%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP671-1 : TPTP v9.3.1. Released v4.0.0.
% 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 10:11:41 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of clauses : 102 ( 102 unt; 0 nHn; 18 RR)
% Number of literals : 102 ( 101 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(mult(a,b),a) != mult(a,mult(b,a)),
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(i(X2),mult(i(X2),mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(X2,X) = ld(i(X2),mult(i(X2),mult(X2,X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(i(A2),mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c6,plain,
mult(i(X2),mult(X2,X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
ld(i(X2),mult(i(X2),mult(X2,X))) = ld(i(X2),X),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
mult(X2,X) = ld(i(X2),X),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
mult(a,b) = ld(i(a),b),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(mult(a,b),a) = mult(ld(i(a),b),a),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
mult(ld(i(a),b),a) = ld(i(ld(i(a),b)),a),
inference(substitution,[status(thm)],[c8]) ).
cnf(c12,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c13,plain,
mult(i(X),ld(i(X),i(ld(X2,X)))) = i(ld(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
i(ld(X2,X)) = mult(i(X),ld(i(X),i(ld(X2,X)))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
mult(mult(A2,B2),i(B2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c16,plain,
mult(mult(rd(X2,X),X),i(X)) = rd(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
rd(X2,X) = mult(mult(rd(X2,X),X),i(X)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c19,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
mult(mult(rd(X2,X),X),i(X)) = mult(X2,i(X)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(X2,i(X)) = ld(i(X2),i(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c22,plain,
mult(mult(rd(X2,X),X),i(X)) = ld(i(X2),i(X)),
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
rd(X2,X) = ld(i(X2),i(X)),
inference(transitivity,[status(thm)],[c17,c22]) ).
cnf(c24,plain,
rd(X2,ld(X,X2)) = ld(i(X2),i(ld(X,X2))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
ld(i(X2),i(ld(X,X2))) = rd(X2,ld(X,X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c27,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c30,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
ld(i(X2),i(ld(X,X2))) = X,
inference(transitivity,[status(thm)],[c25,c31]) ).
cnf(c33,plain,
ld(i(X),i(ld(X2,X))) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
mult(i(X),ld(i(X),i(ld(X2,X)))) = mult(i(X),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
mult(i(X),X2) = ld(i(i(X)),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c36,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c37,plain,
mult(i(i(X)),unit) = i(i(X)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
i(i(X)) = mult(i(i(X)),unit),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c40,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(i(X),X) = mult(i(X),mult(X,unit)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
mult(i(X),mult(X,unit)) = unit,
inference(substitution,[status(thm)],[c5]) ).
cnf(c43,plain,
mult(i(X),X) = unit,
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
mult(i(i(X)),unit) = mult(i(i(X)),mult(i(X),X)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(i(i(X)),mult(i(X),X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c47,plain,
mult(i(i(X)),unit) = X,
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
i(i(X)) = X,
inference(transitivity,[status(thm)],[c38,c47]) ).
cnf(c49,plain,
ld(i(i(X)),X2) = ld(X,X2),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
mult(i(X),X2) = ld(X,X2),
inference(transitivity,[status(thm)],[c35,c49]) ).
cnf(c51,plain,
mult(i(X),ld(i(X),i(ld(X2,X)))) = ld(X,X2),
inference(transitivity,[status(thm)],[c34,c50]) ).
cnf(c52,plain,
i(ld(X2,X)) = ld(X,X2),
inference(transitivity,[status(thm)],[c14,c51]) ).
cnf(c53,plain,
i(ld(i(a),b)) = ld(b,i(a)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
ld(i(ld(i(a),b)),a) = ld(ld(b,i(a)),a),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c56,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ld(X2,i(X)) = ld(mult(unit,X2),i(X)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
ld(ld(X2,i(X)),X) = ld(ld(mult(unit,X2),i(X)),X),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
i(ld(i(X),mult(unit,X2))) = ld(mult(unit,X2),i(X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c61,plain,
ld(mult(unit,X2),i(X)) = i(ld(i(X),mult(unit,X2))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
ld(ld(mult(unit,X2),i(X)),X) = ld(i(ld(i(X),mult(unit,X2))),X),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
mult(X,mult(unit,X2)) = ld(i(X),mult(unit,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c64,plain,
ld(i(X),mult(unit,X2)) = mult(X,mult(unit,X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
i(ld(i(X),mult(unit,X2))) = i(mult(X,mult(unit,X2))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
ld(i(ld(i(X),mult(unit,X2))),X) = ld(i(mult(X,mult(unit,X2))),X),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
mult(mult(X,mult(unit,X2)),X) = ld(i(mult(X,mult(unit,X2))),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c68,plain,
ld(i(mult(X,mult(unit,X2))),X) = mult(mult(X,mult(unit,X2)),X),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
mult(mult(mult(X,mult(unit,X2)),X),unit) = mult(mult(X,mult(unit,X2)),X),
inference(substitution,[status(thm)],[c36]) ).
cnf(c70,plain,
mult(mult(X,mult(unit,X2)),X) = mult(mult(mult(X,mult(unit,X2)),X),unit),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,axiom,
mult(mult(A2,B2),mult(C,mult(A2,B2))) = mult(mult(mult(A2,mult(B2,C)),A2),B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
cnf(c72,plain,
mult(mult(X,unit),mult(X2,mult(X,unit))) = mult(mult(mult(X,mult(unit,X2)),X),unit),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(mult(mult(X,mult(unit,X2)),X),unit) = mult(mult(X,unit),mult(X2,mult(X,unit))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
mult(mult(X,unit),mult(X2,mult(X,unit))) = ld(i(mult(X,unit)),mult(X2,mult(X,unit))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c75,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c76,plain,
i(mult(X,unit)) = i(X),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
ld(i(mult(X,unit)),mult(X2,mult(X,unit))) = ld(i(X),mult(X2,mult(X,unit))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c79,plain,
mult(X2,mult(X,unit)) = mult(X2,X),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
ld(i(X),mult(X2,mult(X,unit))) = ld(i(X),mult(X2,X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
ld(i(X),mult(X2,X)) = ld(i(X),ld(i(X2),X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c82,plain,
ld(i(X),mult(X2,mult(X,unit))) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
ld(i(mult(X,unit)),mult(X2,mult(X,unit))) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c77,c82]) ).
cnf(c84,plain,
mult(mult(X,unit),mult(X2,mult(X,unit))) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c74,c83]) ).
cnf(c85,plain,
mult(mult(mult(X,mult(unit,X2)),X),unit) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c73,c84]) ).
cnf(c86,plain,
mult(mult(X,mult(unit,X2)),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c70,c85]) ).
cnf(c87,plain,
ld(i(mult(X,mult(unit,X2))),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c68,c86]) ).
cnf(c88,plain,
ld(i(ld(i(X),mult(unit,X2))),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c66,c87]) ).
cnf(c89,plain,
ld(ld(mult(unit,X2),i(X)),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c62,c88]) ).
cnf(c90,plain,
ld(ld(X2,i(X)),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c59,c89]) ).
cnf(c91,plain,
ld(ld(b,i(a)),a) = ld(i(a),ld(i(b),a)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
mult(a,ld(i(b),a)) = ld(i(a),ld(i(b),a)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c93,plain,
ld(i(a),ld(i(b),a)) = mult(a,ld(i(b),a)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
mult(b,a) = ld(i(b),a),
inference(substitution,[status(thm)],[c8]) ).
cnf(c95,plain,
ld(i(b),a) = mult(b,a),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(a,ld(i(b),a)) = mult(a,mult(b,a)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
ld(i(a),ld(i(b),a)) = mult(a,mult(b,a)),
inference(transitivity,[status(thm)],[c93,c96]) ).
cnf(c98,plain,
ld(ld(b,i(a)),a) = mult(a,mult(b,a)),
inference(transitivity,[status(thm)],[c91,c97]) ).
cnf(c99,plain,
ld(i(ld(i(a),b)),a) = mult(a,mult(b,a)),
inference(transitivity,[status(thm)],[c54,c98]) ).
cnf(c100,plain,
mult(ld(i(a),b),a) = mult(a,mult(b,a)),
inference(transitivity,[status(thm)],[c11,c99]) ).
cnf(c101,plain,
mult(mult(a,b),a) = mult(a,mult(b,a)),
inference(transitivity,[status(thm)],[c10,c100]) ).
cnf(c102,plain,
$false,
inference(resolution,[status(thm)],[c1,c101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP671-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 10:34:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.44 Command-line arguments: --no-flatten-goal
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.48
% 0.14/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------