%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP728-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 10:11:52 AM UTC 2026
% Result : Unsatisfiable 20.26s 3.21s
% Output : CNFRefutation 22.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 14
% Syntax : Number of clauses : 444 ( 444 unt; 0 nHn; 3 RR)
% Number of literals : 444 ( 443 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 1076 ( 59 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
op_k(op_k(a,b),c) != unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c3,plain,
mult(rd(X,i(op_k(X3,X2))),i(op_k(X3,X2))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X = mult(rd(X,i(op_k(X3,X2))),i(op_k(X3,X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
op_k(op_k(X3,X2),X) = op_k(op_k(X3,X2),mult(rd(X,i(op_k(X3,X2))),i(op_k(X3,X2)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
mult(i(A2),mult(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c7,plain,
mult(i(X2),mult(X2,X)) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
X = mult(i(X2),mult(X2,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
op_k(X2,X) = op_k(X2,mult(i(X2),mult(X2,X))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
i(op_k(X2,X)) = i(op_k(X2,mult(i(X2),mult(X2,X)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c12,plain,
mult(i(i(X)),unit) = i(i(X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
i(i(X)) = mult(i(i(X)),unit),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
mult(i(A2),A2) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c15,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
mult(i(i(X)),unit) = mult(i(i(X)),mult(i(X),X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
mult(i(i(X)),mult(i(X),X)) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c19,plain,
mult(i(i(X)),unit) = X,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
i(i(X)) = X,
inference(transitivity,[status(thm)],[c13,c19]) ).
cnf(c21,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
rd(X2,X) = rd(i(i(X2)),X),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
mult(rd(X2,X),i(X2)) = mult(rd(i(i(X2)),X),i(X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
op_t(A2,B2) = mult(i(B2),mult(A2,B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c14) ).
cnf(c25,plain,
op_t(X,X2) = mult(i(X2),mult(X,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(X2,op_t(X,X2)) = mult(X2,mult(i(X2),mult(X,X2))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c28,plain,
mult(X2,mult(i(X2),X)) = mult(i(i(X2)),mult(i(X2),X)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
mult(i(i(X2)),mult(i(X2),X)) = X,
inference(substitution,[status(thm)],[c6]) ).
cnf(c30,plain,
mult(X2,mult(i(X2),X)) = X,
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
mult(X2,mult(i(X2),mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(X2,op_t(X,X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c26,c31]) ).
cnf(c33,plain,
mult(X2,op_t(rd(i(X2),X),X2)) = mult(rd(i(X2),X),X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
mult(rd(i(X2),X),X2) = mult(X2,op_t(rd(i(X2),X),X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
mult(i(X),mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c36,plain,
X2 = mult(i(X),mult(X,X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
rd(X2,mult(X,X2)) = rd(mult(i(X),mult(X,X2)),mult(X,X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c39,plain,
rd(mult(i(X),mult(X,X2)),mult(X,X2)) = i(X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
rd(X2,mult(X,X2)) = i(X),
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
rd(X,mult(rd(X2,X),X)) = i(rd(X2,X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
i(rd(X2,X)) = rd(X,mult(rd(X2,X),X)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
rd(X,mult(rd(X2,X),X)) = rd(X,X2),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
i(rd(X2,X)) = rd(X,X2),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
i(rd(X,i(X2))) = rd(i(X2),X),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
rd(i(X2),X) = i(rd(X,i(X2))),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
op_t(rd(i(X2),X),X2) = op_t(i(rd(X,i(X2))),X2),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,axiom,
i(mult(A2,B2)) = mult(i(A2),i(B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c50,plain,
i(mult(X,X2)) = mult(i(X),i(X2)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(i(X),i(X2)) = i(mult(X,X2)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(X2,mult(i(X),i(X2))) = mult(X2,i(mult(X,X2))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c54,plain,
mult(X2,i(mult(X,X2))) = mult(i(i(X2)),i(mult(X,X2))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
i(mult(i(X2),mult(X,X2))) = mult(i(i(X2)),i(mult(X,X2))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c56,plain,
mult(i(i(X2)),i(mult(X,X2))) = i(mult(i(X2),mult(X,X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
op_t(X,X2) = mult(i(X2),mult(X,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c58,plain,
mult(i(X2),mult(X,X2)) = op_t(X,X2),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
i(mult(i(X2),mult(X,X2))) = i(op_t(X,X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
mult(i(i(X2)),i(mult(X,X2))) = i(op_t(X,X2)),
inference(transitivity,[status(thm)],[c56,c59]) ).
cnf(c61,plain,
mult(X2,i(mult(X,X2))) = i(op_t(X,X2)),
inference(transitivity,[status(thm)],[c54,c60]) ).
cnf(c62,plain,
mult(X2,mult(i(X),i(X2))) = i(op_t(X,X2)),
inference(transitivity,[status(thm)],[c52,c61]) ).
cnf(c63,plain,
mult(i(X),mult(i(X2),i(i(X)))) = i(op_t(X2,i(X))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
i(op_t(X2,i(X))) = mult(i(X),mult(i(X2),i(i(X)))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
mult(i(X2),i(i(X))) = mult(i(X2),X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c66,plain,
mult(i(X),mult(i(X2),i(i(X)))) = mult(i(X),mult(i(X2),X)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
op_t(i(X2),X) = mult(i(X),mult(i(X2),X)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c68,plain,
mult(i(X),mult(i(X2),X)) = op_t(i(X2),X),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
mult(i(X),mult(i(X2),i(i(X)))) = op_t(i(X2),X),
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
i(op_t(X2,i(X))) = op_t(i(X2),X),
inference(transitivity,[status(thm)],[c64,c69]) ).
cnf(c71,plain,
i(op_t(rd(X,i(X2)),i(X2))) = op_t(i(rd(X,i(X2))),X2),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
op_t(i(rd(X,i(X2))),X2) = i(op_t(rd(X,i(X2)),i(X2))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
op_t(rd(X2,X),X) = mult(i(X),mult(rd(X2,X),X)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c74,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
mult(i(X),mult(rd(X2,X),X)) = mult(i(X),X2),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
op_t(rd(X2,X),X) = mult(i(X),X2),
inference(transitivity,[status(thm)],[c73,c75]) ).
cnf(c77,plain,
op_t(rd(X,i(X2)),i(X2)) = mult(i(i(X2)),X),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
i(op_t(rd(X,i(X2)),i(X2))) = i(mult(i(i(X2)),X)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
i(mult(i(i(X2)),X)) = mult(i(i(i(X2))),i(X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c80,plain,
i(i(i(X))) = i(X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c81,plain,
mult(i(i(i(X2))),i(X)) = mult(i(X2),i(X)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
i(mult(i(i(X2)),X)) = mult(i(X2),i(X)),
inference(transitivity,[status(thm)],[c79,c81]) ).
cnf(c83,plain,
i(op_t(rd(X,i(X2)),i(X2))) = mult(i(X2),i(X)),
inference(transitivity,[status(thm)],[c78,c82]) ).
cnf(c84,plain,
op_t(i(rd(X,i(X2))),X2) = mult(i(X2),i(X)),
inference(transitivity,[status(thm)],[c72,c83]) ).
cnf(c85,plain,
op_t(rd(i(X2),X),X2) = mult(i(X2),i(X)),
inference(transitivity,[status(thm)],[c48,c84]) ).
cnf(c86,plain,
mult(X2,op_t(rd(i(X2),X),X2)) = mult(X2,mult(i(X2),i(X))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
mult(X2,mult(i(X2),i(X))) = i(X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c88,plain,
mult(X2,op_t(rd(i(X2),X),X2)) = i(X),
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
mult(rd(i(X2),X),X2) = i(X),
inference(transitivity,[status(thm)],[c34,c88]) ).
cnf(c90,plain,
mult(rd(i(i(X2)),X),i(X2)) = i(X),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
mult(rd(X2,X),i(X2)) = i(X),
inference(transitivity,[status(thm)],[c23,c90]) ).
cnf(c92,plain,
mult(rd(X,op_k(X2,mult(i(X2),X))),i(X)) = i(op_k(X2,mult(i(X2),X))),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
i(op_k(X2,mult(i(X2),X))) = mult(rd(X,op_k(X2,mult(i(X2),X))),i(X)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c95,plain,
op_k(X,mult(i(X),X2)) = op_k(i(i(X)),mult(i(X),X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
rd(X2,op_k(X,mult(i(X),X2))) = rd(X2,op_k(i(i(X)),mult(i(X),X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
mult(i(X),mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c98,plain,
X2 = mult(i(X),mult(X,X2)),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
rd(X2,op_k(i(X),mult(X,X2))) = rd(mult(i(X),mult(X,X2)),op_k(i(X),mult(X,X2))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,axiom,
mult(A2,B2) = mult(mult(B2,A2),op_k(A2,B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
cnf(c101,plain,
mult(X2,X) = mult(mult(X,X2),op_k(X2,X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
rd(mult(X2,X),op_k(X2,X)) = rd(mult(mult(X,X2),op_k(X2,X)),op_k(X2,X)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
rd(mult(mult(X,X2),op_k(X2,X)),op_k(X2,X)) = mult(X,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c104,plain,
rd(mult(X2,X),op_k(X2,X)) = mult(X,X2),
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
rd(mult(i(X),mult(X,X2)),op_k(i(X),mult(X,X2))) = mult(mult(X,X2),i(X)),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c107,plain,
mult(X,X2) = mult(i(i(X)),X2),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
mult(mult(X,X2),i(X)) = mult(mult(i(i(X)),X2),i(X)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c110,plain,
mult(i(X2),X) = mult(i(X2),i(i(X))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
mult(mult(i(X2),X),X2) = mult(mult(i(X2),i(i(X))),X2),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(X,unit) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c113,plain,
X = mult(X,unit),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
mult(mult(i(X),i(X2)),X) = mult(mult(i(X),i(X2)),mult(X,unit)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,axiom,
mult(A2,i(A2)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c116,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
unit = mult(X,i(X)),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
mult(X,unit) = mult(X,mult(X2,i(X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
mult(mult(i(X),i(X2)),mult(X,unit)) = mult(mult(i(X),i(X2)),mult(X,mult(X2,i(X2)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
i(mult(X2,X)) = mult(i(X2),i(X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c121,plain,
mult(i(X2),i(X)) = i(mult(X2,X)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
mult(mult(i(X3),i(X2)),mult(X3,mult(X2,X))) = mult(i(mult(X3,X2)),mult(X3,mult(X2,X))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,axiom,
op_l(A2,B2,C) = mult(i(mult(C,B2)),mult(C,mult(B2,A2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c12) ).
cnf(c124,plain,
op_l(X,X2,X3) = mult(i(mult(X3,X2)),mult(X3,mult(X2,X))),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
mult(i(mult(X3,X2)),mult(X3,mult(X2,X))) = op_l(X,X2,X3),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
mult(mult(i(X3),i(X2)),mult(X3,mult(X2,X))) = op_l(X,X2,X3),
inference(transitivity,[status(thm)],[c122,c125]) ).
cnf(c127,plain,
mult(mult(i(X),i(X2)),mult(X,mult(X2,i(X2)))) = op_l(i(X2),X2,X),
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
mult(mult(i(X),i(X2)),mult(X,unit)) = op_l(i(X2),X2,X),
inference(transitivity,[status(thm)],[c119,c127]) ).
cnf(c129,plain,
mult(mult(i(X),i(X2)),X) = op_l(i(X2),X2,X),
inference(transitivity,[status(thm)],[c114,c128]) ).
cnf(c130,plain,
mult(mult(i(X2),i(i(X))),X2) = op_l(i(i(X)),i(X),X2),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
op_l(i(i(X)),i(X),X2) = op_l(X,i(X),X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c132,plain,
mult(mult(i(X2),i(i(X))),X2) = op_l(X,i(X),X2),
inference(transitivity,[status(thm)],[c130,c131]) ).
cnf(c133,plain,
mult(mult(i(X2),X),X2) = op_l(X,i(X),X2),
inference(transitivity,[status(thm)],[c111,c132]) ).
cnf(c134,plain,
mult(mult(i(i(X)),X2),i(X)) = op_l(X2,i(X2),i(X)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
mult(mult(X,X2),i(X)) = op_l(X2,i(X2),i(X)),
inference(transitivity,[status(thm)],[c108,c134]) ).
cnf(c136,plain,
rd(mult(i(X),mult(X,X2)),op_k(i(X),mult(X,X2))) = op_l(X2,i(X2),i(X)),
inference(transitivity,[status(thm)],[c105,c135]) ).
cnf(c137,plain,
rd(X2,op_k(i(X),mult(X,X2))) = op_l(X2,i(X2),i(X)),
inference(transitivity,[status(thm)],[c99,c136]) ).
cnf(c138,plain,
rd(X2,op_k(i(i(X)),mult(i(X),X2))) = op_l(X2,i(X2),i(i(X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
op_l(X2,i(X2),i(i(X))) = op_l(X2,i(X2),X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c140,plain,
rd(X2,op_k(i(i(X)),mult(i(X),X2))) = op_l(X2,i(X2),X),
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
rd(X2,op_k(X,mult(i(X),X2))) = op_l(X2,i(X2),X),
inference(transitivity,[status(thm)],[c96,c140]) ).
cnf(c142,plain,
rd(X,op_k(X2,mult(i(X2),X))) = op_l(X,i(X),X2),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
mult(rd(X,op_k(X2,mult(i(X2),X))),i(X)) = mult(op_l(X,i(X),X2),i(X)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c145,plain,
op_l(X,i(X),X2) = op_l(i(i(X)),i(X),X2),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
mult(op_l(X,i(X),X2),i(X)) = mult(op_l(i(i(X)),i(X),X2),i(X)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
i(rd(i(X),X2)) = rd(X2,i(X)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c148,plain,
rd(X2,i(X)) = i(rd(i(X),X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
rd(X,mult(rd(i(X),X2),X)) = i(rd(i(X),X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c150,plain,
i(rd(i(X),X2)) = rd(X,mult(rd(i(X),X2),X)),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
mult(rd(i(X),X2),X) = i(X2),
inference(substitution,[status(thm)],[c89]) ).
cnf(c152,plain,
rd(X,mult(rd(i(X),X2),X)) = rd(X,i(X2)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
i(rd(i(X),X2)) = rd(X,i(X2)),
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
rd(X2,i(X)) = rd(X,i(X2)),
inference(transitivity,[status(thm)],[c148,c153]) ).
cnf(c155,plain,
rd(X,i(i(X2))) = rd(i(X2),i(X)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
rd(i(X2),i(X)) = rd(X,i(i(X2))),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
rd(X,i(i(X2))) = rd(X,X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c158,plain,
rd(i(X2),i(X)) = rd(X,X2),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
rd(i(X2),i(op_k(i(X),mult(X,X2)))) = rd(op_k(i(X),mult(X,X2)),X2),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
i(rd(X2,op_k(i(X),mult(X,X2)))) = rd(op_k(i(X),mult(X,X2)),X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c161,plain,
rd(op_k(i(X),mult(X,X2)),X2) = i(rd(X2,op_k(i(X),mult(X,X2)))),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
i(rd(X2,op_k(i(X),mult(X,X2)))) = i(op_l(X2,i(X2),i(X))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c163,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c164,plain,
op_l(X2,i(X2),X) = op_l(i(i(X2)),i(X2),X),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
i(op_l(X2,i(X2),X)) = i(op_l(i(i(X2)),i(X2),X)),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c167,plain,
mult(X2,X) = mult(X2,i(i(X))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
mult(mult(X2,X),i(X2)) = mult(mult(X2,i(i(X))),i(X2)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c170,plain,
mult(X2,i(i(X))) = mult(i(i(X2)),i(i(X))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
mult(mult(X2,i(i(X))),i(X2)) = mult(mult(i(i(X2)),i(i(X))),i(X2)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
i(mult(i(X2),i(X))) = mult(i(i(X2)),i(i(X))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c173,plain,
mult(i(i(X2)),i(i(X))) = i(mult(i(X2),i(X))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
mult(mult(i(i(X2)),i(i(X))),i(X2)) = mult(i(mult(i(X2),i(X))),i(X2)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
i(mult(mult(i(X2),i(X)),X2)) = mult(i(mult(i(X2),i(X))),i(X2)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c176,plain,
mult(i(mult(i(X2),i(X))),i(X2)) = i(mult(mult(i(X2),i(X)),X2)),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
mult(mult(i(X2),i(X)),X2) = op_l(i(X),X,X2),
inference(substitution,[status(thm)],[c129]) ).
cnf(c178,plain,
i(mult(mult(i(X2),i(X)),X2)) = i(op_l(i(X),X,X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
mult(i(mult(i(X2),i(X))),i(X2)) = i(op_l(i(X),X,X2)),
inference(transitivity,[status(thm)],[c176,c178]) ).
cnf(c180,plain,
mult(mult(i(i(X2)),i(i(X))),i(X2)) = i(op_l(i(X),X,X2)),
inference(transitivity,[status(thm)],[c174,c179]) ).
cnf(c181,plain,
mult(mult(X2,i(i(X))),i(X2)) = i(op_l(i(X),X,X2)),
inference(transitivity,[status(thm)],[c171,c180]) ).
cnf(c182,plain,
mult(mult(X2,X),i(X2)) = i(op_l(i(X),X,X2)),
inference(transitivity,[status(thm)],[c168,c181]) ).
cnf(c183,plain,
mult(mult(X,X2),i(X)) = i(op_l(i(X2),X2,X)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
i(op_l(i(X2),X2,X)) = mult(mult(X,X2),i(X)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
i(op_l(i(X2),X2,X)) = op_l(X2,i(X2),i(X)),
inference(transitivity,[status(thm)],[c184,c135]) ).
cnf(c186,plain,
i(op_l(i(i(X2)),i(X2),X)) = op_l(i(X2),i(i(X2)),i(X)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
op_l(i(X2),i(i(X2)),i(X)) = op_l(i(X2),X2,i(X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c188,plain,
i(op_l(i(i(X2)),i(X2),X)) = op_l(i(X2),X2,i(X)),
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
i(op_l(X2,i(X2),X)) = op_l(i(X2),X2,i(X)),
inference(transitivity,[status(thm)],[c165,c188]) ).
cnf(c190,plain,
i(op_l(X2,i(X2),i(X))) = op_l(i(X2),X2,i(i(X))),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
op_l(i(X2),X2,i(i(X))) = op_l(i(X2),X2,X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c192,plain,
i(op_l(X2,i(X2),i(X))) = op_l(i(X2),X2,X),
inference(transitivity,[status(thm)],[c190,c191]) ).
cnf(c193,plain,
i(rd(X2,op_k(i(X),mult(X,X2)))) = op_l(i(X2),X2,X),
inference(transitivity,[status(thm)],[c162,c192]) ).
cnf(c194,plain,
rd(op_k(i(X),mult(X,X2)),X2) = op_l(i(X2),X2,X),
inference(transitivity,[status(thm)],[c161,c193]) ).
cnf(c195,plain,
rd(i(X2),i(op_k(i(X),mult(X,X2)))) = op_l(i(X2),X2,X),
inference(transitivity,[status(thm)],[c159,c194]) ).
cnf(c196,plain,
rd(i(X),i(op_k(i(X2),mult(X2,X)))) = op_l(i(X),X,X2),
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
op_l(i(X),X,X2) = rd(i(X),i(op_k(i(X2),mult(X2,X)))),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
mult(op_l(i(X),X,X2),X) = mult(rd(i(X),i(op_k(i(X2),mult(X2,X)))),X),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
mult(rd(i(X),i(op_k(i(X2),mult(X2,X)))),X) = i(i(op_k(i(X2),mult(X2,X)))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c200,plain,
i(i(op_k(i(X2),mult(X2,X)))) = op_k(i(X2),mult(X2,X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c201,plain,
mult(rd(i(X),i(op_k(i(X2),mult(X2,X)))),X) = op_k(i(X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
mult(op_l(i(X),X,X2),X) = op_k(i(X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c198,c201]) ).
cnf(c203,plain,
mult(op_l(i(i(X)),i(X),X2),i(X)) = op_k(i(X2),mult(X2,i(X))),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
mult(op_l(X,i(X),X2),i(X)) = op_k(i(X2),mult(X2,i(X))),
inference(transitivity,[status(thm)],[c146,c203]) ).
cnf(c205,plain,
mult(rd(X,op_k(X2,mult(i(X2),X))),i(X)) = op_k(i(X2),mult(X2,i(X))),
inference(transitivity,[status(thm)],[c143,c204]) ).
cnf(c206,plain,
i(op_k(X2,mult(i(X2),X))) = op_k(i(X2),mult(X2,i(X))),
inference(transitivity,[status(thm)],[c93,c205]) ).
cnf(c207,plain,
i(op_k(X2,mult(i(X2),mult(X2,X)))) = op_k(i(X2),mult(X2,i(mult(X2,X)))),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
i(mult(X2,X)) = mult(i(X2),i(X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c209,plain,
mult(X2,i(mult(X2,X))) = mult(X2,mult(i(X2),i(X))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
op_k(i(X2),mult(X2,i(mult(X2,X)))) = op_k(i(X2),mult(X2,mult(i(X2),i(X)))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
mult(X2,mult(i(X2),i(X))) = i(X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c212,plain,
op_k(i(X2),mult(X2,mult(i(X2),i(X)))) = op_k(i(X2),i(X)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
op_k(i(X2),mult(X2,i(mult(X2,X)))) = op_k(i(X2),i(X)),
inference(transitivity,[status(thm)],[c210,c212]) ).
cnf(c214,plain,
i(op_k(X2,mult(i(X2),mult(X2,X)))) = op_k(i(X2),i(X)),
inference(transitivity,[status(thm)],[c207,c213]) ).
cnf(c215,plain,
i(op_k(X2,X)) = op_k(i(X2),i(X)),
inference(transitivity,[status(thm)],[c10,c214]) ).
cnf(c216,plain,
op_t(X3,i(op_k(X2,X))) = op_t(X3,op_k(i(X2),i(X))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
i(X) = rd(X2,mult(X,X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c218,plain,
op_k(i(X),i(X2)) = op_k(rd(X2,mult(X,X2)),i(X2)),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
i(rd(X,X2)) = rd(X2,X),
inference(substitution,[status(thm)],[c45]) ).
cnf(c220,plain,
rd(X2,X) = i(rd(X,X2)),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
op_k(rd(X2,X),i(X2)) = op_k(i(rd(X,X2)),i(X2)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
i(op_k(rd(X,X2),X2)) = op_k(i(rd(X,X2)),i(X2)),
inference(substitution,[status(thm)],[c215]) ).
cnf(c223,plain,
op_k(i(rd(X,X2)),i(X2)) = i(op_k(rd(X,X2),X2)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c225,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
op_k(rd(X2,X),X) = op_k(rd(X2,X),mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
i(rd(X,X2)) = rd(X2,X),
inference(substitution,[status(thm)],[c45]) ).
cnf(c228,plain,
rd(X2,X) = i(rd(X,X2)),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
op_k(rd(X2,X),mult(rd(X,X2),X2)) = op_k(i(rd(X,X2)),mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
mult(op_l(i(X2),X2,rd(X,X2)),X2) = op_k(i(rd(X,X2)),mult(rd(X,X2),X2)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c231,plain,
op_k(i(rd(X,X2)),mult(rd(X,X2),X2)) = mult(op_l(i(X2),X2,rd(X,X2)),X2),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
mult(mult(i(i(X2)),i(mult(X2,X))),mult(i(X2),mult(mult(X2,X),X3))) = op_l(X3,mult(X2,X),i(X2)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c233,plain,
op_l(X3,mult(X2,X),i(X2)) = mult(mult(i(i(X2)),i(mult(X2,X))),mult(i(X2),mult(mult(X2,X),X3))),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
mult(i(X),mult(X,mult(X3,mult(X2,asoc(X,X3,X2))))) = mult(X3,mult(X2,asoc(X,X3,X2))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c235,plain,
mult(X3,mult(X2,asoc(X,X3,X2))) = mult(i(X),mult(X,mult(X3,mult(X2,asoc(X,X3,X2))))),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,axiom,
mult(mult(A2,B2),C2) = mult(mult(A2,mult(B2,C2)),asoc(A2,B2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
cnf(c237,plain,
mult(mult(X3,X2),asoc(X,X5,X4)) = mult(mult(X3,mult(X2,asoc(X,X5,X4))),asoc(X3,X2,asoc(X,X5,X4))),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,axiom,
asoc(A2,B2,asoc(C2,D,E)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c22) ).
cnf(c239,plain,
asoc(X5,X4,asoc(X3,X2,X)) = unit,
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
mult(mult(X5,mult(X4,asoc(X3,X2,X))),asoc(X5,X4,asoc(X3,X2,X))) = mult(mult(X5,mult(X4,asoc(X3,X2,X))),unit),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
mult(mult(X5,mult(X4,asoc(X3,X2,X))),unit) = mult(X5,mult(X4,asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c242,plain,
mult(mult(X5,mult(X4,asoc(X3,X2,X))),asoc(X5,X4,asoc(X3,X2,X))) = mult(X5,mult(X4,asoc(X3,X2,X))),
inference(transitivity,[status(thm)],[c240,c241]) ).
cnf(c243,plain,
mult(mult(X5,X4),asoc(X3,X2,X)) = mult(X5,mult(X4,asoc(X3,X2,X))),
inference(transitivity,[status(thm)],[c237,c242]) ).
cnf(c244,plain,
mult(mult(X2,X),asoc(X3,X2,X)) = mult(X2,mult(X,asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c243]) ).
cnf(c245,plain,
mult(X2,mult(X,asoc(X3,X2,X))) = mult(mult(X2,X),asoc(X3,X2,X)),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
mult(X3,mult(X2,mult(X,asoc(X3,X2,X)))) = mult(X3,mult(mult(X2,X),asoc(X3,X2,X))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
mult(mult(X3,mult(X2,X)),asoc(X3,X2,X)) = mult(X3,mult(mult(X2,X),asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c243]) ).
cnf(c248,plain,
mult(X3,mult(mult(X2,X),asoc(X3,X2,X))) = mult(mult(X3,mult(X2,X)),asoc(X3,X2,X)),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(mult(X3,X2),X) = mult(mult(X3,mult(X2,X)),asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c250,plain,
mult(mult(X3,mult(X2,X)),asoc(X3,X2,X)) = mult(mult(X3,X2),X),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
mult(X3,mult(mult(X2,X),asoc(X3,X2,X))) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c248,c250]) ).
cnf(c252,plain,
mult(X3,mult(X2,mult(X,asoc(X3,X2,X)))) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c246,c251]) ).
cnf(c253,plain,
mult(X,mult(X3,mult(X2,asoc(X,X3,X2)))) = mult(mult(X,X3),X2),
inference(substitution,[status(thm)],[c252]) ).
cnf(c254,plain,
mult(i(X),mult(X,mult(X3,mult(X2,asoc(X,X3,X2))))) = mult(i(X),mult(mult(X,X3),X2)),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
mult(X3,mult(X2,asoc(X,X3,X2))) = mult(i(X),mult(mult(X,X3),X2)),
inference(transitivity,[status(thm)],[c235,c254]) ).
cnf(c256,plain,
mult(X,mult(X3,asoc(X2,X,X3))) = mult(i(X2),mult(mult(X2,X),X3)),
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
mult(i(X2),mult(mult(X2,X),X3)) = mult(X,mult(X3,asoc(X2,X,X3))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
mult(mult(i(i(X2)),i(mult(X2,X))),mult(i(X2),mult(mult(X2,X),X3))) = mult(mult(i(i(X2)),i(mult(X2,X))),mult(X,mult(X3,asoc(X2,X,X3)))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
mult(i(i(X2)),i(mult(X2,X))) = mult(X2,i(mult(X2,X))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c260,plain,
mult(mult(i(i(X2)),i(mult(X2,X))),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(mult(X2,i(mult(X2,X))),mult(X,mult(X3,asoc(X2,X,X3)))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
i(mult(X2,X)) = mult(i(X2),i(X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c262,plain,
mult(X2,i(mult(X2,X))) = mult(X2,mult(i(X2),i(X))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
mult(mult(X2,i(mult(X2,X))),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(mult(X2,mult(i(X2),i(X))),mult(X,mult(X3,asoc(X2,X,X3)))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
mult(X2,mult(i(X2),i(X))) = i(X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c265,plain,
mult(mult(X2,mult(i(X2),i(X))),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(i(X),mult(X,mult(X3,asoc(X2,X,X3)))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
mult(i(X),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(X3,asoc(X2,X,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c267,plain,
mult(mult(X2,mult(i(X2),i(X))),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(X3,asoc(X2,X,X3)),
inference(transitivity,[status(thm)],[c265,c266]) ).
cnf(c268,plain,
mult(mult(X2,i(mult(X2,X))),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(X3,asoc(X2,X,X3)),
inference(transitivity,[status(thm)],[c263,c267]) ).
cnf(c269,plain,
mult(mult(i(i(X2)),i(mult(X2,X))),mult(X,mult(X3,asoc(X2,X,X3)))) = mult(X3,asoc(X2,X,X3)),
inference(transitivity,[status(thm)],[c260,c268]) ).
cnf(c270,plain,
mult(mult(i(i(X2)),i(mult(X2,X))),mult(i(X2),mult(mult(X2,X),X3))) = mult(X3,asoc(X2,X,X3)),
inference(transitivity,[status(thm)],[c258,c269]) ).
cnf(c271,plain,
op_l(X3,mult(X2,X),i(X2)) = mult(X3,asoc(X2,X,X3)),
inference(transitivity,[status(thm)],[c233,c270]) ).
cnf(c272,plain,
op_l(X3,mult(rd(X2,X),X),i(rd(X2,X))) = mult(X3,asoc(rd(X2,X),X,X3)),
inference(substitution,[status(thm)],[c271]) ).
cnf(c273,plain,
mult(X3,asoc(rd(X2,X),X,X3)) = op_l(X3,mult(rd(X2,X),X),i(rd(X2,X))),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c275,plain,
op_l(X3,mult(rd(X2,X),X),i(rd(X2,X))) = op_l(X3,X2,i(rd(X2,X))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
op_l(X3,X2,i(rd(X2,X))) = op_l(X3,X2,rd(X,X2)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c277,plain,
op_l(X3,mult(rd(X2,X),X),i(rd(X2,X))) = op_l(X3,X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c275,c276]) ).
cnf(c278,plain,
mult(X3,asoc(rd(X2,X),X,X3)) = op_l(X3,X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c273,c277]) ).
cnf(c279,plain,
mult(i(X2),asoc(rd(X2,X),X,i(X2))) = op_l(i(X2),X2,rd(X,X2)),
inference(substitution,[status(thm)],[c278]) ).
cnf(c280,plain,
op_l(i(X2),X2,rd(X,X2)) = mult(i(X2),asoc(rd(X2,X),X,i(X2))),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c281,plain,
mult(op_l(i(X2),X2,rd(X,X2)),X2) = mult(mult(i(X2),asoc(rd(X2,X),X,i(X2))),X2),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
op_t(X4,asoc(X3,X2,X)) = mult(i(asoc(X3,X2,X)),mult(X4,asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c283,plain,
mult(mult(i(asoc(X3,X2,X)),X4),asoc(X3,X2,X)) = mult(i(asoc(X3,X2,X)),mult(X4,asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c243]) ).
cnf(c284,plain,
mult(i(asoc(X3,X2,X)),mult(X4,asoc(X3,X2,X))) = mult(mult(i(asoc(X3,X2,X)),X4),asoc(X3,X2,X)),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
mult(mult(i(asoc(X3,X2,X)),X4),asoc(X3,X2,X)) = op_l(X4,i(X4),asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c286,plain,
mult(mult(i(asoc(X3,X2,X)),i(X4)),mult(asoc(X3,X2,X),mult(X4,X5))) = op_l(X5,X4,asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c287,plain,
op_l(X5,X4,asoc(X3,X2,X)) = mult(mult(i(asoc(X3,X2,X)),i(X4)),mult(asoc(X3,X2,X),mult(X4,X5))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
i(mult(asoc(X3,X2,X),X4)) = mult(i(asoc(X3,X2,X)),i(X4)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c289,plain,
mult(i(asoc(X3,X2,X)),i(X4)) = i(mult(asoc(X3,X2,X),X4)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
mult(mult(i(asoc(X3,X2,X)),i(X4)),mult(asoc(X3,X2,X),mult(X4,X5))) = mult(i(mult(asoc(X3,X2,X),X4)),mult(asoc(X3,X2,X),mult(X4,X5))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
mult(mult(asoc(X5,X4,X3),X2),X) = mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c292,axiom,
asoc(asoc(A2,B2,C2),D2,E2) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21) ).
cnf(c293,plain,
asoc(asoc(X5,X4,X3),X2,X) = unit,
inference(substitution,[status(thm)],[c292]) ).
cnf(c294,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)) = mult(mult(asoc(X5,X4,X3),mult(X2,X)),unit),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),unit) = mult(asoc(X5,X4,X3),mult(X2,X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c296,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)) = mult(asoc(X5,X4,X3),mult(X2,X)),
inference(transitivity,[status(thm)],[c294,c295]) ).
cnf(c297,plain,
mult(mult(asoc(X5,X4,X3),X2),X) = mult(asoc(X5,X4,X3),mult(X2,X)),
inference(transitivity,[status(thm)],[c291,c296]) ).
cnf(c298,plain,
mult(mult(asoc(X3,X2,X),X4),X5) = mult(asoc(X3,X2,X),mult(X4,X5)),
inference(substitution,[status(thm)],[c297]) ).
cnf(c299,plain,
mult(asoc(X3,X2,X),mult(X4,X5)) = mult(mult(asoc(X3,X2,X),X4),X5),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
mult(i(mult(asoc(X3,X2,X),X4)),mult(asoc(X3,X2,X),mult(X4,X5))) = mult(i(mult(asoc(X3,X2,X),X4)),mult(mult(asoc(X3,X2,X),X4),X5)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
mult(i(mult(asoc(X3,X2,X),X4)),mult(mult(asoc(X3,X2,X),X4),X5)) = X5,
inference(substitution,[status(thm)],[c6]) ).
cnf(c302,plain,
mult(i(mult(asoc(X3,X2,X),X4)),mult(asoc(X3,X2,X),mult(X4,X5))) = X5,
inference(transitivity,[status(thm)],[c300,c301]) ).
cnf(c303,plain,
mult(mult(i(asoc(X3,X2,X)),i(X4)),mult(asoc(X3,X2,X),mult(X4,X5))) = X5,
inference(transitivity,[status(thm)],[c290,c302]) ).
cnf(c304,plain,
op_l(X5,X4,asoc(X3,X2,X)) = X5,
inference(transitivity,[status(thm)],[c287,c303]) ).
cnf(c305,plain,
op_l(X4,i(X4),asoc(X3,X2,X)) = X4,
inference(substitution,[status(thm)],[c304]) ).
cnf(c306,plain,
mult(mult(i(asoc(X3,X2,X)),X4),asoc(X3,X2,X)) = X4,
inference(transitivity,[status(thm)],[c285,c305]) ).
cnf(c307,plain,
mult(i(asoc(X3,X2,X)),mult(X4,asoc(X3,X2,X))) = X4,
inference(transitivity,[status(thm)],[c284,c306]) ).
cnf(c308,plain,
op_t(X4,asoc(X3,X2,X)) = X4,
inference(transitivity,[status(thm)],[c282,c307]) ).
cnf(c309,plain,
X4 = op_t(X4,asoc(X3,X2,X)),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
mult(asoc(X3,X2,X),X4) = mult(asoc(X3,X2,X),op_t(X4,asoc(X3,X2,X))),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
mult(asoc(X3,X2,X),op_t(X4,asoc(X3,X2,X))) = mult(X4,asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c312,plain,
mult(asoc(X3,X2,X),X4) = mult(X4,asoc(X3,X2,X)),
inference(transitivity,[status(thm)],[c310,c311]) ).
cnf(c313,plain,
mult(X4,asoc(X3,X2,X)) = mult(asoc(X3,X2,X),X4),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
mult(mult(X5,asoc(X4,X3,X2)),X) = mult(mult(asoc(X4,X3,X2),X5),X),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
mult(mult(asoc(X4,X3,X2),X5),X) = mult(mult(asoc(X4,X3,X2),mult(X5,X)),asoc(asoc(X4,X3,X2),X5,X)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c316,plain,
asoc(asoc(X4,X3,X2),X5,X) = unit,
inference(substitution,[status(thm)],[c292]) ).
cnf(c317,plain,
mult(mult(asoc(X4,X3,X2),mult(X5,X)),asoc(asoc(X4,X3,X2),X5,X)) = mult(mult(asoc(X4,X3,X2),mult(X5,X)),unit),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
mult(mult(asoc(X4,X3,X2),mult(X5,X)),unit) = mult(asoc(X4,X3,X2),mult(X5,X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c319,plain,
mult(asoc(X4,X3,X2),mult(X5,X)) = mult(mult(X5,X),asoc(X4,X3,X2)),
inference(substitution,[status(thm)],[c312]) ).
cnf(c320,plain,
mult(mult(X5,X),asoc(X4,X3,X2)) = mult(X5,mult(X,asoc(X4,X3,X2))),
inference(substitution,[status(thm)],[c243]) ).
cnf(c321,plain,
mult(asoc(X4,X3,X2),mult(X5,X)) = mult(X5,mult(X,asoc(X4,X3,X2))),
inference(transitivity,[status(thm)],[c319,c320]) ).
cnf(c322,plain,
mult(mult(asoc(X4,X3,X2),mult(X5,X)),unit) = mult(X5,mult(X,asoc(X4,X3,X2))),
inference(transitivity,[status(thm)],[c318,c321]) ).
cnf(c323,plain,
mult(mult(asoc(X4,X3,X2),mult(X5,X)),asoc(asoc(X4,X3,X2),X5,X)) = mult(X5,mult(X,asoc(X4,X3,X2))),
inference(transitivity,[status(thm)],[c317,c322]) ).
cnf(c324,plain,
mult(mult(asoc(X4,X3,X2),X5),X) = mult(X5,mult(X,asoc(X4,X3,X2))),
inference(transitivity,[status(thm)],[c315,c323]) ).
cnf(c325,plain,
mult(mult(X5,asoc(X4,X3,X2)),X) = mult(X5,mult(X,asoc(X4,X3,X2))),
inference(transitivity,[status(thm)],[c314,c324]) ).
cnf(c326,plain,
mult(mult(i(X2),asoc(rd(X2,X),X,i(X2))),X2) = mult(i(X2),mult(X2,asoc(rd(X2,X),X,i(X2)))),
inference(substitution,[status(thm)],[c325]) ).
cnf(c327,plain,
mult(i(X2),mult(X2,asoc(rd(X2,X),X,i(X2)))) = asoc(rd(X2,X),X,i(X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c328,plain,
mult(X2,mult(i(X2),asoc(rd(X2,X),X,i(X2)))) = asoc(rd(X2,X),X,i(X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c329,plain,
asoc(rd(X2,X),X,i(X2)) = mult(X2,mult(i(X2),asoc(rd(X2,X),X,i(X2)))),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
mult(i(X2),asoc(rd(X2,X),X,i(X2))) = op_l(i(X2),X2,rd(X,X2)),
inference(substitution,[status(thm)],[c278]) ).
cnf(c331,plain,
mult(X2,mult(i(X2),asoc(rd(X2,X),X,i(X2)))) = mult(X2,op_l(i(X2),X2,rd(X,X2))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c333,plain,
op_l(i(X),X,X2) = op_l(i(X),i(i(X)),X2),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
mult(X,op_l(i(X),X,X2)) = mult(X,op_l(i(X),i(i(X)),X2)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c336,plain,
op_k(mult(i(X),X2),X) = op_k(mult(i(X),X2),i(i(X))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
mult(X2,op_k(mult(i(X),X2),X)) = mult(X2,op_k(mult(i(X),X2),i(i(X)))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
mult(i(X),mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c339,plain,
X2 = mult(i(X),mult(X,X2)),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
mult(X2,op_k(mult(X,X2),i(X))) = mult(mult(i(X),mult(X,X2)),op_k(mult(X,X2),i(X))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
mult(mult(X,X2),i(X)) = mult(mult(i(X),mult(X,X2)),op_k(mult(X,X2),i(X))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c342,plain,
mult(mult(i(X),mult(X,X2)),op_k(mult(X,X2),i(X))) = mult(mult(X,X2),i(X)),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
mult(mult(i(X),mult(X,X2)),op_k(mult(X,X2),i(X))) = op_l(X2,i(X2),i(X)),
inference(transitivity,[status(thm)],[c342,c135]) ).
cnf(c344,plain,
mult(X2,op_k(mult(X,X2),i(X))) = op_l(X2,i(X2),i(X)),
inference(transitivity,[status(thm)],[c340,c343]) ).
cnf(c345,plain,
mult(X2,op_k(mult(i(X),X2),i(i(X)))) = op_l(X2,i(X2),i(i(X))),
inference(substitution,[status(thm)],[c344]) ).
cnf(c346,plain,
op_l(X2,i(X2),i(i(X))) = op_l(X2,i(X2),X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c347,plain,
mult(X2,op_k(mult(i(X),X2),i(i(X)))) = op_l(X2,i(X2),X),
inference(transitivity,[status(thm)],[c345,c346]) ).
cnf(c348,plain,
mult(X2,op_k(mult(i(X),X2),X)) = op_l(X2,i(X2),X),
inference(transitivity,[status(thm)],[c337,c347]) ).
cnf(c349,plain,
mult(i(X),op_k(mult(i(X2),i(X)),X2)) = op_l(i(X),i(i(X)),X2),
inference(substitution,[status(thm)],[c348]) ).
cnf(c350,plain,
op_l(i(X),i(i(X)),X2) = mult(i(X),op_k(mult(i(X2),i(X)),X2)),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
mult(X,op_l(i(X),i(i(X)),X2)) = mult(X,mult(i(X),op_k(mult(i(X2),i(X)),X2))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
mult(X,mult(i(X),op_k(mult(i(X2),i(X)),X2))) = op_k(mult(i(X2),i(X)),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c353,plain,
mult(X,op_l(i(X),i(i(X)),X2)) = op_k(mult(i(X2),i(X)),X2),
inference(transitivity,[status(thm)],[c351,c352]) ).
cnf(c354,plain,
mult(X,op_l(i(X),X,X2)) = op_k(mult(i(X2),i(X)),X2),
inference(transitivity,[status(thm)],[c334,c353]) ).
cnf(c355,plain,
mult(X2,op_l(i(X2),X2,rd(X,X2))) = op_k(mult(i(rd(X,X2)),i(X2)),rd(X,X2)),
inference(substitution,[status(thm)],[c354]) ).
cnf(c356,plain,
i(rd(X,X2)) = rd(X2,X),
inference(substitution,[status(thm)],[c45]) ).
cnf(c357,plain,
mult(i(rd(X,X2)),i(X2)) = mult(rd(X2,X),i(X2)),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
op_k(mult(i(rd(X,X2)),i(X2)),rd(X,X2)) = op_k(mult(rd(X2,X),i(X2)),rd(X,X2)),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
op_k(mult(rd(X2,X),i(X2)),rd(X,X2)) = op_k(i(X),rd(X,X2)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c360,plain,
op_k(mult(i(rd(X,X2)),i(X2)),rd(X,X2)) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c358,c359]) ).
cnf(c361,plain,
mult(X2,op_l(i(X2),X2,rd(X,X2))) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c355,c360]) ).
cnf(c362,plain,
mult(X2,mult(i(X2),asoc(rd(X2,X),X,i(X2)))) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c331,c361]) ).
cnf(c363,plain,
asoc(rd(X2,X),X,i(X2)) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c329,c362]) ).
cnf(c364,plain,
mult(i(X2),mult(X2,asoc(rd(X2,X),X,i(X2)))) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c327,c363]) ).
cnf(c365,plain,
mult(mult(i(X2),asoc(rd(X2,X),X,i(X2))),X2) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c326,c364]) ).
cnf(c366,plain,
mult(op_l(i(X2),X2,rd(X,X2)),X2) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c281,c365]) ).
cnf(c367,plain,
op_k(i(rd(X,X2)),mult(rd(X,X2),X2)) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c231,c366]) ).
cnf(c368,plain,
op_k(rd(X2,X),mult(rd(X,X2),X2)) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c229,c367]) ).
cnf(c369,plain,
op_k(rd(X2,X),X) = op_k(i(X),rd(X,X2)),
inference(transitivity,[status(thm)],[c226,c368]) ).
cnf(c370,plain,
op_k(rd(X,X2),X2) = op_k(i(X2),rd(X2,X)),
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
i(op_k(rd(X,X2),X2)) = i(op_k(i(X2),rd(X2,X))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
i(op_k(i(X2),rd(X2,X))) = op_k(i(i(X2)),i(rd(X2,X))),
inference(substitution,[status(thm)],[c215]) ).
cnf(c373,plain,
op_k(i(i(X2)),i(rd(X2,X))) = op_k(X2,i(rd(X2,X))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c374,plain,
op_k(X2,i(rd(X2,X))) = op_k(X2,rd(X,X2)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c375,plain,
op_k(i(i(X2)),i(rd(X2,X))) = op_k(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c373,c374]) ).
cnf(c376,plain,
i(op_k(i(X2),rd(X2,X))) = op_k(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c372,c375]) ).
cnf(c377,plain,
i(op_k(rd(X,X2),X2)) = op_k(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c371,c376]) ).
cnf(c378,plain,
op_k(i(rd(X,X2)),i(X2)) = op_k(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c223,c377]) ).
cnf(c379,plain,
op_k(rd(X2,X),i(X2)) = op_k(X2,rd(X,X2)),
inference(transitivity,[status(thm)],[c221,c378]) ).
cnf(c380,plain,
op_k(rd(X2,mult(X,X2)),i(X2)) = op_k(X2,rd(mult(X,X2),X2)),
inference(substitution,[status(thm)],[c379]) ).
cnf(c381,plain,
rd(mult(X,X2),X2) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c382,plain,
op_k(X2,rd(mult(X,X2),X2)) = op_k(X2,X),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
op_k(rd(X2,mult(X,X2)),i(X2)) = op_k(X2,X),
inference(transitivity,[status(thm)],[c380,c382]) ).
cnf(c384,plain,
op_k(i(X),i(X2)) = op_k(X2,X),
inference(transitivity,[status(thm)],[c218,c383]) ).
cnf(c385,plain,
op_k(X2,X) = op_k(i(X),i(X2)),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
op_t(X3,op_k(X2,X)) = op_t(X3,op_k(i(X),i(X2))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
rd(X,mult(X2,X)) = i(X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c388,plain,
i(X2) = rd(X,mult(X2,X)),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
op_k(i(X),i(X2)) = op_k(i(X),rd(X,mult(X2,X))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
op_t(X3,op_k(i(X),i(X2))) = op_t(X3,op_k(i(X),rd(X,mult(X2,X)))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
asoc(rd(X,X2),X2,i(X)) = op_k(i(X2),rd(X2,X)),
inference(substitution,[status(thm)],[c363]) ).
cnf(c392,plain,
op_k(i(X2),rd(X2,X)) = asoc(rd(X,X2),X2,i(X)),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
op_t(X3,op_k(i(X2),rd(X2,X))) = op_t(X3,asoc(rd(X,X2),X2,i(X))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
op_t(X3,asoc(rd(X,X2),X2,i(X))) = X3,
inference(substitution,[status(thm)],[c308]) ).
cnf(c395,plain,
op_t(X3,op_k(i(X2),rd(X2,X))) = X3,
inference(transitivity,[status(thm)],[c393,c394]) ).
cnf(c396,plain,
op_t(X3,op_k(i(X),rd(X,mult(X2,X)))) = X3,
inference(substitution,[status(thm)],[c395]) ).
cnf(c397,plain,
op_t(X3,op_k(i(X),i(X2))) = X3,
inference(transitivity,[status(thm)],[c390,c396]) ).
cnf(c398,plain,
op_t(X3,op_k(X2,X)) = X3,
inference(transitivity,[status(thm)],[c386,c397]) ).
cnf(c399,plain,
op_t(X3,op_k(i(X2),i(X))) = X3,
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
op_t(X3,i(op_k(X2,X))) = X3,
inference(transitivity,[status(thm)],[c216,c399]) ).
cnf(c401,plain,
X3 = op_t(X3,i(op_k(X2,X))),
inference(symmetry,[status(thm)],[c400]) ).
cnf(c402,plain,
mult(i(op_k(X2,X)),X3) = mult(i(op_k(X2,X)),op_t(X3,i(op_k(X2,X)))),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
mult(i(op_k(X2,X)),op_t(X3,i(op_k(X2,X)))) = mult(X3,i(op_k(X2,X))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c404,plain,
mult(i(op_k(X2,X)),X3) = mult(X3,i(op_k(X2,X))),
inference(transitivity,[status(thm)],[c402,c403]) ).
cnf(c405,plain,
mult(i(op_k(X3,X2)),X) = mult(X,i(op_k(X3,X2))),
inference(substitution,[status(thm)],[c404]) ).
cnf(c406,plain,
mult(X,i(op_k(X3,X2))) = mult(i(op_k(X3,X2)),X),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
op_k(op_k(X3,X2),mult(X,i(op_k(X3,X2)))) = op_k(op_k(X3,X2),mult(i(op_k(X3,X2)),X)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
op_t(rd(X3,op_k(X2,X)),op_k(X2,X)) = rd(X3,op_k(X2,X)),
inference(substitution,[status(thm)],[c398]) ).
cnf(c409,plain,
rd(X3,op_k(X2,X)) = op_t(rd(X3,op_k(X2,X)),op_k(X2,X)),
inference(symmetry,[status(thm)],[c408]) ).
cnf(c410,plain,
op_t(rd(X3,op_k(X2,X)),op_k(X2,X)) = mult(i(op_k(X2,X)),X3),
inference(substitution,[status(thm)],[c76]) ).
cnf(c411,plain,
rd(X3,op_k(X2,X)) = mult(i(op_k(X2,X)),X3),
inference(transitivity,[status(thm)],[c409,c410]) ).
cnf(c412,plain,
rd(X,op_k(X3,X2)) = mult(i(op_k(X3,X2)),X),
inference(substitution,[status(thm)],[c411]) ).
cnf(c413,plain,
mult(i(op_k(X3,X2)),X) = rd(X,op_k(X3,X2)),
inference(symmetry,[status(thm)],[c412]) ).
cnf(c414,plain,
op_k(op_k(X3,X2),mult(i(op_k(X3,X2)),X)) = op_k(op_k(X3,X2),rd(X,op_k(X3,X2))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c416,plain,
X2 = mult(rd(X2,X),X),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
mult(X2,op_k(X,rd(X2,X))) = mult(mult(rd(X2,X),X),op_k(X,rd(X2,X))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
mult(X,rd(X2,X)) = mult(mult(rd(X2,X),X),op_k(X,rd(X2,X))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c419,plain,
mult(mult(rd(X2,X),X),op_k(X,rd(X2,X))) = mult(X,rd(X2,X)),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
mult(X2,op_k(X,rd(X2,X))) = mult(X,rd(X2,X)),
inference(transitivity,[status(thm)],[c417,c419]) ).
cnf(c421,plain,
mult(X,rd(X2,X)) = mult(X2,op_k(X,rd(X2,X))),
inference(symmetry,[status(thm)],[c420]) ).
cnf(c422,plain,
mult(i(X2),mult(X,rd(X2,X))) = mult(i(X2),mult(X2,op_k(X,rd(X2,X)))),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
mult(i(X2),mult(X2,op_k(X,rd(X2,X)))) = op_k(X,rd(X2,X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c424,plain,
mult(i(X2),mult(X,rd(X2,X))) = op_k(X,rd(X2,X)),
inference(transitivity,[status(thm)],[c422,c423]) ).
cnf(c425,plain,
mult(i(X),mult(op_k(X3,X2),rd(X,op_k(X3,X2)))) = op_k(op_k(X3,X2),rd(X,op_k(X3,X2))),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
op_k(op_k(X3,X2),rd(X,op_k(X3,X2))) = mult(i(X),mult(op_k(X3,X2),rd(X,op_k(X3,X2)))),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
X3 = op_t(X3,op_k(X2,X)),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c428,plain,
mult(op_k(X2,X),X3) = mult(op_k(X2,X),op_t(X3,op_k(X2,X))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
mult(op_k(X2,X),op_t(X3,op_k(X2,X))) = mult(X3,op_k(X2,X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c430,plain,
mult(op_k(X2,X),X3) = mult(X3,op_k(X2,X)),
inference(transitivity,[status(thm)],[c428,c429]) ).
cnf(c431,plain,
mult(op_k(X3,X2),rd(X,op_k(X3,X2))) = mult(rd(X,op_k(X3,X2)),op_k(X3,X2)),
inference(substitution,[status(thm)],[c430]) ).
cnf(c432,plain,
mult(i(X),mult(op_k(X3,X2),rd(X,op_k(X3,X2)))) = mult(i(X),mult(rd(X,op_k(X3,X2)),op_k(X3,X2))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
mult(rd(X,op_k(X3,X2)),op_k(X3,X2)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c434,plain,
mult(i(X),mult(rd(X,op_k(X3,X2)),op_k(X3,X2))) = mult(i(X),X),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c436,plain,
mult(i(X),mult(rd(X,op_k(X3,X2)),op_k(X3,X2))) = unit,
inference(transitivity,[status(thm)],[c434,c435]) ).
cnf(c437,plain,
mult(i(X),mult(op_k(X3,X2),rd(X,op_k(X3,X2)))) = unit,
inference(transitivity,[status(thm)],[c432,c436]) ).
cnf(c438,plain,
op_k(op_k(X3,X2),rd(X,op_k(X3,X2))) = unit,
inference(transitivity,[status(thm)],[c426,c437]) ).
cnf(c439,plain,
op_k(op_k(X3,X2),mult(i(op_k(X3,X2)),X)) = unit,
inference(transitivity,[status(thm)],[c414,c438]) ).
cnf(c440,plain,
op_k(op_k(X3,X2),mult(X,i(op_k(X3,X2)))) = unit,
inference(transitivity,[status(thm)],[c407,c439]) ).
cnf(c441,plain,
op_k(op_k(X3,X2),mult(rd(X,i(op_k(X3,X2))),i(op_k(X3,X2)))) = unit,
inference(substitution,[status(thm)],[c440]) ).
cnf(c442,plain,
op_k(op_k(X3,X2),X) = unit,
inference(transitivity,[status(thm)],[c5,c441]) ).
cnf(c443,plain,
op_k(op_k(a,b),c) = unit,
inference(substitution,[status(thm)],[c442]) ).
cnf(c444,plain,
$false,
inference(resolution,[status(thm)],[c1,c443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP728-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 10:42:19 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.26/3.21 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 20.26/3.21
% 20.26/3.21 % SZS status Unsatisfiable
% 20.26/3.21
% 20.26/3.24 % SZS output start CNFRefutation
% See solution above
% 22.84/3.47
% 22.84/3.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------