%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP670-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 10:11:40 AM UTC 2026
% Result : Unsatisfiable 54.86s 7.35s
% Output : CNFRefutation 56.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 10
% Syntax : Number of clauses : 335 ( 335 unt; 0 nHn; 59 RR)
% Number of literals : 335 ( 334 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 674 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/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/sandbox2/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),mult(mult(c,b),c)) = mult(ld(i(a),b),mult(mult(c,b),c)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
mult(ld(i(a),b),mult(mult(c,b),c)) = ld(i(ld(i(a),b)),mult(mult(c,b),c)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c12,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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)),mult(mult(c,b),c)) = ld(ld(b,i(a)),mult(mult(c,b),c)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
mult(c,b) = ld(i(c),b),
inference(substitution,[status(thm)],[c8]) ).
cnf(c56,plain,
mult(mult(c,b),c) = mult(ld(i(c),b),c),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
ld(ld(b,i(a)),mult(mult(c,b),c)) = ld(ld(b,i(a)),mult(ld(i(c),b),c)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
mult(ld(i(c),b),c) = ld(i(ld(i(c),b)),c),
inference(substitution,[status(thm)],[c8]) ).
cnf(c59,plain,
ld(ld(b,i(a)),mult(ld(i(c),b),c)) = ld(ld(b,i(a)),ld(i(ld(i(c),b)),c)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
i(ld(i(c),b)) = ld(b,i(c)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c61,plain,
ld(i(ld(i(c),b)),c) = ld(ld(b,i(c)),c),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
ld(ld(b,i(a)),ld(i(ld(i(c),b)),c)) = ld(ld(b,i(a)),ld(ld(b,i(c)),c)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c64,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
X = mult(unit,X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
ld(X2,i(X)) = ld(mult(unit,X2),i(X)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
ld(ld(X2,i(X)),X) = ld(ld(mult(unit,X2),i(X)),X),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
i(ld(i(X),mult(unit,X2))) = ld(mult(unit,X2),i(X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c69,plain,
ld(mult(unit,X2),i(X)) = i(ld(i(X),mult(unit,X2))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
ld(ld(mult(unit,X2),i(X)),X) = ld(i(ld(i(X),mult(unit,X2))),X),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
mult(X,mult(unit,X2)) = ld(i(X),mult(unit,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c72,plain,
ld(i(X),mult(unit,X2)) = mult(X,mult(unit,X2)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
i(ld(i(X),mult(unit,X2))) = i(mult(X,mult(unit,X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
ld(i(ld(i(X),mult(unit,X2))),X) = ld(i(mult(X,mult(unit,X2))),X),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
mult(mult(X,mult(unit,X2)),X) = ld(i(mult(X,mult(unit,X2))),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c76,plain,
ld(i(mult(X,mult(unit,X2))),X) = mult(mult(X,mult(unit,X2)),X),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
mult(mult(mult(X,mult(unit,X2)),X),unit) = mult(mult(X,mult(unit,X2)),X),
inference(substitution,[status(thm)],[c36]) ).
cnf(c78,plain,
mult(mult(X,mult(unit,X2)),X) = mult(mult(mult(X,mult(unit,X2)),X),unit),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,axiom,
mult(mult(A2,B2),mult(C,mult(A2,B2))) = mult(mult(mult(A2,mult(B2,C)),A2),B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c80,plain,
mult(mult(X,unit),mult(X2,mult(X,unit))) = mult(mult(mult(X,mult(unit,X2)),X),unit),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
mult(mult(mult(X,mult(unit,X2)),X),unit) = mult(mult(X,unit),mult(X2,mult(X,unit))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,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(c83,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c84,plain,
i(mult(X,unit)) = i(X),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
ld(i(mult(X,unit)),mult(X2,mult(X,unit))) = ld(i(X),mult(X2,mult(X,unit))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c87,plain,
mult(X2,mult(X,unit)) = mult(X2,X),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
ld(i(X),mult(X2,mult(X,unit))) = ld(i(X),mult(X2,X)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
ld(i(X),mult(X2,X)) = ld(i(X),ld(i(X2),X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c90,plain,
ld(i(X),mult(X2,mult(X,unit))) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c88,c89]) ).
cnf(c91,plain,
ld(i(mult(X,unit)),mult(X2,mult(X,unit))) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c85,c90]) ).
cnf(c92,plain,
mult(mult(X,unit),mult(X2,mult(X,unit))) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c82,c91]) ).
cnf(c93,plain,
mult(mult(mult(X,mult(unit,X2)),X),unit) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c81,c92]) ).
cnf(c94,plain,
mult(mult(X,mult(unit,X2)),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c78,c93]) ).
cnf(c95,plain,
ld(i(mult(X,mult(unit,X2))),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c76,c94]) ).
cnf(c96,plain,
ld(i(ld(i(X),mult(unit,X2))),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c74,c95]) ).
cnf(c97,plain,
ld(ld(mult(unit,X2),i(X)),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c70,c96]) ).
cnf(c98,plain,
ld(ld(X2,i(X)),X) = ld(i(X),ld(i(X2),X)),
inference(transitivity,[status(thm)],[c67,c97]) ).
cnf(c99,plain,
ld(ld(b,i(c)),c) = ld(i(c),ld(i(b),c)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
ld(ld(b,i(a)),ld(ld(b,i(c)),c)) = ld(ld(b,i(a)),ld(i(c),ld(i(b),c))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
i(ld(X,ld(ld(i(X2),ld(i(X),X2)),X3))) = ld(ld(ld(i(X2),ld(i(X),X2)),X3),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c102,plain,
ld(ld(ld(i(X3),ld(i(X2),X3)),X),X2) = i(ld(X2,ld(ld(i(X3),ld(i(X2),X3)),X))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c104,plain,
ld(X,X2) = ld(X,i(i(X2))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
ld(X,ld(X2,X3)) = ld(X,ld(X2,i(i(X3)))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
ld(ld(X3,X2),ld(X,ld(X2,X3))) = ld(ld(X3,X2),ld(X,ld(X2,i(i(X3))))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c108,plain,
ld(X2,X) = ld(i(i(X2)),X),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
ld(ld(X3,X2),ld(X,ld(X2,i(i(X3))))) = ld(ld(i(i(X3)),X2),ld(X,ld(X2,i(i(X3))))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
ld(i(i(X2)),i(ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2)))) = ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c111,plain,
ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))) = ld(i(i(X2)),i(ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2)))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
i(ld(i(X2),X)) = ld(X,i(X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c113,plain,
ld(X,i(X2)) = i(ld(i(X2),X)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
ld(X,ld(X2,i(X3))) = ld(X,i(ld(i(X3),X2))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))) = ld(ld(i(X3),X2),ld(X,i(ld(i(X3),X2)))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2)) = ld(ld(ld(i(X3),X2),ld(X,i(ld(i(X3),X2)))),i(X2)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c118,plain,
ld(X,i(ld(i(X3),X2))) = ld(i(i(X)),i(ld(i(X3),X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
ld(ld(i(X3),X2),ld(X,i(ld(i(X3),X2)))) = ld(ld(i(X3),X2),ld(i(i(X)),i(ld(i(X3),X2)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
ld(ld(ld(i(X3),X2),ld(X,i(ld(i(X3),X2)))),i(X2)) = ld(ld(ld(i(X3),X2),ld(i(i(X)),i(ld(i(X3),X2)))),i(X2)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
ld(i(X2),X) = mult(X2,X),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c122,plain,
ld(ld(i(X3),X2),ld(i(i(X)),i(ld(i(X3),X2)))) = ld(mult(X3,X2),ld(i(i(X)),i(ld(i(X3),X2)))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
ld(ld(ld(i(X3),X2),ld(i(i(X)),i(ld(i(X3),X2)))),i(X2)) = ld(ld(mult(X3,X2),ld(i(i(X)),i(ld(i(X3),X2)))),i(X2)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
ld(i(X2),X) = mult(X2,X),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c125,plain,
i(ld(i(X2),X)) = i(mult(X2,X)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
ld(i(i(X)),i(ld(i(X3),X2))) = ld(i(i(X)),i(mult(X3,X2))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
ld(mult(X3,X2),ld(i(i(X)),i(ld(i(X3),X2)))) = ld(mult(X3,X2),ld(i(i(X)),i(mult(X3,X2)))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
ld(ld(mult(X3,X2),ld(i(i(X)),i(ld(i(X3),X2)))),i(X2)) = ld(ld(mult(X3,X2),ld(i(i(X)),i(mult(X3,X2)))),i(X2)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c130,plain,
ld(X2,X) = ld(X2,i(i(X))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
ld(ld(X2,X),i(X)) = ld(ld(X2,i(i(X))),i(X)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
ld(ld(X2,i(i(X))),i(X)) = ld(i(i(X)),ld(i(X2),i(X))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c133,plain,
ld(i(i(X)),ld(i(X2),i(X))) = ld(X,ld(i(X2),i(X))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c134,plain,
ld(ld(X2,i(i(X))),i(X)) = ld(X,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
ld(ld(X2,X),i(X)) = ld(X,ld(i(X2),i(X))),
inference(transitivity,[status(thm)],[c131,c134]) ).
cnf(c136,plain,
ld(ld(i(X),mult(X3,X2)),i(mult(X3,X2))) = ld(mult(X3,X2),ld(i(i(X)),i(mult(X3,X2)))),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
ld(mult(X3,X2),ld(i(i(X)),i(mult(X3,X2)))) = ld(ld(i(X),mult(X3,X2)),i(mult(X3,X2))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
ld(ld(mult(X3,X2),ld(i(i(X)),i(mult(X3,X2)))),i(X2)) = ld(ld(ld(i(X),mult(X3,X2)),i(mult(X3,X2))),i(X2)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
mult(X,mult(X3,X2)) = ld(i(X),mult(X3,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c140,plain,
ld(i(X),mult(X3,X2)) = mult(X,mult(X3,X2)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
ld(ld(i(X),mult(X3,X2)),i(mult(X3,X2))) = ld(mult(X,mult(X3,X2)),i(mult(X3,X2))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
ld(ld(ld(i(X),mult(X3,X2)),i(mult(X3,X2))),i(X2)) = ld(ld(mult(X,mult(X3,X2)),i(mult(X3,X2))),i(X2)),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
i(ld(i(mult(X3,X2)),mult(X,mult(X3,X2)))) = ld(mult(X,mult(X3,X2)),i(mult(X3,X2))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c144,plain,
ld(mult(X,mult(X3,X2)),i(mult(X3,X2))) = i(ld(i(mult(X3,X2)),mult(X,mult(X3,X2)))),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
ld(ld(mult(X,mult(X3,X2)),i(mult(X3,X2))),i(X2)) = ld(i(ld(i(mult(X3,X2)),mult(X,mult(X3,X2)))),i(X2)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
mult(mult(X3,X2),mult(X,mult(X3,X2))) = ld(i(mult(X3,X2)),mult(X,mult(X3,X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c147,plain,
ld(i(mult(X3,X2)),mult(X,mult(X3,X2))) = mult(mult(X3,X2),mult(X,mult(X3,X2))),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
i(ld(i(mult(X3,X2)),mult(X,mult(X3,X2)))) = i(mult(mult(X3,X2),mult(X,mult(X3,X2)))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
ld(i(ld(i(mult(X3,X2)),mult(X,mult(X3,X2)))),i(X2)) = ld(i(mult(mult(X3,X2),mult(X,mult(X3,X2)))),i(X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
rd(mult(mult(X3,X2),mult(X,mult(X3,X2))),X2) = ld(i(mult(mult(X3,X2),mult(X,mult(X3,X2)))),i(X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c151,plain,
ld(i(mult(mult(X3,X2),mult(X,mult(X3,X2)))),i(X2)) = rd(mult(mult(X3,X2),mult(X,mult(X3,X2))),X2),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
mult(mult(X3,X2),mult(X,mult(X3,X2))) = mult(mult(mult(X3,mult(X2,X)),X3),X2),
inference(substitution,[status(thm)],[c79]) ).
cnf(c153,plain,
rd(mult(mult(X3,X2),mult(X,mult(X3,X2))),X2) = rd(mult(mult(mult(X3,mult(X2,X)),X3),X2),X2),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
rd(mult(mult(mult(X3,mult(X2,X)),X3),X2),X2) = mult(mult(X3,mult(X2,X)),X3),
inference(substitution,[status(thm)],[c29]) ).
cnf(c155,plain,
mult(mult(X3,mult(X2,X)),X3) = ld(i(mult(X3,mult(X2,X))),X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c156,plain,
mult(X3,mult(X2,X)) = ld(i(X3),mult(X2,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c157,plain,
i(mult(X3,mult(X2,X))) = i(ld(i(X3),mult(X2,X))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
ld(i(mult(X3,mult(X2,X))),X3) = ld(i(ld(i(X3),mult(X2,X))),X3),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
i(ld(i(X3),mult(X2,X))) = ld(mult(X2,X),i(X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c160,plain,
ld(i(ld(i(X3),mult(X2,X))),X3) = ld(ld(mult(X2,X),i(X3)),X3),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
ld(ld(mult(X2,X),i(X3)),X3) = ld(i(X3),ld(i(mult(X2,X)),X3)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c162,plain,
i(mult(X2,X)) = i(ld(i(X2),X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c163,plain,
ld(i(mult(X2,X)),X3) = ld(i(ld(i(X2),X)),X3),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
ld(i(X3),ld(i(mult(X2,X)),X3)) = ld(i(X3),ld(i(ld(i(X2),X)),X3)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
i(ld(i(X2),X)) = ld(X,i(X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c166,plain,
ld(i(ld(i(X2),X)),X3) = ld(ld(X,i(X2)),X3),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
ld(i(X3),ld(i(ld(i(X2),X)),X3)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
ld(i(X3),ld(i(mult(X2,X)),X3)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c164,c167]) ).
cnf(c169,plain,
ld(ld(mult(X2,X),i(X3)),X3) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c161,c168]) ).
cnf(c170,plain,
ld(i(ld(i(X3),mult(X2,X))),X3) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c160,c169]) ).
cnf(c171,plain,
ld(i(mult(X3,mult(X2,X))),X3) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c158,c170]) ).
cnf(c172,plain,
mult(mult(X3,mult(X2,X)),X3) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c155,c171]) ).
cnf(c173,plain,
rd(mult(mult(mult(X3,mult(X2,X)),X3),X2),X2) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c154,c172]) ).
cnf(c174,plain,
rd(mult(mult(X3,X2),mult(X,mult(X3,X2))),X2) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c153,c173]) ).
cnf(c175,plain,
ld(i(mult(mult(X3,X2),mult(X,mult(X3,X2)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c151,c174]) ).
cnf(c176,plain,
ld(i(ld(i(mult(X3,X2)),mult(X,mult(X3,X2)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c149,c175]) ).
cnf(c177,plain,
ld(ld(mult(X,mult(X3,X2)),i(mult(X3,X2))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c145,c176]) ).
cnf(c178,plain,
ld(ld(ld(i(X),mult(X3,X2)),i(mult(X3,X2))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c142,c177]) ).
cnf(c179,plain,
ld(ld(mult(X3,X2),ld(i(i(X)),i(mult(X3,X2)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c138,c178]) ).
cnf(c180,plain,
ld(ld(mult(X3,X2),ld(i(i(X)),i(ld(i(X3),X2)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c128,c179]) ).
cnf(c181,plain,
ld(ld(ld(i(X3),X2),ld(i(i(X)),i(ld(i(X3),X2)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c123,c180]) ).
cnf(c182,plain,
ld(ld(ld(i(X3),X2),ld(X,i(ld(i(X3),X2)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c120,c181]) ).
cnf(c183,plain,
ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2)) = ld(i(X3),ld(ld(X,i(X2)),X3)),
inference(transitivity,[status(thm)],[c116,c182]) ).
cnf(c184,plain,
i(ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2))) = i(ld(i(X3),ld(ld(X,i(X2)),X3))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
ld(i(i(X2)),i(ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2)))) = ld(i(i(X2)),i(ld(i(X3),ld(ld(X,i(X2)),X3)))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ld(i(i(X2)),i(ld(i(X3),ld(ld(X,i(X2)),X3)))) = ld(X2,i(ld(i(X3),ld(ld(X,i(X2)),X3)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c187,plain,
i(ld(i(X3),ld(ld(X,i(X2)),X3))) = ld(ld(ld(X,i(X2)),X3),i(X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c188,plain,
ld(X2,i(ld(i(X3),ld(ld(X,i(X2)),X3)))) = ld(X2,ld(ld(ld(X,i(X2)),X3),i(X3))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
ld(ld(ld(X,i(X2)),X3),i(X3)) = ld(X3,ld(i(ld(X,i(X2))),i(X3))),
inference(substitution,[status(thm)],[c135]) ).
cnf(c190,plain,
ld(X2,ld(ld(ld(X,i(X2)),X3),i(X3))) = ld(X2,ld(X3,ld(i(ld(X,i(X2))),i(X3)))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
i(ld(X,i(X2))) = ld(i(X2),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c192,plain,
ld(i(ld(X,i(X2))),i(X3)) = ld(ld(i(X2),X),i(X3)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
ld(X3,ld(i(ld(X,i(X2))),i(X3))) = ld(X3,ld(ld(i(X2),X),i(X3))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
ld(X2,ld(X3,ld(i(ld(X,i(X2))),i(X3)))) = ld(X2,ld(X3,ld(ld(i(X2),X),i(X3)))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
ld(X2,ld(ld(ld(X,i(X2)),X3),i(X3))) = ld(X2,ld(X3,ld(ld(i(X2),X),i(X3)))),
inference(transitivity,[status(thm)],[c190,c194]) ).
cnf(c196,plain,
ld(X2,i(ld(i(X3),ld(ld(X,i(X2)),X3)))) = ld(X2,ld(X3,ld(ld(i(X2),X),i(X3)))),
inference(transitivity,[status(thm)],[c188,c195]) ).
cnf(c197,plain,
ld(i(i(X2)),i(ld(i(X3),ld(ld(X,i(X2)),X3)))) = ld(X2,ld(X3,ld(ld(i(X2),X),i(X3)))),
inference(transitivity,[status(thm)],[c186,c196]) ).
cnf(c198,plain,
ld(i(i(X2)),i(ld(ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))),i(X2)))) = ld(X2,ld(X3,ld(ld(i(X2),X),i(X3)))),
inference(transitivity,[status(thm)],[c185,c197]) ).
cnf(c199,plain,
ld(ld(i(X3),X2),ld(X,ld(X2,i(X3)))) = ld(X2,ld(X3,ld(ld(i(X2),X),i(X3)))),
inference(transitivity,[status(thm)],[c111,c198]) ).
cnf(c200,plain,
ld(ld(i(i(X3)),X2),ld(X,ld(X2,i(i(X3))))) = ld(X2,ld(i(X3),ld(ld(i(X2),X),i(i(X3))))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
ld(ld(i(X2),X),i(i(X3))) = ld(ld(i(X2),X),X3),
inference(congruence,[status(thm)],[c48]) ).
cnf(c202,plain,
ld(i(X3),ld(ld(i(X2),X),i(i(X3)))) = ld(i(X3),ld(ld(i(X2),X),X3)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
ld(X2,ld(i(X3),ld(ld(i(X2),X),i(i(X3))))) = ld(X2,ld(i(X3),ld(ld(i(X2),X),X3))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
ld(ld(i(i(X3)),X2),ld(X,ld(X2,i(i(X3))))) = ld(X2,ld(i(X3),ld(ld(i(X2),X),X3))),
inference(transitivity,[status(thm)],[c200,c203]) ).
cnf(c205,plain,
ld(ld(X3,X2),ld(X,ld(X2,i(i(X3))))) = ld(X2,ld(i(X3),ld(ld(i(X2),X),X3))),
inference(transitivity,[status(thm)],[c109,c204]) ).
cnf(c206,plain,
ld(ld(X3,X2),ld(X,ld(X2,X3))) = ld(X2,ld(i(X3),ld(ld(i(X2),X),X3))),
inference(transitivity,[status(thm)],[c106,c205]) ).
cnf(c207,plain,
ld(ld(X2,X3),ld(ld(X,X2),ld(X3,X2))) = ld(X3,ld(i(X2),ld(ld(i(X3),ld(X,X2)),X2))),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
ld(X3,ld(i(X2),ld(ld(i(X3),ld(X,X2)),X2))) = ld(ld(X2,X3),ld(ld(X,X2),ld(X3,X2))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c210,plain,
ld(X,X2) = ld(X,i(i(X2))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
ld(ld(X,X2),ld(X3,X2)) = ld(ld(X,i(i(X2))),ld(X3,X2)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
ld(ld(X2,X3),ld(ld(X,X2),ld(X3,X2))) = ld(ld(X2,X3),ld(ld(X,i(i(X2))),ld(X3,X2))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
ld(X,X2) = i(ld(X2,X)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c214,plain,
ld(ld(X2,X3),ld(ld(X,i(i(X2))),ld(X3,X2))) = ld(i(ld(X3,X2)),ld(ld(X,i(i(X2))),ld(X3,X2))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,ld(i(X2),i(ld(X3,X2))))),i(i(X2))) = ld(i(ld(X3,X2)),ld(ld(X,i(i(X2))),ld(X3,X2))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c216,plain,
ld(i(ld(X3,X2)),ld(ld(X,i(i(X2))),ld(X3,X2))) = ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,ld(i(X2),i(ld(X3,X2))))),i(i(X2))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
ld(i(X),i(ld(X2,X))) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c218,plain,
ld(X,ld(i(X2),i(ld(X3,X2)))) = ld(X,X3),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
ld(ld(i(ld(X3,X2)),i(X2)),ld(X,ld(i(X2),i(ld(X3,X2))))) = ld(ld(i(ld(X3,X2)),i(X2)),ld(X,X3)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,ld(i(X2),i(ld(X3,X2))))),i(i(X2))) = ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,X3)),i(i(X2))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
ld(i(ld(X2,X)),i(X)) = ld(ld(X,X2),i(X)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c222,plain,
ld(ld(i(ld(X3,X2)),i(X2)),ld(X,X3)) = ld(ld(ld(X2,X3),i(X2)),ld(X,X3)),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,X3)),i(i(X2))) = ld(ld(ld(ld(X2,X3),i(X2)),ld(X,X3)),i(i(X2))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
i(i(ld(X2,X))) = ld(X2,X),
inference(substitution,[status(thm)],[c48]) ).
cnf(c225,plain,
ld(X2,X) = i(i(ld(X2,X))),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
ld(ld(X2,X),i(X2)) = ld(i(i(ld(X2,X))),i(X2)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
ld(i(X),i(ld(X2,X))) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c228,plain,
X2 = ld(i(X),i(ld(X2,X))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
i(X2) = i(ld(i(X),i(ld(X2,X)))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
ld(i(i(ld(X2,X))),i(X2)) = ld(i(i(ld(X2,X))),i(ld(i(X),i(ld(X2,X))))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
ld(i(i(ld(X2,X))),i(ld(i(X),i(ld(X2,X))))) = i(X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c232,plain,
ld(i(i(ld(X2,X))),i(X2)) = i(X),
inference(transitivity,[status(thm)],[c230,c231]) ).
cnf(c233,plain,
ld(ld(X2,X),i(X2)) = i(X),
inference(transitivity,[status(thm)],[c226,c232]) ).
cnf(c234,plain,
ld(ld(X,X2),i(X)) = i(X2),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
ld(ld(ld(X2,X3),i(X2)),ld(X,X3)) = ld(i(X3),ld(X,X3)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
ld(ld(ld(ld(X2,X3),i(X2)),ld(X,X3)),i(i(X2))) = ld(ld(i(X3),ld(X,X3)),i(i(X2))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
ld(ld(i(X3),ld(X,X3)),i(i(X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(congruence,[status(thm)],[c48]) ).
cnf(c238,plain,
ld(ld(ld(ld(X2,X3),i(X2)),ld(X,X3)),i(i(X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c236,c237]) ).
cnf(c239,plain,
ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,X3)),i(i(X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c223,c238]) ).
cnf(c240,plain,
ld(ld(ld(i(ld(X3,X2)),i(X2)),ld(X,ld(i(X2),i(ld(X3,X2))))),i(i(X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c220,c239]) ).
cnf(c241,plain,
ld(i(ld(X3,X2)),ld(ld(X,i(i(X2))),ld(X3,X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c216,c240]) ).
cnf(c242,plain,
ld(ld(X2,X3),ld(ld(X,i(i(X2))),ld(X3,X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c214,c241]) ).
cnf(c243,plain,
ld(ld(X2,X3),ld(ld(X,X2),ld(X3,X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c212,c242]) ).
cnf(c244,plain,
ld(X3,ld(i(X2),ld(ld(i(X3),ld(X,X2)),X2))) = ld(ld(i(X3),ld(X,X3)),X2),
inference(transitivity,[status(thm)],[c208,c243]) ).
cnf(c245,plain,
ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),ld(i(X2),ld(X2,X))),ld(X2,X)))) = ld(ld(i(X3),ld(i(X2),X3)),ld(X2,X)),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
ld(ld(i(X3),ld(i(X2),X3)),ld(X2,X)) = ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),ld(i(X2),ld(X2,X))),ld(X2,X)))),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
mult(X2,ld(X2,X)) = ld(i(X2),ld(X2,X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c248,plain,
ld(i(X2),ld(X2,X)) = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c250,plain,
ld(i(X2),ld(X2,X)) = X,
inference(transitivity,[status(thm)],[c248,c249]) ).
cnf(c251,plain,
ld(i(X3),ld(i(X2),ld(X2,X))) = ld(i(X3),X),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
ld(ld(i(X3),ld(i(X2),ld(X2,X))),ld(X2,X)) = ld(ld(i(X3),X),ld(X2,X)),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
ld(i(ld(X2,X)),ld(ld(i(X3),ld(i(X2),ld(X2,X))),ld(X2,X))) = ld(i(ld(X2,X)),ld(ld(i(X3),X),ld(X2,X))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),ld(i(X2),ld(X2,X))),ld(X2,X)))) = ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),X),ld(X2,X)))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
ld(i(ld(X2,X)),ld(ld(i(X3),X),ld(X2,X))) = ld(ld(X,X2),ld(ld(i(X3),X),ld(X2,X))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c256,plain,
ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),X),ld(X2,X)))) = ld(X3,ld(ld(X,X2),ld(ld(i(X3),X),ld(X2,X)))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c258,plain,
ld(X,X2) = ld(X,i(i(X2))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
ld(ld(X,X3),ld(X2,X3)) = ld(ld(X,i(i(X3))),ld(X2,X3)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
ld(ld(X3,X2),ld(ld(X,X3),ld(X2,X3))) = ld(ld(X3,X2),ld(ld(X,i(i(X3))),ld(X2,X3))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
i(ld(X,X2)) = ld(X2,X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c262,plain,
ld(X2,X) = i(ld(X,X2)),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
ld(ld(X3,X2),ld(ld(X,i(i(X3))),ld(X2,X3))) = ld(i(ld(X2,X3)),ld(ld(X,i(i(X3))),ld(X2,X3))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,ld(i(X3),i(ld(X2,X3))))),i(i(X3))) = ld(i(ld(X2,X3)),ld(ld(X,i(i(X3))),ld(X2,X3))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c265,plain,
ld(i(ld(X2,X3)),ld(ld(X,i(i(X3))),ld(X2,X3))) = ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,ld(i(X3),i(ld(X2,X3))))),i(i(X3))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
ld(X,ld(i(X3),i(ld(X2,X3)))) = ld(X,X2),
inference(congruence,[status(thm)],[c32]) ).
cnf(c267,plain,
ld(ld(i(ld(X2,X3)),i(X3)),ld(X,ld(i(X3),i(ld(X2,X3))))) = ld(ld(i(ld(X2,X3)),i(X3)),ld(X,X2)),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,ld(i(X3),i(ld(X2,X3))))),i(i(X3))) = ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,X2)),i(i(X3))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
i(ld(X,X2)) = ld(X2,X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c270,plain,
ld(i(ld(X,X2)),i(X2)) = ld(ld(X2,X),i(X2)),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
ld(ld(i(ld(X2,X3)),i(X3)),ld(X,X2)) = ld(ld(ld(X3,X2),i(X3)),ld(X,X2)),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,X2)),i(i(X3))) = ld(ld(ld(ld(X3,X2),i(X3)),ld(X,X2)),i(i(X3))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
ld(ld(ld(X3,X2),i(X3)),ld(X,X2)) = ld(i(X2),ld(X,X2)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c274,plain,
ld(ld(ld(ld(X3,X2),i(X3)),ld(X,X2)),i(i(X3))) = ld(ld(i(X2),ld(X,X2)),i(i(X3))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
ld(ld(i(X2),ld(X,X2)),i(i(X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(congruence,[status(thm)],[c48]) ).
cnf(c276,plain,
ld(ld(ld(ld(X3,X2),i(X3)),ld(X,X2)),i(i(X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(transitivity,[status(thm)],[c274,c275]) ).
cnf(c277,plain,
ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,X2)),i(i(X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(transitivity,[status(thm)],[c272,c276]) ).
cnf(c278,plain,
ld(ld(ld(i(ld(X2,X3)),i(X3)),ld(X,ld(i(X3),i(ld(X2,X3))))),i(i(X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(transitivity,[status(thm)],[c268,c277]) ).
cnf(c279,plain,
ld(i(ld(X2,X3)),ld(ld(X,i(i(X3))),ld(X2,X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(transitivity,[status(thm)],[c265,c278]) ).
cnf(c280,plain,
ld(ld(X3,X2),ld(ld(X,i(i(X3))),ld(X2,X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(transitivity,[status(thm)],[c263,c279]) ).
cnf(c281,plain,
ld(ld(X3,X2),ld(ld(X,X3),ld(X2,X3))) = ld(ld(i(X2),ld(X,X2)),X3),
inference(transitivity,[status(thm)],[c260,c280]) ).
cnf(c282,plain,
ld(ld(X,X2),ld(ld(i(X3),X),ld(X2,X))) = ld(ld(i(X2),ld(i(X3),X2)),X),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
ld(X3,ld(ld(X,X2),ld(ld(i(X3),X),ld(X2,X)))) = ld(X3,ld(ld(i(X2),ld(i(X3),X2)),X)),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),X),ld(X2,X)))) = ld(X3,ld(ld(i(X2),ld(i(X3),X2)),X)),
inference(transitivity,[status(thm)],[c256,c283]) ).
cnf(c285,plain,
ld(X3,ld(i(ld(X2,X)),ld(ld(i(X3),ld(i(X2),ld(X2,X))),ld(X2,X)))) = ld(X3,ld(ld(i(X2),ld(i(X3),X2)),X)),
inference(transitivity,[status(thm)],[c254,c284]) ).
cnf(c286,plain,
ld(ld(i(X3),ld(i(X2),X3)),ld(X2,X)) = ld(X3,ld(ld(i(X2),ld(i(X3),X2)),X)),
inference(transitivity,[status(thm)],[c246,c285]) ).
cnf(c287,plain,
ld(ld(i(X2),ld(i(X3),X2)),ld(X3,X)) = ld(X2,ld(ld(i(X3),ld(i(X2),X3)),X)),
inference(substitution,[status(thm)],[c286]) ).
cnf(c288,plain,
ld(X2,ld(ld(i(X3),ld(i(X2),X3)),X)) = ld(ld(i(X2),ld(i(X3),X2)),ld(X3,X)),
inference(symmetry,[status(thm)],[c287]) ).
cnf(c289,plain,
i(ld(X2,ld(ld(i(X3),ld(i(X2),X3)),X))) = i(ld(ld(i(X2),ld(i(X3),X2)),ld(X3,X))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
i(ld(ld(i(X2),ld(i(X3),X2)),ld(X3,X))) = ld(ld(X3,X),ld(i(X2),ld(i(X3),X2))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c291,plain,
i(ld(X2,ld(ld(i(X3),ld(i(X2),X3)),X))) = ld(ld(X3,X),ld(i(X2),ld(i(X3),X2))),
inference(transitivity,[status(thm)],[c289,c290]) ).
cnf(c292,plain,
ld(ld(ld(i(X3),ld(i(X2),X3)),X),X2) = ld(ld(X3,X),ld(i(X2),ld(i(X3),X2))),
inference(transitivity,[status(thm)],[c102,c291]) ).
cnf(c293,plain,
ld(ld(ld(i(b),ld(i(c),b)),i(a)),c) = ld(ld(b,i(a)),ld(i(c),ld(i(b),c))),
inference(substitution,[status(thm)],[c292]) ).
cnf(c294,plain,
ld(ld(b,i(a)),ld(i(c),ld(i(b),c))) = ld(ld(ld(i(b),ld(i(c),b)),i(a)),c),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
ld(ld(c,i(b)),b) = ld(i(b),ld(i(c),b)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c296,plain,
ld(i(b),ld(i(c),b)) = ld(ld(c,i(b)),b),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
ld(ld(i(b),ld(i(c),b)),i(a)) = ld(ld(ld(c,i(b)),b),i(a)),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
ld(ld(ld(i(b),ld(i(c),b)),i(a)),c) = ld(ld(ld(ld(c,i(b)),b),i(a)),c),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
i(ld(i(b),c)) = ld(c,i(b)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c300,plain,
ld(c,i(b)) = i(ld(i(b),c)),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
ld(ld(c,i(b)),b) = ld(i(ld(i(b),c)),b),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
ld(ld(ld(c,i(b)),b),i(a)) = ld(ld(i(ld(i(b),c)),b),i(a)),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
ld(ld(ld(ld(c,i(b)),b),i(a)),c) = ld(ld(ld(i(ld(i(b),c)),b),i(a)),c),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
mult(ld(i(b),c),b) = ld(i(ld(i(b),c)),b),
inference(substitution,[status(thm)],[c8]) ).
cnf(c305,plain,
ld(i(ld(i(b),c)),b) = mult(ld(i(b),c),b),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
ld(ld(i(ld(i(b),c)),b),i(a)) = ld(mult(ld(i(b),c),b),i(a)),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
ld(ld(ld(i(ld(i(b),c)),b),i(a)),c) = ld(ld(mult(ld(i(b),c),b),i(a)),c),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
mult(b,c) = ld(i(b),c),
inference(substitution,[status(thm)],[c8]) ).
cnf(c309,plain,
ld(i(b),c) = mult(b,c),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(ld(i(b),c),b) = mult(mult(b,c),b),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
ld(mult(ld(i(b),c),b),i(a)) = ld(mult(mult(b,c),b),i(a)),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
ld(ld(mult(ld(i(b),c),b),i(a)),c) = ld(ld(mult(mult(b,c),b),i(a)),c),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
i(ld(i(a),mult(mult(b,c),b))) = ld(mult(mult(b,c),b),i(a)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c314,plain,
ld(mult(mult(b,c),b),i(a)) = i(ld(i(a),mult(mult(b,c),b))),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
ld(ld(mult(mult(b,c),b),i(a)),c) = ld(i(ld(i(a),mult(mult(b,c),b))),c),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
mult(ld(i(a),mult(mult(b,c),b)),c) = ld(i(ld(i(a),mult(mult(b,c),b))),c),
inference(substitution,[status(thm)],[c8]) ).
cnf(c317,plain,
ld(i(ld(i(a),mult(mult(b,c),b))),c) = mult(ld(i(a),mult(mult(b,c),b)),c),
inference(symmetry,[status(thm)],[c316]) ).
cnf(c318,plain,
mult(a,mult(mult(b,c),b)) = ld(i(a),mult(mult(b,c),b)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c319,plain,
ld(i(a),mult(mult(b,c),b)) = mult(a,mult(mult(b,c),b)),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
mult(ld(i(a),mult(mult(b,c),b)),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
ld(i(ld(i(a),mult(mult(b,c),b))),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c317,c320]) ).
cnf(c322,plain,
ld(ld(mult(mult(b,c),b),i(a)),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c315,c321]) ).
cnf(c323,plain,
ld(ld(mult(ld(i(b),c),b),i(a)),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c312,c322]) ).
cnf(c324,plain,
ld(ld(ld(i(ld(i(b),c)),b),i(a)),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c307,c323]) ).
cnf(c325,plain,
ld(ld(ld(ld(c,i(b)),b),i(a)),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c303,c324]) ).
cnf(c326,plain,
ld(ld(ld(i(b),ld(i(c),b)),i(a)),c) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c298,c325]) ).
cnf(c327,plain,
ld(ld(b,i(a)),ld(i(c),ld(i(b),c))) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c294,c326]) ).
cnf(c328,plain,
ld(ld(b,i(a)),ld(ld(b,i(c)),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c100,c327]) ).
cnf(c329,plain,
ld(ld(b,i(a)),ld(i(ld(i(c),b)),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c62,c328]) ).
cnf(c330,plain,
ld(ld(b,i(a)),mult(ld(i(c),b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c59,c329]) ).
cnf(c331,plain,
ld(ld(b,i(a)),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c57,c330]) ).
cnf(c332,plain,
ld(i(ld(i(a),b)),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c54,c331]) ).
cnf(c333,plain,
mult(ld(i(a),b),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c11,c332]) ).
cnf(c334,plain,
mult(mult(a,b),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(transitivity,[status(thm)],[c10,c333]) ).
cnf(c335,plain,
$false,
inference(resolution,[status(thm)],[c1,c334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP670-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 10:36:52 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.86/7.35 Command-line arguments: --no-flatten-goal
% 54.86/7.35
% 54.86/7.35 % SZS status Unsatisfiable
% 54.86/7.35
% 54.86/7.36 % SZS output start CNFRefutation
% See solution above
% 56.40/7.53
% 56.40/7.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------