%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:11:43 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.50s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 3 RR)
% Number of literals : 72 ( 71 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; 3 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c3,plain,
rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)) = mult(X3,rd(mult(X2,X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(X3,rd(mult(X2,X),X)) = rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
rd(mult(A2,A2),A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c6,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(mult(X3,X2),rd(mult(X,X),X)) = mult(mult(X3,X2),X),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)) = rd(mult(mult(X3,X2),X),rd(mult(X,X),X)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c10,plain,
rd(mult(mult(X3,X2),X),rd(mult(X,X),X)) = rd(mult(mult(X3,X2),X),X),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)) = rd(mult(mult(X3,X2),X),X),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
mult(X3,rd(mult(X2,X),X)) = rd(mult(mult(X3,X2),X),X),
inference(transitivity,[status(thm)],[c4,c11]) ).
cnf(c13,plain,
mult(X2,rd(mult(X,X),X)) = rd(mult(mult(X2,X),X),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
rd(mult(mult(X2,X),X),X) = mult(X2,rd(mult(X,X),X)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c16,plain,
mult(X2,rd(mult(X,X),X)) = mult(X2,X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
rd(mult(mult(X2,X),X),X) = mult(X2,X),
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
mult(X2,X) = rd(mult(mult(X2,X),X),X),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
rd(mult(X3,mult(X2,X)),mult(X2,X)) = rd(mult(X3,mult(X2,X)),rd(mult(mult(X2,X),X),X)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
mult(X2,X) = rd(mult(mult(X2,X),X),X),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c21,plain,
mult(X3,mult(X2,X)) = mult(X3,rd(mult(mult(X2,X),X),X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
rd(mult(X3,mult(X2,X)),rd(mult(mult(X2,X),X),X)) = rd(mult(X3,rd(mult(mult(X2,X),X),X)),rd(mult(mult(X2,X),X),X)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c24,plain,
X = rd(mult(X,X),X),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
rd(X,X) = rd(rd(mult(X,X),X),X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
mult(rd(A2,B2),B2) = rd(mult(A2,B2),B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c27,plain,
mult(rd(X,X),X) = rd(mult(X,X),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
rd(mult(X,X),X) = mult(rd(X,X),X),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
rd(rd(mult(X,X),X),X) = rd(mult(rd(X,X),X),X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
ld(A2,mult(A2,ld(B2,B2))) = rd(mult(rd(A2,A2),B2),B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c31,plain,
ld(X,mult(X,ld(X,X))) = rd(mult(rd(X,X),X),X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
rd(mult(rd(X,X),X),X) = ld(X,mult(X,ld(X,X))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,axiom,
mult(A2,ld(A2,B2)) = ld(A2,mult(A2,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c34,plain,
mult(X,ld(X,X)) = ld(X,mult(X,X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
ld(X,mult(X,ld(X,X))) = ld(X,ld(X,mult(X,X))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
ld(A2,mult(A2,A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c37,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
ld(X,ld(X,mult(X,X))) = ld(X,X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
ld(X,mult(X,ld(X,X))) = ld(X,X),
inference(transitivity,[status(thm)],[c35,c38]) ).
cnf(c40,plain,
rd(mult(rd(X,X),X),X) = ld(X,X),
inference(transitivity,[status(thm)],[c32,c39]) ).
cnf(c41,plain,
rd(rd(mult(X,X),X),X) = ld(X,X),
inference(transitivity,[status(thm)],[c29,c40]) ).
cnf(c42,plain,
rd(X,X) = ld(X,X),
inference(transitivity,[status(thm)],[c25,c41]) ).
cnf(c43,plain,
ld(X,X) = rd(X,X),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
mult(ld(X,X),X) = mult(rd(X,X),X),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
mult(rd(X,X),X) = rd(mult(X,X),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c46,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c47,plain,
mult(rd(X,X),X) = X,
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
mult(ld(X,X),X) = X,
inference(transitivity,[status(thm)],[c44,c47]) ).
cnf(c49,plain,
X = mult(ld(X,X),X),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
mult(X2,rd(X3,X)) = mult(mult(ld(X2,X2),X2),rd(X3,X)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
rd(mult(X3,rd(X,X2)),rd(X,X2)) = rd(mult(mult(ld(X3,X3),X3),rd(X,X2)),rd(X,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
rd(mult(mult(ld(X3,X3),X3),rd(X,X2)),rd(X,X2)) = mult(ld(X3,X3),rd(mult(X3,X2),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
rd(mult(mult(ld(X3,X3),X3),rd(X2,X)),rd(X2,X)) = mult(ld(X3,X3),rd(mult(X3,X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
mult(ld(X3,X3),rd(mult(X3,X),X)) = rd(mult(mult(ld(X3,X3),X3),rd(X2,X)),rd(X2,X)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(mult(ld(X3,X3),X3),rd(X2,X)) = mult(X3,rd(X2,X)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c56,plain,
rd(mult(mult(ld(X3,X3),X3),rd(X2,X)),rd(X2,X)) = rd(mult(X3,rd(X2,X)),rd(X2,X)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
mult(ld(X3,X3),rd(mult(X3,X),X)) = rd(mult(X3,rd(X2,X)),rd(X2,X)),
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
rd(mult(mult(ld(X4,X4),X4),rd(X,X2)),rd(X,X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c52,c57]) ).
cnf(c59,plain,
rd(mult(X4,rd(X,X2)),rd(X,X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c51,c58]) ).
cnf(c60,plain,
rd(mult(X3,rd(X2,X)),rd(X2,X)) = rd(mult(X3,rd(mult(X,X),X)),rd(mult(X,X),X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c62,plain,
mult(X2,rd(mult(X,X),X)) = mult(X2,X),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
rd(mult(X2,rd(mult(X,X),X)),rd(mult(X,X),X)) = rd(mult(X2,X),rd(mult(X,X),X)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c65,plain,
rd(mult(X2,X),rd(mult(X,X),X)) = rd(mult(X2,X),X),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
rd(mult(X2,rd(mult(X,X),X)),rd(mult(X,X),X)) = rd(mult(X2,X),X),
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
rd(mult(X3,rd(X2,X)),rd(X2,X)) = rd(mult(X3,X),X),
inference(transitivity,[status(thm)],[c60,c66]) ).
cnf(c68,plain,
rd(mult(X3,rd(mult(mult(X2,X),X),X)),rd(mult(mult(X2,X),X),X)) = rd(mult(X3,X),X),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
rd(mult(X3,mult(X2,X)),rd(mult(mult(X2,X),X),X)) = rd(mult(X3,X),X),
inference(transitivity,[status(thm)],[c22,c68]) ).
cnf(c70,plain,
rd(mult(X3,mult(X2,X)),mult(X2,X)) = rd(mult(X3,X),X),
inference(transitivity,[status(thm)],[c19,c69]) ).
cnf(c71,plain,
rd(mult(a,mult(b,c)),mult(b,c)) = rd(mult(a,c),c),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
$false,
inference(resolution,[status(thm)],[c1,c71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 10:35:46 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.50 Command-line arguments: --no-flatten-goal
% 0.14/0.50
% 0.14/0.50 % SZS status Unsatisfiable
% 0.14/0.50
% 0.14/0.53 % SZS output start CNFRefutation
% See solution above
% 0.89/0.56
% 0.89/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------