%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP660-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:11:36 AM UTC 2026
% Result : Unsatisfiable 1.32s 0.62s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 6
% Syntax : Number of clauses : 334 ( 334 unt; 0 nHn; 2 RR)
% Number of literals : 334 ( 333 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 720 ( 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/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(c3,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(ld(X2,X2),X) = mult(ld(X2,X2),mult(X2,ld(X2,X))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(c7,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
X = ld(X,mult(X,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(X,X2) = mult(X,ld(X2,mult(X2,X2))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(X2,mult(X,X2)) = mult(X2,mult(X,ld(X2,mult(X2,X2)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,X2))) = ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,ld(X2,mult(X2,X2))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
ld(X,mult(X,mult(ld(X,X),X))) = mult(ld(X,X),X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c13,plain,
mult(ld(X,X),X) = ld(X,mult(X,mult(ld(X,X),X))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(c15,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
rd(X,X2) = rd(X,mult(rd(X2,X),X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
mult(mult(X2,rd(X2,X)),rd(X,X2)) = mult(mult(X2,rd(X2,X)),rd(X,mult(rd(X2,X),X))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c20,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(X2,rd(X2,X)) = mult(mult(rd(X2,X),X),rd(X2,X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
mult(mult(X2,rd(X2,X)),rd(X,mult(rd(X2,X),X))) = mult(mult(mult(rd(X2,X),X),rd(X2,X)),rd(X,mult(rd(X2,X),X))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c24,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
mult(X2,X) = mult(X2,mult(rd(X,X3),X3)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(rd(X,X3),X3))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
rd(mult(X3,mult(X2,X)),X3) = rd(mult(X3,mult(X2,mult(rd(X,X3),X3))),X3),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
mult(mult(mult(A2,B2),C),A2) = mult(A2,mult(B2,mult(C,A2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(c29,plain,
mult(mult(mult(X3,X2),X),X3) = mult(X3,mult(X2,mult(X,X3))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
mult(X3,mult(X2,mult(X,X3))) = mult(mult(mult(X3,X2),X),X3),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
rd(mult(X3,mult(X2,mult(X,X3))),X3) = rd(mult(mult(mult(X3,X2),X),X3),X3),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(c33,plain,
rd(mult(mult(mult(X3,X2),X),X3),X3) = mult(mult(X3,X2),X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
rd(mult(X3,mult(X2,mult(X,X3))),X3) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
rd(mult(X3,mult(X2,mult(rd(X,X3),X3))),X3) = mult(mult(X3,X2),rd(X,X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
rd(mult(X3,mult(X2,X)),X3) = mult(mult(X3,X2),rd(X,X3)),
inference(transitivity,[status(thm)],[c27,c35]) ).
cnf(c37,plain,
rd(mult(mult(X2,X),mult(X2,X)),mult(X2,X)) = mult(mult(mult(X2,X),X2),rd(X,mult(X2,X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
mult(mult(mult(X2,X),X2),rd(X,mult(X2,X))) = rd(mult(mult(X2,X),mult(X2,X)),mult(X2,X)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
rd(mult(mult(X2,X),mult(X2,X)),mult(X2,X)) = mult(X2,X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c40,plain,
mult(mult(mult(X2,X),X2),rd(X,mult(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
mult(mult(mult(rd(X2,X),X),rd(X2,X)),rd(X,mult(rd(X2,X),X))) = mult(rd(X2,X),X),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c43,plain,
mult(mult(mult(rd(X2,X),X),rd(X2,X)),rd(X,mult(rd(X2,X),X))) = X2,
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
mult(mult(X2,rd(X2,X)),rd(X,mult(rd(X2,X),X))) = X2,
inference(transitivity,[status(thm)],[c22,c43]) ).
cnf(c45,plain,
mult(mult(X2,rd(X2,X)),rd(X,X2)) = X2,
inference(transitivity,[status(thm)],[c18,c44]) ).
cnf(c46,plain,
X2 = mult(mult(X2,rd(X2,X)),rd(X,X2)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
rd(X2,rd(X,X2)) = rd(mult(mult(X2,rd(X2,X)),rd(X,X2)),rd(X,X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
rd(mult(mult(X2,rd(X2,X)),rd(X,X2)),rd(X,X2)) = mult(X2,rd(X2,X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c49,plain,
rd(X2,rd(X,X2)) = mult(X2,rd(X2,X)),
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
rd(X,rd(X,X)) = mult(X,rd(X,X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(X,rd(X,X)) = rd(X,rd(X,X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
X2 = mult(mult(X2,rd(X2,X)),rd(X,X2)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c53,plain,
ld(mult(X2,rd(X2,X)),X2) = ld(mult(X2,rd(X2,X)),mult(mult(X2,rd(X2,X)),rd(X,X2))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
ld(mult(X2,rd(X2,X)),mult(mult(X2,rd(X2,X)),rd(X,X2))) = rd(X,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c55,plain,
ld(mult(X2,rd(X2,X)),X2) = rd(X,X2),
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
ld(mult(rd(X,X),rd(rd(X,X),X)),rd(X,X)) = rd(X,rd(X,X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
rd(X,rd(X,X)) = ld(mult(rd(X,X),rd(rd(X,X),X)),rd(X,X)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ld(X2,mult(X2,mult(X3,mult(ld(mult(X2,X3),X),X2)))) = mult(X3,mult(ld(mult(X2,X3),X),X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c59,plain,
mult(X3,mult(ld(mult(X2,X3),X),X2)) = ld(X2,mult(X2,mult(X3,mult(ld(mult(X2,X3),X),X2)))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
mult(mult(mult(X3,X2),ld(mult(X3,X2),X)),X3) = mult(X3,mult(X2,mult(ld(mult(X3,X2),X),X3))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c61,plain,
mult(X3,mult(X2,mult(ld(mult(X3,X2),X),X3))) = mult(mult(mult(X3,X2),ld(mult(X3,X2),X)),X3),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
mult(mult(X3,X2),ld(mult(X3,X2),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
mult(mult(mult(X3,X2),ld(mult(X3,X2),X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
mult(X3,mult(X2,mult(ld(mult(X3,X2),X),X3))) = mult(X,X3),
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
mult(X2,mult(X3,mult(ld(mult(X2,X3),X),X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
ld(X2,mult(X2,mult(X3,mult(ld(mult(X2,X3),X),X2)))) = ld(X2,mult(X,X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
mult(X3,mult(ld(mult(X2,X3),X),X2)) = ld(X2,mult(X,X2)),
inference(transitivity,[status(thm)],[c59,c66]) ).
cnf(c68,plain,
mult(X2,mult(ld(mult(rd(X3,X2),X2),X),rd(X3,X2))) = ld(rd(X3,X2),mult(X,rd(X3,X2))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
ld(rd(X3,X2),mult(X,rd(X3,X2))) = mult(X2,mult(ld(mult(rd(X3,X2),X2),X),rd(X3,X2))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c71,plain,
ld(mult(rd(X3,X2),X2),X) = ld(X3,X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
mult(ld(mult(rd(X3,X2),X2),X),rd(X3,X2)) = mult(ld(X3,X),rd(X3,X2)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(X2,mult(ld(mult(rd(X3,X2),X2),X),rd(X3,X2))) = mult(X2,mult(ld(X3,X),rd(X3,X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
ld(rd(X3,X2),mult(X,rd(X3,X2))) = mult(X2,mult(ld(X3,X),rd(X3,X2))),
inference(transitivity,[status(thm)],[c69,c73]) ).
cnf(c75,plain,
ld(rd(X,X2),mult(rd(X,X2),rd(X,X2))) = mult(X2,mult(ld(X,rd(X,X2)),rd(X,X2))),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
mult(X2,mult(ld(X,rd(X,X2)),rd(X,X2))) = ld(rd(X,X2),mult(rd(X,X2),rd(X,X2))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
ld(rd(X,X2),mult(rd(X,X2),rd(X,X2))) = rd(X,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c78,plain,
mult(X2,mult(ld(X,rd(X,X2)),rd(X,X2))) = rd(X,X2),
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
mult(X,mult(ld(X,rd(X,X)),rd(X,X))) = rd(X,X),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
rd(X,X) = mult(X,mult(ld(X,rd(X,X)),rd(X,X))),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
ld(mult(rd(X,X),rd(rd(X,X),X)),rd(X,X)) = ld(mult(rd(X,X),rd(rd(X,X),X)),mult(X,mult(ld(X,rd(X,X)),rd(X,X)))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
mult(X3,rd(X2,X)) = mult(mult(X,ld(X,X3)),rd(X2,X)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
ld(mult(X3,rd(X2,X)),mult(X,mult(ld(X,X3),X2))) = ld(mult(mult(X,ld(X,X3)),rd(X2,X)),mult(X,mult(ld(X,X3),X2))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c14]) ).
cnf(c87,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
mult(X2,X) = mult(X2,mult(rd(X,X3),X3)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(rd(X,X3),X3))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ld(mult(mult(X3,X2),rd(X,X3)),mult(X3,mult(X2,X))) = ld(mult(mult(X3,X2),rd(X,X3)),mult(X3,mult(X2,mult(rd(X,X3),X3)))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
mult(mult(mult(X3,X2),X),X3) = mult(X3,mult(X2,mult(X,X3))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c92,plain,
mult(X3,mult(X2,mult(X,X3))) = mult(mult(mult(X3,X2),X),X3),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
ld(mult(mult(X3,X2),X),mult(X3,mult(X2,mult(X,X3)))) = ld(mult(mult(X3,X2),X),mult(mult(mult(X3,X2),X),X3)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
ld(mult(mult(X3,X2),X),mult(mult(mult(X3,X2),X),X3)) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c95,plain,
ld(mult(mult(X3,X2),X),mult(X3,mult(X2,mult(X,X3)))) = X3,
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
ld(mult(mult(X3,X2),rd(X,X3)),mult(X3,mult(X2,mult(rd(X,X3),X3)))) = X3,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
ld(mult(mult(X3,X2),rd(X,X3)),mult(X3,mult(X2,X))) = X3,
inference(transitivity,[status(thm)],[c90,c96]) ).
cnf(c98,plain,
ld(mult(mult(X,ld(X,X3)),rd(X2,X)),mult(X,mult(ld(X,X3),X2))) = X,
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
ld(mult(X3,rd(X2,X)),mult(X,mult(ld(X,X3),X2))) = X,
inference(transitivity,[status(thm)],[c85,c98]) ).
cnf(c100,plain,
ld(mult(rd(X,X),rd(rd(X,X),X)),mult(X,mult(ld(X,rd(X,X)),rd(X,X)))) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
ld(mult(rd(X,X),rd(rd(X,X),X)),rd(X,X)) = X,
inference(transitivity,[status(thm)],[c81,c100]) ).
cnf(c102,plain,
rd(X,rd(X,X)) = X,
inference(transitivity,[status(thm)],[c57,c101]) ).
cnf(c103,plain,
mult(X,rd(X,X)) = X,
inference(transitivity,[status(thm)],[c51,c102]) ).
cnf(c104,plain,
X = mult(X,rd(X,X)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
ld(X,mult(X,mult(ld(X,X),X))) = ld(mult(X,rd(X,X)),mult(X,mult(ld(X,X),X))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
ld(mult(X,rd(X,X)),mult(X,mult(ld(X,X),X))) = X,
inference(substitution,[status(thm)],[c99]) ).
cnf(c107,plain,
ld(X,mult(X,mult(ld(X,X),X))) = X,
inference(transitivity,[status(thm)],[c105,c106]) ).
cnf(c108,plain,
mult(ld(X,X),X) = X,
inference(transitivity,[status(thm)],[c13,c107]) ).
cnf(c109,plain,
X = mult(ld(X,X),X),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
mult(X2,mult(X,ld(X2,mult(X2,X2)))) = mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2)))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,ld(X2,mult(X2,X2))))) = ld(mult(ld(X2,X2),mult(X2,X)),mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2))))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(ld(X,X),mult(ld(X,X),mult(ld(mult(ld(X,X),ld(X,X)),X2),ld(X,X)))) = mult(X2,ld(X,X)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c113,plain,
mult(X2,ld(X,X)) = mult(ld(X,X),mult(ld(X,X),mult(ld(mult(ld(X,X),ld(X,X)),X2),ld(X,X)))),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
ld(X,mult(X,rd(X,X))) = rd(X,X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c115,plain,
rd(X,X) = ld(X,mult(X,rd(X,X))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
ld(X,mult(X,rd(X,X))) = ld(X,X),
inference(congruence,[status(thm)],[c103]) ).
cnf(c117,plain,
rd(X,X) = ld(X,X),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
ld(X,X) = rd(X,X),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
ld(ld(X,X),ld(X,X)) = ld(rd(X,X),ld(X,X)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c121,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
mult(X3,X2) = mult(mult(rd(X3,X),X),X2),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
rd(mult(X3,X2),mult(ld(X2,rd(X3,X)),mult(X,X2))) = rd(mult(mult(rd(X3,X),X),X2),mult(ld(X2,rd(X3,X)),mult(X,X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
mult(mult(mult(X3,ld(X3,X2)),X),X3) = mult(X3,mult(ld(X3,X2),mult(X,X3))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c125,plain,
mult(X3,mult(ld(X3,X2),mult(X,X3))) = mult(mult(mult(X3,ld(X3,X2)),X),X3),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c127,plain,
mult(mult(X3,ld(X3,X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
mult(mult(mult(X3,ld(X3,X2)),X),X3) = mult(mult(X2,X),X3),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
mult(X3,mult(ld(X3,X2),mult(X,X3))) = mult(mult(X2,X),X3),
inference(transitivity,[status(thm)],[c125,c128]) ).
cnf(c130,plain,
mult(X,mult(ld(X,X3),mult(X2,X))) = mult(mult(X3,X2),X),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(mult(X3,X2),X) = mult(X,mult(ld(X,X3),mult(X2,X))),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
rd(mult(mult(X3,X2),X),mult(ld(X,X3),mult(X2,X))) = rd(mult(X,mult(ld(X,X3),mult(X2,X))),mult(ld(X,X3),mult(X2,X))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
rd(mult(X,mult(ld(X,X3),mult(X2,X))),mult(ld(X,X3),mult(X2,X))) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c134,plain,
rd(mult(mult(X3,X2),X),mult(ld(X,X3),mult(X2,X))) = X,
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
rd(mult(mult(rd(X3,X),X),X2),mult(ld(X2,rd(X3,X)),mult(X,X2))) = X2,
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
rd(mult(X3,X2),mult(ld(X2,rd(X3,X)),mult(X,X2))) = X2,
inference(transitivity,[status(thm)],[c123,c135]) ).
cnf(c137,plain,
rd(mult(X2,X),mult(ld(X,rd(X2,X2)),mult(X2,X))) = X,
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
X = rd(mult(X2,X),mult(ld(X,rd(X2,X2)),mult(X2,X))),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
mult(mult(X2,X),X) = mult(mult(X2,X),rd(mult(X2,X),mult(ld(X,rd(X2,X2)),mult(X2,X)))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
ld(mult(mult(X2,X),X),mult(X2,X)) = ld(mult(mult(X2,X),rd(mult(X2,X),mult(ld(X,rd(X2,X2)),mult(X2,X)))),mult(X2,X)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c142,plain,
X = rd(mult(X,X),X),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
ld(mult(X2,rd(X2,mult(X,X2))),X2) = ld(mult(X2,rd(X2,mult(X,X2))),rd(mult(X2,X2),X2)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
rd(mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))),X3) = mult(mult(X3,rd(X2,mult(X,X3))),X),
inference(substitution,[status(thm)],[c34]) ).
cnf(c145,plain,
mult(mult(X3,rd(X2,mult(X,X3))),X) = rd(mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))),X3),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
mult(rd(X2,mult(X,X3)),mult(X,X3)) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c147,plain,
mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))) = mult(X3,X2),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
rd(mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))),X3) = rd(mult(X3,X2),X3),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
mult(mult(X3,rd(X2,mult(X,X3))),X) = rd(mult(X3,X2),X3),
inference(transitivity,[status(thm)],[c145,c148]) ).
cnf(c150,plain,
rd(mult(X3,X2),X3) = mult(mult(X3,rd(X2,mult(X,X3))),X),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
ld(mult(X3,rd(X2,mult(X,X3))),rd(mult(X3,X2),X3)) = ld(mult(X3,rd(X2,mult(X,X3))),mult(mult(X3,rd(X2,mult(X,X3))),X)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
ld(mult(X3,rd(X2,mult(X,X3))),mult(mult(X3,rd(X2,mult(X,X3))),X)) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c153,plain,
ld(mult(X3,rd(X2,mult(X,X3))),rd(mult(X3,X2),X3)) = X,
inference(transitivity,[status(thm)],[c151,c152]) ).
cnf(c154,plain,
ld(mult(X2,rd(X2,mult(X,X2))),rd(mult(X2,X2),X2)) = X,
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
ld(mult(X2,rd(X2,mult(X,X2))),X2) = X,
inference(transitivity,[status(thm)],[c143,c154]) ).
cnf(c156,plain,
ld(mult(mult(X2,X),rd(mult(X2,X),mult(ld(X,rd(X2,X2)),mult(X2,X)))),mult(X2,X)) = ld(X,rd(X2,X2)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
ld(X,rd(X2,X2)) = ld(X,ld(X2,X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c158,plain,
ld(mult(mult(X2,X),rd(mult(X2,X),mult(ld(X,rd(X2,X2)),mult(X2,X)))),mult(X2,X)) = ld(X,ld(X2,X2)),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
ld(mult(mult(X2,X),X),mult(X2,X)) = ld(X,ld(X2,X2)),
inference(transitivity,[status(thm)],[c140,c158]) ).
cnf(c160,plain,
ld(mult(mult(X,rd(X,X)),rd(X,X)),mult(X,rd(X,X))) = ld(rd(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
ld(rd(X,X),ld(X,X)) = ld(mult(mult(X,rd(X,X)),rd(X,X)),mult(X,rd(X,X))),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
mult(mult(X,rd(X,X)),rd(X,X)) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c163,plain,
ld(mult(mult(X,rd(X,X)),rd(X,X)),mult(X,rd(X,X))) = ld(X,mult(X,rd(X,X))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
ld(X,mult(X,rd(X,X))) = rd(X,X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c165,plain,
ld(X,mult(X,rd(X,X))) = ld(X,X),
inference(transitivity,[status(thm)],[c164,c117]) ).
cnf(c166,plain,
ld(mult(mult(X,rd(X,X)),rd(X,X)),mult(X,rd(X,X))) = ld(X,X),
inference(transitivity,[status(thm)],[c163,c165]) ).
cnf(c167,plain,
ld(rd(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c161,c166]) ).
cnf(c168,plain,
ld(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c119,c167]) ).
cnf(c169,plain,
ld(X,X) = ld(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
mult(X,ld(X2,X2)) = mult(X,ld(ld(X2,X2),ld(X2,X2))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
mult(ld(X2,X2),mult(X,ld(X2,X2))) = mult(ld(X2,X2),mult(X,ld(ld(X2,X2),ld(X2,X2)))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
mult(ld(ld(X2,X2),ld(X2,X2)),ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2))))) = mult(X,ld(ld(X2,X2),ld(X2,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c173,plain,
mult(X,ld(ld(X2,X2),ld(X2,X2))) = mult(ld(ld(X2,X2),ld(X2,X2)),ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2))))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
mult(ld(X2,X2),mult(X,ld(ld(X2,X2),ld(X2,X2)))) = mult(ld(X2,X2),mult(ld(ld(X2,X2),ld(X2,X2)),ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
mult(X,mult(ld(X,X3),mult(rd(X2,X),X))) = mult(mult(X3,rd(X2,X)),X),
inference(substitution,[status(thm)],[c129]) ).
cnf(c176,plain,
mult(mult(X3,rd(X2,X)),X) = mult(X,mult(ld(X,X3),mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c178,plain,
mult(ld(X,X3),mult(rd(X2,X),X)) = mult(ld(X,X3),X2),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
mult(X,mult(ld(X,X3),mult(rd(X2,X),X))) = mult(X,mult(ld(X,X3),X2)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
mult(mult(X3,rd(X2,X)),X) = mult(X,mult(ld(X,X3),X2)),
inference(transitivity,[status(thm)],[c176,c179]) ).
cnf(c181,plain,
mult(mult(ld(X2,X2),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(ld(X2,X2),ld(X2,X2)),ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),ld(X2,X2)),ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))))) = mult(mult(ld(X2,X2),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),ld(X2,X2)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
ld(X,X) = ld(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c184,plain,
mult(ld(X2,X2),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))) = mult(ld(ld(X2,X2),ld(X2,X2)),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
mult(mult(ld(X2,X2),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),ld(X2,X2)) = mult(mult(ld(ld(X2,X2),ld(X2,X2)),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),ld(X2,X2)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
mult(X4,mult(ld(mult(ld(X3,X2),X4),X),ld(X3,X2))) = ld(ld(X3,X2),mult(X,ld(X3,X2))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c187,plain,
ld(ld(X4,X3),mult(X2,ld(X4,X3))) = mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
rd(ld(ld(X4,X3),mult(X2,ld(X4,X3))),X3) = rd(mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),X3),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
mult(ld(X4,X3),rd(ld(ld(X4,X3),mult(X2,ld(X4,X3))),X3)) = mult(ld(X4,X3),rd(mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),X3)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
mult(mult(ld(X4,X3),rd(ld(ld(X4,X3),mult(X2,ld(X4,X3))),X3)),X4) = mult(mult(ld(X4,X3),rd(mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),X3)),X4),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
mult(mult(ld(X3,X2),rd(X,mult(X3,ld(X3,X2)))),X3) = rd(mult(ld(X3,X2),X),ld(X3,X2)),
inference(substitution,[status(thm)],[c149]) ).
cnf(c192,plain,
rd(mult(ld(X3,X2),X),ld(X3,X2)) = mult(mult(ld(X3,X2),rd(X,mult(X3,ld(X3,X2)))),X3),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c194,plain,
rd(X,mult(X3,ld(X3,X2))) = rd(X,X2),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
mult(ld(X3,X2),rd(X,mult(X3,ld(X3,X2)))) = mult(ld(X3,X2),rd(X,X2)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
mult(mult(ld(X3,X2),rd(X,mult(X3,ld(X3,X2)))),X3) = mult(mult(ld(X3,X2),rd(X,X2)),X3),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
rd(mult(ld(X3,X2),X),ld(X3,X2)) = mult(mult(ld(X3,X2),rd(X,X2)),X3),
inference(transitivity,[status(thm)],[c192,c196]) ).
cnf(c198,plain,
rd(mult(ld(X4,X3),mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3)))),ld(X4,X3)) = mult(mult(ld(X4,X3),rd(mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),X3)),X4),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
mult(mult(ld(X4,X3),rd(mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),X3)),X4) = rd(mult(ld(X4,X3),mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3)))),ld(X4,X3)),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
mult(ld(X4,X3),mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3)))) = mult(X2,ld(X4,X3)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c201,plain,
rd(mult(ld(X4,X3),mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3)))),ld(X4,X3)) = rd(mult(X2,ld(X4,X3)),ld(X4,X3)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
rd(mult(X,ld(X3,X2)),ld(X3,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c203,plain,
rd(mult(ld(X4,X3),mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3)))),ld(X4,X3)) = X2,
inference(transitivity,[status(thm)],[c201,c202]) ).
cnf(c204,plain,
mult(mult(ld(X4,X3),rd(mult(X,mult(ld(mult(ld(X4,X3),X),X2),ld(X4,X3))),X3)),X4) = X2,
inference(transitivity,[status(thm)],[c199,c203]) ).
cnf(c205,plain,
mult(mult(ld(X3,X2),rd(ld(ld(X3,X2),mult(X,ld(X3,X2))),X2)),X3) = X,
inference(transitivity,[status(thm)],[c190,c204]) ).
cnf(c206,plain,
mult(mult(ld(ld(X2,X2),ld(X2,X2)),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),ld(X2,X2)) = X,
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
mult(mult(ld(X2,X2),rd(ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))),ld(X2,X2)) = X,
inference(transitivity,[status(thm)],[c185,c206]) ).
cnf(c208,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),ld(X2,X2)),ld(ld(ld(X2,X2),ld(X2,X2)),mult(X,ld(ld(X2,X2),ld(X2,X2)))))) = X,
inference(transitivity,[status(thm)],[c182,c207]) ).
cnf(c209,plain,
mult(ld(X2,X2),mult(X,ld(ld(X2,X2),ld(X2,X2)))) = X,
inference(transitivity,[status(thm)],[c174,c208]) ).
cnf(c210,plain,
mult(ld(X2,X2),mult(X,ld(X2,X2))) = X,
inference(transitivity,[status(thm)],[c171,c209]) ).
cnf(c211,plain,
mult(ld(X,X),mult(ld(mult(ld(X,X),ld(X,X)),X2),ld(X,X))) = ld(mult(ld(X,X),ld(X,X)),X2),
inference(substitution,[status(thm)],[c210]) ).
cnf(c212,plain,
mult(ld(X,X),mult(ld(X,X),mult(ld(mult(ld(X,X),ld(X,X)),X2),ld(X,X)))) = mult(ld(X,X),ld(mult(ld(X,X),ld(X,X)),X2)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
rd(mult(mult(ld(X,X),ld(X,X)),X),X) = mult(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c214,plain,
mult(ld(X,X),ld(X,X)) = rd(mult(mult(ld(X,X),ld(X,X)),X),X),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c216,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c32]) ).
cnf(c219,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
rd(X,ld(mult(mult(ld(X,X),ld(X,X)),X),X)) = mult(mult(ld(X,X),ld(X,X)),X),
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
mult(mult(ld(X,X),ld(X,X)),X) = rd(X,ld(mult(mult(ld(X,X),ld(X,X)),X),X)),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c223,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
mult(ld(X,X2),X2) = mult(ld(X,X2),mult(X,ld(X,X2))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
mult(ld(X2,X),mult(ld(X,X2),X2)) = mult(ld(X2,X),mult(ld(X,X2),mult(X,ld(X,X2)))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c227,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
ld(X2,X) = ld(mult(X,ld(X,X2)),X),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
mult(ld(X2,X),mult(ld(X,X2),mult(X,ld(X,X2)))) = mult(ld(mult(X,ld(X,X2)),X),mult(ld(X,X2),mult(X,ld(X,X2)))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
mult(mult(X2,X),X3) = mult(X3,mult(ld(X3,X2),mult(X,X3))),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c231,plain,
ld(X3,mult(mult(X2,X),X3)) = ld(X3,mult(X3,mult(ld(X3,X2),mult(X,X3)))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
ld(X3,mult(X3,mult(ld(X3,X2),mult(X,X3)))) = mult(ld(X3,X2),mult(X,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c233,plain,
ld(X3,mult(mult(X2,X),X3)) = mult(ld(X3,X2),mult(X,X3)),
inference(transitivity,[status(thm)],[c231,c232]) ).
cnf(c234,plain,
ld(mult(X2,X),mult(mult(X2,X),mult(X2,X))) = mult(ld(mult(X2,X),X2),mult(X,mult(X2,X))),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
mult(ld(mult(X2,X),X2),mult(X,mult(X2,X))) = ld(mult(X2,X),mult(mult(X2,X),mult(X2,X))),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
ld(mult(X2,X),mult(mult(X2,X),mult(X2,X))) = mult(X2,X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c237,plain,
mult(ld(mult(X2,X),X2),mult(X,mult(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
mult(ld(mult(X,ld(X,X2)),X),mult(ld(X,X2),mult(X,ld(X,X2)))) = mult(X,ld(X,X2)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c240,plain,
mult(ld(mult(X,ld(X,X2)),X),mult(ld(X,X2),mult(X,ld(X,X2)))) = X2,
inference(transitivity,[status(thm)],[c238,c239]) ).
cnf(c241,plain,
mult(ld(X2,X),mult(ld(X,X2),mult(X,ld(X,X2)))) = X2,
inference(transitivity,[status(thm)],[c229,c240]) ).
cnf(c242,plain,
mult(ld(X2,X),mult(ld(X,X2),X2)) = X2,
inference(transitivity,[status(thm)],[c225,c241]) ).
cnf(c243,plain,
mult(ld(X,X),mult(ld(X,X),X)) = X,
inference(substitution,[status(thm)],[c242]) ).
cnf(c244,plain,
X = mult(ld(X,X),mult(ld(X,X),X)),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
ld(mult(mult(ld(X,X),ld(X,X)),X),X) = ld(mult(mult(ld(X,X),ld(X,X)),X),mult(ld(X,X),mult(ld(X,X),X))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c247,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
mult(X,X2) = mult(X,mult(X3,ld(X3,X2))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(ld(X3,X2),mult(X,X2)) = mult(ld(X3,X2),mult(X,mult(X3,ld(X3,X2)))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
ld(mult(mult(ld(X3,X2),X),X3),mult(ld(X3,X2),mult(X,X2))) = ld(mult(mult(ld(X3,X2),X),X3),mult(ld(X3,X2),mult(X,mult(X3,ld(X3,X2))))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
ld(mult(mult(ld(X3,X2),X),X3),mult(ld(X3,X2),mult(X,mult(X3,ld(X3,X2))))) = ld(X3,X2),
inference(substitution,[status(thm)],[c95]) ).
cnf(c252,plain,
ld(mult(mult(ld(X3,X2),X),X3),mult(ld(X3,X2),mult(X,X2))) = ld(X3,X2),
inference(transitivity,[status(thm)],[c250,c251]) ).
cnf(c253,plain,
ld(mult(mult(ld(X,X),ld(X,X)),X),mult(ld(X,X),mult(ld(X,X),X))) = ld(X,X),
inference(substitution,[status(thm)],[c252]) ).
cnf(c254,plain,
ld(mult(mult(ld(X,X),ld(X,X)),X),X) = ld(X,X),
inference(transitivity,[status(thm)],[c245,c253]) ).
cnf(c255,plain,
rd(X,ld(mult(mult(ld(X,X),ld(X,X)),X),X)) = rd(X,ld(X,X)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
rd(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c219]) ).
cnf(c257,plain,
rd(X,ld(mult(mult(ld(X,X),ld(X,X)),X),X)) = X,
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
mult(mult(ld(X,X),ld(X,X)),X) = X,
inference(transitivity,[status(thm)],[c221,c257]) ).
cnf(c259,plain,
rd(mult(mult(ld(X,X),ld(X,X)),X),X) = rd(X,X),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
rd(mult(mult(ld(X,X),ld(X,X)),X),X) = ld(X,X),
inference(transitivity,[status(thm)],[c259,c117]) ).
cnf(c261,plain,
mult(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c214,c260]) ).
cnf(c262,plain,
ld(mult(ld(X,X),ld(X,X)),X2) = ld(ld(X,X),X2),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
mult(ld(X,X),ld(mult(ld(X,X),ld(X,X)),X2)) = mult(ld(X,X),ld(ld(X,X),X2)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
mult(ld(X,X),ld(ld(X,X),X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c265,plain,
mult(ld(X,X),ld(mult(ld(X,X),ld(X,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c263,c264]) ).
cnf(c266,plain,
mult(ld(X,X),mult(ld(X,X),mult(ld(mult(ld(X,X),ld(X,X)),X2),ld(X,X)))) = X2,
inference(transitivity,[status(thm)],[c212,c265]) ).
cnf(c267,plain,
mult(X2,ld(X,X)) = X2,
inference(transitivity,[status(thm)],[c113,c266]) ).
cnf(c268,plain,
mult(X,ld(X2,X2)) = X,
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
X = mult(X,ld(X2,X2)),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
mult(X2,X) = mult(X2,mult(X,ld(X2,X2))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
mult(ld(X2,X2),mult(X2,X)) = mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
ld(mult(ld(X2,X2),mult(X2,X)),mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2))))) = ld(mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2))))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c274,plain,
X = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
ld(X2,X) = ld(mult(X3,ld(X3,X2)),X),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
mult(ld(X2,X),X3) = mult(ld(mult(X3,ld(X3,X2)),X),X3),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
mult(ld(X3,X2),mult(ld(X2,X),X3)) = mult(ld(X3,X2),mult(ld(mult(X3,ld(X3,X2)),X),X3)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
mult(ld(X3,X2),mult(ld(mult(X3,ld(X3,X2)),X),X3)) = ld(X3,mult(X,X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c279,plain,
mult(ld(X3,X2),mult(ld(X2,X),X3)) = ld(X3,mult(X,X3)),
inference(transitivity,[status(thm)],[c277,c278]) ).
cnf(c280,plain,
mult(ld(X,X),mult(ld(X,X),X)) = ld(X,mult(X,X)),
inference(substitution,[status(thm)],[c279]) ).
cnf(c281,plain,
ld(X,mult(X,X)) = mult(ld(X,X),mult(ld(X,X),X)),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
mult(X,ld(X2,mult(X2,X2))) = mult(X,mult(ld(X2,X2),mult(ld(X2,X2),X2))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2)))) = mult(mult(ld(X2,X2),X2),mult(X,mult(ld(X2,X2),mult(ld(X2,X2),X2)))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
ld(mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2))))) = ld(mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),X2),mult(X,mult(ld(X2,X2),mult(ld(X2,X2),X2))))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
mult(mult(mult(X3,X2),X),X3) = mult(X3,mult(X2,mult(X,X3))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c286,plain,
mult(X3,mult(X2,mult(X,X3))) = mult(mult(mult(X3,X2),X),X3),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
ld(mult(X3,mult(X2,mult(X,X3))),mult(mult(X3,X2),mult(X,mult(X3,mult(X3,X2))))) = ld(mult(mult(mult(X3,X2),X),X3),mult(mult(X3,X2),mult(X,mult(X3,mult(X3,X2))))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
ld(mult(mult(mult(X3,X2),X),X3),mult(mult(X3,X2),mult(X,mult(X3,mult(X3,X2))))) = mult(X3,X2),
inference(substitution,[status(thm)],[c95]) ).
cnf(c289,plain,
ld(mult(X3,mult(X2,mult(X,X3))),mult(mult(X3,X2),mult(X,mult(X3,mult(X3,X2))))) = mult(X3,X2),
inference(transitivity,[status(thm)],[c287,c288]) ).
cnf(c290,plain,
ld(mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),X2),mult(X,mult(ld(X2,X2),mult(ld(X2,X2),X2))))) = mult(ld(X2,X2),X2),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
ld(mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),X2),mult(X,mult(ld(X2,X2),mult(ld(X2,X2),X2))))) = X2,
inference(transitivity,[status(thm)],[c290,c108]) ).
cnf(c292,plain,
ld(mult(ld(X2,X2),mult(X2,mult(X,ld(X2,X2)))),mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2))))) = X2,
inference(transitivity,[status(thm)],[c284,c291]) ).
cnf(c293,plain,
ld(mult(ld(X2,X2),mult(X2,X)),mult(mult(ld(X2,X2),X2),mult(X,ld(X2,mult(X2,X2))))) = X2,
inference(transitivity,[status(thm)],[c272,c292]) ).
cnf(c294,plain,
ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,ld(X2,mult(X2,X2))))) = X2,
inference(transitivity,[status(thm)],[c111,c293]) ).
cnf(c295,plain,
ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,X2))) = X2,
inference(transitivity,[status(thm)],[c11,c294]) ).
cnf(c296,plain,
X2 = ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
rd(mult(X2,mult(X,X2)),X2) = rd(mult(X2,mult(X,X2)),ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
rd(mult(X2,mult(X,X2)),ld(mult(ld(X2,X2),mult(X2,X)),mult(X2,mult(X,X2)))) = mult(ld(X2,X2),mult(X2,X)),
inference(substitution,[status(thm)],[c219]) ).
cnf(c299,plain,
rd(mult(X2,mult(X,X2)),X2) = mult(ld(X2,X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c297,c298]) ).
cnf(c300,plain,
rd(mult(X2,mult(ld(X2,X),X2)),X2) = mult(ld(X2,X2),mult(X2,ld(X2,X))),
inference(substitution,[status(thm)],[c299]) ).
cnf(c301,plain,
mult(ld(X2,X2),mult(X2,ld(X2,X))) = rd(mult(X2,mult(ld(X2,X),X2)),X2),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
X = mult(ld(X,X),X),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c303,plain,
ld(X,X2) = ld(mult(ld(X,X),X),X2),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
mult(ld(X,X2),X) = mult(ld(mult(ld(X,X),X),X2),X),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
mult(X,mult(ld(X,X2),X)) = mult(X,mult(ld(mult(ld(X,X),X),X2),X)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
ld(X2,mult(X,mult(ld(X,X2),X))) = ld(X2,mult(X,mult(ld(mult(ld(X,X),X),X2),X))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
mult(ld(mult(ld(X,X),X),X2),ld(X,X)) = ld(mult(ld(X,X),X),X2),
inference(substitution,[status(thm)],[c267]) ).
cnf(c308,plain,
ld(mult(ld(X,X),X),X2) = mult(ld(mult(ld(X,X),X),X2),ld(X,X)),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
mult(ld(mult(ld(X,X),X),X2),X) = mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(X,mult(ld(mult(ld(X,X),X),X2),X)) = mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
ld(X2,mult(X,mult(ld(mult(ld(X,X),X),X2),X))) = ld(X2,mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
X2 = mult(X2,ld(X,X)),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c313,plain,
ld(X2,mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))) = ld(mult(X2,ld(X,X)),mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
mult(ld(X,X),mult(X,mult(ld(mult(ld(X,X),X),X2),ld(X,X)))) = mult(X2,ld(X,X)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c315,plain,
mult(X2,ld(X,X)) = mult(ld(X,X),mult(X,mult(ld(mult(ld(X,X),X),X2),ld(X,X)))),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
ld(mult(X2,ld(X,X)),mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))) = ld(mult(ld(X,X),mult(X,mult(ld(mult(ld(X,X),X),X2),ld(X,X)))),mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
ld(mult(ld(X,X),mult(X,mult(ld(mult(ld(X,X),X),X2),ld(X,X)))),mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))) = X,
inference(substitution,[status(thm)],[c295]) ).
cnf(c318,plain,
ld(mult(X2,ld(X,X)),mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))) = X,
inference(transitivity,[status(thm)],[c316,c317]) ).
cnf(c319,plain,
ld(X2,mult(X,mult(mult(ld(mult(ld(X,X),X),X2),ld(X,X)),X))) = X,
inference(transitivity,[status(thm)],[c313,c318]) ).
cnf(c320,plain,
ld(X2,mult(X,mult(ld(mult(ld(X,X),X),X2),X))) = X,
inference(transitivity,[status(thm)],[c311,c319]) ).
cnf(c321,plain,
ld(X2,mult(X,mult(ld(X,X2),X))) = X,
inference(transitivity,[status(thm)],[c306,c320]) ).
cnf(c322,plain,
ld(X,mult(X2,mult(ld(X2,X),X2))) = X2,
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
X2 = ld(X,mult(X2,mult(ld(X2,X),X2))),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
rd(mult(X2,mult(ld(X2,X),X2)),X2) = rd(mult(X2,mult(ld(X2,X),X2)),ld(X,mult(X2,mult(ld(X2,X),X2)))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
rd(mult(X2,mult(ld(X2,X),X2)),ld(X,mult(X2,mult(ld(X2,X),X2)))) = X,
inference(substitution,[status(thm)],[c219]) ).
cnf(c326,plain,
rd(mult(X2,mult(ld(X2,X),X2)),X2) = X,
inference(transitivity,[status(thm)],[c324,c325]) ).
cnf(c327,plain,
mult(ld(X2,X2),mult(X2,ld(X2,X))) = X,
inference(transitivity,[status(thm)],[c301,c326]) ).
cnf(c328,plain,
mult(ld(X2,X2),X) = X,
inference(transitivity,[status(thm)],[c5,c327]) ).
cnf(c329,plain,
mult(ld(X,X),x1(ld(X,X))) = x1(ld(X,X)),
inference(substitution,[status(thm)],[c328]) ).
cnf(c330,plain,
tuple(mult(ld(X,X),x1(ld(X,X))),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(x1(ld(X,X)),mult(x1_2(ld(X,X)),ld(X,X))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
mult(x1_2(ld(X,X)),ld(X,X)) = x1_2(ld(X,X)),
inference(substitution,[status(thm)],[c267]) ).
cnf(c332,plain,
tuple(x1(ld(X,X)),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(x1(ld(X,X)),x1_2(ld(X,X))),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,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)],[c330,c332]) ).
cnf(c334,plain,
$false,
inference(resolution,[status(thm)],[c1,c333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP660-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 10:34:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.32/0.62 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 1.32/0.62
% 1.32/0.62 % SZS status Unsatisfiable
% 1.32/0.62
% 1.32/0.66 % SZS output start CNFRefutation
% See solution above
% 3.00/0.84
% 3.00/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------