%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP698-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:11:45 AM UTC 2026
% Result : Unsatisfiable 1.55s 0.72s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 9 RR)
% Number of literals : 60 ( 59 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c3,plain,
ld(a,mult(a,b)) = b,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
b = ld(a,mult(a,b)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(b,c) = mult(ld(a,mult(a,b)),c),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
mult(a,mult(b,c)) = mult(a,mult(ld(a,mult(a,b)),c)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c8,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(X,X2) = mult(mult(rd(X,X2),X2),X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
ld(X2,mult(X,X2)) = ld(X2,mult(mult(rd(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
mult(ld(X2,mult(X,X2)),X3) = mult(ld(X2,mult(mult(rd(X,X2),X2),X2)),X3),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(X3,mult(ld(X3,mult(X2,X3)),X)) = mult(X3,mult(ld(X3,mult(mult(rd(X2,X3),X3),X3)),X)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
ld(X2,mult(X2,mult(mult(ld(X2,X),X2),X2))) = mult(mult(ld(X2,X),X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
mult(mult(ld(X2,X),X2),X2) = ld(X2,mult(X2,mult(mult(ld(X2,X),X2),X2))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c17,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
mult(mult(mult(X2,X),X2),X2) = mult(mult(mult(X2,X),X2),mult(X2,unit)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
mult(mult(mult(A2,B2),A2),mult(A2,C)) = mult(A2,mult(mult(mult(B2,A2),A2),C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c21,plain,
mult(mult(mult(X2,X),X2),mult(X2,unit)) = mult(X2,mult(mult(mult(X,X2),X2),unit)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
mult(mult(mult(X,X2),X2),unit) = mult(mult(X,X2),X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c23,plain,
mult(X2,mult(mult(mult(X,X2),X2),unit)) = mult(X2,mult(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
mult(mult(mult(X2,X),X2),mult(X2,unit)) = mult(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
mult(mult(mult(X2,X),X2),X2) = mult(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c19,c24]) ).
cnf(c26,plain,
mult(mult(mult(X2,ld(X2,X)),X2),X2) = mult(X2,mult(mult(ld(X2,X),X2),X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
mult(X2,mult(mult(ld(X2,X),X2),X2)) = mult(mult(mult(X2,ld(X2,X)),X2),X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c29,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
mult(mult(X2,ld(X2,X)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
mult(mult(mult(X2,ld(X2,X)),X2),X2) = mult(mult(X,X2),X2),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(X2,mult(mult(ld(X2,X),X2),X2)) = mult(mult(X,X2),X2),
inference(transitivity,[status(thm)],[c27,c31]) ).
cnf(c33,plain,
ld(X2,mult(X2,mult(mult(ld(X2,X),X2),X2))) = ld(X2,mult(mult(X,X2),X2)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
mult(mult(ld(X2,X),X2),X2) = ld(X2,mult(mult(X,X2),X2)),
inference(transitivity,[status(thm)],[c15,c33]) ).
cnf(c35,plain,
ld(X2,mult(mult(X,X2),X2)) = mult(mult(ld(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
mult(ld(X3,mult(mult(X2,X3),X3)),X) = mult(mult(mult(ld(X3,X2),X3),X3),X),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
mult(X3,mult(ld(X3,mult(mult(X2,X3),X3)),X)) = mult(X3,mult(mult(mult(ld(X3,X2),X3),X3),X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
mult(mult(mult(X3,ld(X3,X2)),X3),mult(X3,X)) = mult(X3,mult(mult(mult(ld(X3,X2),X3),X3),X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c39,plain,
mult(X3,mult(mult(mult(ld(X3,X2),X3),X3),X)) = mult(mult(mult(X3,ld(X3,X2)),X3),mult(X3,X)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c41,plain,
mult(mult(X2,ld(X2,X)),X2) = mult(X,X2),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
mult(mult(mult(X3,ld(X3,X2)),X3),mult(X3,X)) = mult(mult(X2,X3),mult(X3,X)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(X3,mult(mult(mult(ld(X3,X2),X3),X3),X)) = mult(mult(X2,X3),mult(X3,X)),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
mult(X3,mult(ld(X3,mult(mult(X2,X3),X3)),X)) = mult(mult(X2,X3),mult(X3,X)),
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
mult(X3,mult(ld(X3,mult(mult(rd(X2,X3),X3),X3)),X)) = mult(mult(rd(X2,X3),X3),mult(X3,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c47,plain,
mult(mult(rd(X2,X3),X3),mult(X3,X)) = mult(X2,mult(X3,X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(X3,mult(ld(X3,mult(mult(rd(X2,X3),X3),X3)),X)) = mult(X2,mult(X3,X)),
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
mult(X3,mult(ld(X3,mult(X2,X3)),X)) = mult(X2,mult(X3,X)),
inference(transitivity,[status(thm)],[c13,c48]) ).
cnf(c50,plain,
mult(X2,mult(ld(X2,mult(rd(X3,X2),X2)),X)) = mult(rd(X3,X2),mult(X2,X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(rd(X3,X2),mult(X2,X)) = mult(X2,mult(ld(X2,mult(rd(X3,X2),X2)),X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c53,plain,
ld(X,mult(rd(X2,X),X)) = ld(X,X2),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
mult(ld(X2,mult(rd(X3,X2),X2)),X) = mult(ld(X2,X3),X),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(X2,mult(ld(X2,mult(rd(X3,X2),X2)),X)) = mult(X2,mult(ld(X2,X3),X)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(rd(X3,X2),mult(X2,X)) = mult(X2,mult(ld(X2,X3),X)),
inference(transitivity,[status(thm)],[c51,c55]) ).
cnf(c57,plain,
mult(rd(mult(a,b),a),mult(a,c)) = mult(a,mult(ld(a,mult(a,b)),c)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
mult(a,mult(ld(a,mult(a,b)),c)) = mult(rd(mult(a,b),a),mult(a,c)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
mult(a,mult(b,c)) = mult(rd(mult(a,b),a),mult(a,c)),
inference(transitivity,[status(thm)],[c6,c58]) ).
cnf(c60,plain,
$false,
inference(resolution,[status(thm)],[c1,c59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP698-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 10:35:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.55/0.72 Command-line arguments: --no-flatten-goal
% 1.55/0.72
% 1.55/0.72 % SZS status Unsatisfiable
% 1.55/0.72
% 1.55/0.73 % SZS output start CNFRefutation
% See solution above
% 1.55/0.77
% 1.55/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------