(ld(X2,X2),X) = X,
inference(transitivity,[status(thm)],[c20,c24]) ).
cnf(c26,plain,
mult(ld(X,X),X2) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
X2 = mult(ld(X,X),X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
rd(X2,X2) = rd(mult(ld(X,X),X2),X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
rd(mult(ld(X,X),X2),X2) = ld(X,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c30,plain,
rd(X2,X2) = ld(X,X),
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
rd(rd(X,X3),rd(X,X3)) = ld(X2,X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
ld(X2,X2) = rd(rd(X,X3),rd(X,X3)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
mult(X3,ld(X2,X2)) = mult(X3,rd(rd(X,X3),rd(X,X3))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
rd(mult(mult(X3,rd(X2,rd(X,X3))),X),X) = mult(X3,rd(X2,rd(X,X3))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c35,plain,
mult(X3,rd(X2,rd(X,X3))) = rd(mult(mult(X3,rd(X2,rd(X,X3))),X),X),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
mult(mult(X3,X2),mult(rd(X,X3),X3)) = mult(X3,mult(mult(X2,rd(X,X3)),X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c37,plain,
mult(X3,mult(mult(X2,rd(X,X3)),X3)) = mult(mult(X3,X2),mult(rd(X,X3),X3)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(c39,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
mult(mult(X3,X2),mult(rd(X,X3),X3)) = mult(mult(X3,X2),X),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(X3,mult(mult(X2,rd(X,X3)),X3)) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
mult(X3,mult(mult(rd(X2,rd(X,X3)),rd(X,X3)),X3)) = mult(mult(X3,rd(X2,rd(X,X3))),X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(mult(X3,rd(X2,rd(X,X3))),X) = mult(X3,mult(mult(rd(X2,rd(X,X3)),rd(X,X3)),X3)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
mult(rd(X2,rd(X,X3)),rd(X,X3)) = X2,
inference(substitution,[status(thm)],[c38]) ).
cnf(c45,plain,
mult(mult(rd(X2,rd(X,X3)),rd(X,X3)),X3) = mult(X2,X3),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(X3,mult(mult(rd(X2,rd(X,X3)),rd(X,X3)),X3)) = mult(X3,mult(X2,X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
mult(mult(X3,rd(X2,rd(X,X3))),X) = mult(X3,mult(X2,X3)),
inference(transitivity,[status(thm)],[c43,c46]) ).
cnf(c48,plain,
rd(mult(mult(X3,rd(X2,rd(X,X3))),X),X) = rd(mult(X3,mult(X2,X3)),X),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(X3,rd(X2,rd(X,X3))) = rd(mult(X3,mult(X2,X3)),X),
inference(transitivity,[status(thm)],[c35,c48]) ).
cnf(c50,plain,
mult(X2,rd(rd(X,X2),rd(X,X2))) = rd(mult(X2,mult(rd(X,X2),X2)),X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c52,plain,
mult(X2,mult(rd(X,X2),X2)) = mult(X2,X),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
rd(mult(X2,mult(rd(X,X2),X2)),X) = rd(mult(X2,X),X),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
rd(mult(X2,X),X) = X2,
inference(substitution,[status(thm)],[c16]) ).
cnf(c55,plain,
rd(mult(X2,mult(rd(X,X2),X2)),X) = X2,
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
mult(X2,rd(rd(X,X2),rd(X,X2))) = X2,
inference(transitivity,[status(thm)],[c50,c55]) ).
cnf(c57,plain,
mult(X2,ld(X,X)) = X2,
inference(transitivity,[status(thm)],[c33,c56]) ).
cnf(c58,plain,
mult(x1_2(ld(X,X)),ld(X,X)) = x1_2(ld(X,X)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
tuple(mult(ld(X,X),x1(ld(X,X))),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(mult(ld(X,X),x1(ld(X,X))),x1_2(ld(X,X))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
mult(ld(X,X),x1(ld(X,X))) = x1(ld(X,X)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c61,plain,
tuple(mult(ld(X,X),x1(ld(X,X))),x1_2(ld(X,X))) = tuple(x1(ld(X,X)),x1_2(ld(X,X))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
tuple(mult(ld(X,X),x1(ld(X,X))),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(x1(ld(X,X)),x1_2(ld(X,X))),
inference(transitivity,[status(thm)],[c59,c61]) ).
cnf(c63,plain,
$false,
inference(resolution,[status(thm)],[c1,c62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:38:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 Command-line arguments: --no-flatten-goal
% 0.11/0.44
% 0.11/0.44 % SZS status Unsatisfiable
% 0.11/0.44
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46
% 0.11/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------