%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP688-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:43 AM UTC 2025
% Result : Unsatisfiable 74.47s 74.60s
% Output : CNFRefutation 74.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of clauses : 172 ( 172 unt; 0 nHn; 37 RR)
% Number of literals : 172 ( 171 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 273 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(op_c,op_d) != mult(op_d,op_c),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c06) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c4,plain,
rd(X,unit) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c6,plain,
rd(X,X) = unit,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c8,plain,
ld(unit,X) = X,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c9,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c10,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c11,axiom,
mult(op_d,mult(op_d,op_d)) = unit,
file('theBenchmark.p',c11) ).
cnf(c12,plain,
mult(op_d,op_d) = ld(op_d,unit),
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c14,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c15,axiom,
i(mult(X,Y)) = mult(i(X),i(Y)),
file('theBenchmark.p',c09) ).
cnf(c16,plain,
mult(i(X),i(Y)) = i(mult(X,Y)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,axiom,
mult(i(X),mult(X,Y)) = Y,
file('theBenchmark.p',c08) ).
cnf(c18,plain,
ld(op_d,unit) = i(op_d),
inference(equational,[status(thm)],[c1,c11,c12,c17]) ).
cnf(c19,plain,
mult(i(X),X) = unit,
inference(equational,[status(thm)],[c1,c17]) ).
cnf(c20,plain,
i(unit) = unit,
inference(equational,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
i(i(X)) = X,
inference(equational,[status(thm)],[c1,c17,c19]) ).
cnf(c23,plain,
mult(i(X),Y) = ld(X,Y),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c24,plain,
ld(X,unit) = i(X),
inference(equational,[status(thm)],[c1,c23]) ).
cnf(c25,plain,
ld(i(X),Y) = mult(X,Y),
inference(equational,[status(thm)],[c9,c17]) ).
cnf(c26,plain,
mult(X,i(X)) = unit,
inference(equational,[status(thm)],[c10,c25]) ).
cnf(c27,plain,
rd(X,mult(Y,X)) = i(Y),
inference(equational,[status(thm)],[c5,c17]) ).
cnf(c28,plain,
i(rd(X,Y)) = rd(Y,X),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c29,plain,
rd(op_d,i(op_d)) = i(op_d),
inference(equational,[status(thm)],[c12,c18,c27]) ).
cnf(c30,plain,
i(mult(X,Y)) = ld(X,i(Y)),
inference(equational,[status(thm)],[c16,c23]) ).
cnf(c32,plain,
rd(i(op_d),op_d) = op_d,
inference(equational,[status(thm)],[c21,c28,c29]) ).
cnf(c33,plain,
rd(ld(X,Y),Y) = i(X),
inference(equational,[status(thm)],[c5,c23]) ).
cnf(c34,plain,
mult(X,i(Y)) = i(ld(X,Y)),
inference(equational,[status(thm)],[c23,c25,c30]) ).
cnf(c35,plain,
i(ld(X,i(Y))) = mult(X,Y),
inference(equational,[status(thm)],[c21,c30]) ).
cnf(c36,axiom,
mult(op_c,mult(op_c,mult(op_c,op_c))) = unit,
file('theBenchmark.p',c10) ).
cnf(c37,plain,
mult(op_c,mult(op_c,op_c)) = i(op_c),
inference(equational,[status(thm)],[c17,c23,c24,c36]) ).
cnf(c38,plain,
ld(op_c,i(op_c)) = mult(op_c,op_c),
inference(equational,[status(thm)],[c16,c17,c30,c37]) ).
cnf(c40,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c25,c28]) ).
cnf(c42,plain,
ld(rd(X,Y),i(Y)) = i(X),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c43,plain,
rd(i(X),i(Y)) = rd(Y,X),
inference(equational,[status(thm)],[c28,c33,c42]) ).
cnf(c44,plain,
rd(X,i(Y)) = rd(Y,i(X)),
inference(equational,[status(thm)],[c21,c43]) ).
cnf(c45,plain,
rd(i(X),Y) = rd(i(Y),X),
inference(equational,[status(thm)],[c21,c43]) ).
cnf(c46,plain,
ld(X,i(ld(X,Y))) = i(Y),
inference(equational,[status(thm)],[c7,c30]) ).
cnf(c47,axiom,
mult(X,mult(Y,mult(X,Z))) = mult(mult(X,mult(Y,X)),Z),
file('theBenchmark.p',c07) ).
cnf(c48,plain,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c2,c48]) ).
cnf(c50,plain,
mult(op_d,mult(op_d,X)) = ld(op_d,X),
inference(equational,[status(thm)],[c12,c18,c23,c49]) ).
cnf(c51,plain,
ld(op_d,ld(op_d,X)) = mult(op_d,X),
inference(equational,[status(thm)],[c17,c23,c50]) ).
cnf(c52,plain,
mult(ld(X,i(X)),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c23,c49]) ).
cnf(c53,plain,
mult(op_c,mult(op_c,X)) = ld(op_c,ld(op_c,X)),
inference(equational,[status(thm)],[c38,c49,c52]) ).
cnf(c54,plain,
rd(mult(X,mult(X,Y)),Y) = mult(X,X),
inference(equational,[status(thm)],[c5,c49]) ).
cnf(c55,plain,
rd(X,i(X)) = mult(X,X),
inference(equational,[status(thm)],[c1,c26,c54]) ).
cnf(c56,plain,
rd(i(X),X) = ld(X,i(X)),
inference(equational,[status(thm)],[c16,c19,c23,c24,c30,c54]) ).
cnf(c58,plain,
ld(mult(X,X),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c40,c52,c55,c56]) ).
cnf(c60,plain,
ld(ld(X,i(Y)),Z) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c25,c30]) ).
cnf(c61,plain,
mult(ld(X,i(Y)),Z) = ld(mult(X,Y),Z),
inference(equational,[status(thm)],[c23,c30]) ).
cnf(c62,plain,
rd(X,mult(Y,mult(Y,X))) = ld(Y,i(Y)),
inference(equational,[status(thm)],[c27,c30,c49]) ).
cnf(c64,plain,
i(ld(rd(X,Y),Z)) = ld(rd(Y,X),i(Z)),
inference(equational,[status(thm)],[c16,c28,c40]) ).
cnf(c67,plain,
i(ld(X,rd(Y,Z))) = mult(X,rd(Z,Y)),
inference(equational,[status(thm)],[c28,c35]) ).
cnf(c70,plain,
mult(mult(X,ld(Y,X)),Z) = mult(X,ld(Y,mult(X,Z))),
inference(equational,[status(thm)],[c23,c48]) ).
cnf(c71,plain,
mult(X,ld(Y,i(Z))) = i(ld(X,mult(Y,Z))),
inference(equational,[status(thm)],[c35]) ).
cnf(c72,plain,
ld(op_c,ld(op_c,ld(op_c,X))) = mult(op_c,X),
inference(equational,[status(thm)],[c17,c23,c38,c70]) ).
cnf(c73,plain,
rd(i(X),rd(Y,Z)) = rd(rd(Z,Y),X),
inference(equational,[status(thm)],[c28,c43]) ).
cnf(c75,plain,
i(ld(op_c,ld(op_c,X))) = ld(op_c,ld(op_c,i(X))),
inference(equational,[status(thm)],[c30,c53]) ).
cnf(c76,plain,
mult(ld(X,ld(Y,i(X))),Z) = ld(X,ld(Y,ld(X,Z))),
inference(equational,[status(thm)],[c16,c23,c30,c48]) ).
cnf(c80,plain,
rd(X,ld(rd(X,Y),Y)) = ld(rd(Y,X),rd(X,Y)),
inference(equational,[status(thm)],[c3,c28,c40,c62]) ).
cnf(c81,plain,
rd(i(X),mult(Y,Z)) = rd(ld(Y,i(Z)),X),
inference(equational,[status(thm)],[c35,c43]) ).
cnf(c82,plain,
rd(mult(X,Y),i(Z)) = rd(Z,ld(X,i(Y))),
inference(equational,[status(thm)],[c35,c43]) ).
cnf(c83,plain,
i(ld(X,mult(op_c,op_c))) = mult(X,mult(op_c,op_c)),
inference(equational,[status(thm)],[c38,c71]) ).
cnf(c84,plain,
i(ld(X,ld(Y,i(Z)))) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c34,c35]) ).
cnf(c85,plain,
rd(mult(X,mult(Y,mult(X,Z))),Z) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c5,c48]) ).
cnf(c86,plain,
ld(X,i(ld(Y,X))) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c1,c16,c19,c23,c30,c34,c85]) ).
cnf(c87,plain,
mult(X,ld(Y,X)) = rd(X,ld(X,Y)),
inference(equational,[status(thm)],[c28,c35,c86]) ).
cnf(c90,plain,
rd(X,ld(X,i(Y))) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c1,c26,c82,c85]) ).
cnf(c91,plain,
rd(i(X),mult(X,Y)) = ld(X,ld(Y,i(X))),
inference(equational,[status(thm)],[c25,c30,c81,c86]) ).
cnf(c92,plain,
rd(ld(X,rd(X,Y)),X) = ld(X,i(Y)),
inference(equational,[status(thm)],[c14,c86]) ).
cnf(c93,plain,
ld(mult(X,Y),X) = ld(X,rd(X,Y)),
inference(equational,[status(thm)],[c3,c61,c92]) ).
cnf(c94,plain,
mult(X,rd(ld(X,Y),X)) = i(ld(Y,X)),
inference(equational,[status(thm)],[c7,c86]) ).
cnf(c96,plain,
ld(X,rd(X,ld(X,Y))) = ld(Y,X),
inference(equational,[status(thm)],[c21,c28,c30,c94]) ).
cnf(c98,plain,
ld(X,rd(X,i(Y))) = mult(ld(X,Y),X),
inference(equational,[status(thm)],[c25,c46,c96]) ).
cnf(c99,plain,
mult(X,mult(ld(X,Y),X)) = rd(X,i(Y)),
inference(equational,[status(thm)],[c46,c90]) ).
cnf(c100,plain,
mult(X,rd(i(X),Y)) = ld(ld(X,Y),i(X)),
inference(equational,[status(thm)],[c23,c25,c93]) ).
cnf(c101,plain,
mult(X,ld(rd(X,Y),mult(X,Z))) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c3,c40,c48]) ).
cnf(c102,plain,
ld(X,rd(Y,i(X))) = mult(ld(X,Y),X),
inference(equational,[status(thm)],[c19,c23,c24,c28,c101]) ).
cnf(c103,plain,
ld(rd(X,Y),mult(X,Z)) = ld(X,mult(mult(X,Y),Z)),
inference(equational,[status(thm)],[c9,c101]) ).
cnf(c104,plain,
mult(X,ld(Y,mult(X,Z))) = ld(rd(ld(X,Y),X),Z),
inference(equational,[status(thm)],[c13,c40,c87,c101]) ).
cnf(c105,plain,
mult(mult(X,Y),ld(X,Z)) = mult(X,ld(rd(X,Y),Z)),
inference(equational,[status(thm)],[c7,c101]) ).
cnf(c106,plain,
ld(mult(X,Y),mult(X,Z)) = ld(X,ld(rd(Y,X),Z)),
inference(equational,[status(thm)],[c16,c23,c25,c30,c43,c61,c105]) ).
cnf(c108,plain,
ld(op_d,mult(mult(op_d,X),op_d)) = ld(rd(op_d,X),i(op_d)),
inference(equational,[status(thm)],[c12,c18,c103]) ).
cnf(c110,plain,
ld(X,ld(rd(i(X),Y),Z)) = mult(ld(X,Y),mult(X,Z)),
inference(equational,[status(thm)],[c17,c23,c101]) ).
cnf(c114,plain,
ld(rd(X,Y),ld(rd(Y,X),Z)) = Z,
inference(equational,[status(thm)],[c17,c28,c40]) ).
cnf(c115,plain,
rd(i(op_d),ld(op_d,ld(X,op_d))) = mult(op_d,mult(X,op_d)),
inference(equational,[status(thm)],[c12,c18,c34,c45,c85]) ).
cnf(c133,plain,
rd(i(X),mult(op_c,op_c)) = rd(mult(op_c,op_c),X),
inference(equational,[status(thm)],[c38,c81]) ).
cnf(c136,plain,
rd(X,ld(X,rd(mult(X,Y),Z))) = rd(mult(X,Z),Y),
inference(equational,[status(thm)],[c3,c40,c85,c87]) ).
cnf(c137,plain,
ld(rd(mult(X,Y),Z),X) = ld(X,rd(mult(X,Z),Y)),
inference(equational,[status(thm)],[c14,c136]) ).
cnf(c138,plain,
rd(mult(X,Y),ld(X,Z)) = rd(X,ld(X,rd(Z,Y))),
inference(equational,[status(thm)],[c7,c136]) ).
cnf(c139,plain,
ld(rd(X,ld(Y,Z)),Y) = ld(Y,rd(Z,ld(Y,X))),
inference(equational,[status(thm)],[c23,c25,c28,c30,c35,c40,c137]) ).
cnf(c140,plain,
rd(ld(X,rd(Y,Z)),X) = rd(ld(X,Y),mult(X,Z)),
inference(equational,[status(thm)],[c28,c138]) ).
cnf(c154,plain,
rd(ld(X,mult(Y,Z)),mult(X,Z)) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c16,c17,c23,c30,c34,c85,c86]) ).
cnf(c155,plain,
rd(ld(X,i(op_d)),mult(X,op_d)) = rd(ld(X,op_d),X),
inference(equational,[status(thm)],[c12,c18,c154]) ).
cnf(c160,plain,
ld(rd(op_d,i(X)),i(op_d)) = ld(op_d,ld(ld(op_d,X),op_d)),
inference(equational,[status(thm)],[c23,c34,c108]) ).
cnf(c161,plain,
mult(X,ld(Y,ld(Y,X))) = rd(X,ld(X,mult(Y,Y))),
inference(equational,[status(thm)],[c58,c87]) ).
cnf(c162,plain,
mult(ld(X,Y),ld(X,Y)) = rd(ld(X,mult(Y,Y)),X),
inference(equational,[status(thm)],[c34,c55,c140]) ).
cnf(c168,plain,
ld(rd(X,rd(Y,Z)),rd(Z,Y)) = i(X),
inference(equational,[status(thm)],[c28,c42]) ).
cnf(c170,plain,
rd(X,ld(Y,ld(Z,ld(Y,X)))) = mult(Y,mult(Z,Y)),
inference(equational,[status(thm)],[c27,c76,c84]) ).
cnf(c174,plain,
rd(X,ld(Y,mult(Z,ld(Y,X)))) = rd(Y,ld(Y,Z)),
inference(equational,[status(thm)],[c23,c25,c87,c170]) ).
cnf(c176,plain,
ld(rd(ld(X,Y),X),ld(X,Z)) = mult(X,ld(Y,Z)),
inference(equational,[status(thm)],[c7,c104]) ).
cnf(c177,plain,
ld(X,ld(rd(ld(X,Y),X),Z)) = ld(Y,mult(X,Z)),
inference(equational,[status(thm)],[c9,c104]) ).
cnf(c185,plain,
ld(rd(X,i(Y)),mult(Y,Z)) = ld(Y,ld(ld(Y,X),Z)),
inference(equational,[status(thm)],[c5,c102,c177]) ).
cnf(c186,plain,
rd(X,ld(X,ld(Y,i(Z)))) = mult(X,mult(mult(Y,Z),X)),
inference(equational,[status(thm)],[c61,c170,c174]) ).
cnf(c187,plain,
mult(mult(X,Y),mult(X,Y)) = mult(X,mult(Y,mult(Y,X))),
inference(equational,[status(thm)],[c30,c49,c55,c56,c138,c186]) ).
cnf(c188,plain,
ld(rd(i(X),Y),ld(Y,Z)) = mult(Y,mult(ld(Y,X),Z)),
inference(equational,[status(thm)],[c25,c46,c176]) ).
cnf(c191,plain,
mult(ld(X,ld(Y,i(Z))),W) = ld(mult(X,mult(Y,Z)),W),
inference(equational,[status(thm)],[c30,c61]) ).
cnf(c192,plain,
mult(ld(X,mult(op_c,op_c)),Y) = ld(mult(X,mult(op_c,op_c)),Y),
inference(equational,[status(thm)],[c38,c191]) ).
cnf(c195,plain,
mult(X,ld(rd(X,i(Y)),Z)) = ld(ld(X,Y),ld(X,Z)),
inference(equational,[status(thm)],[c23,c34,c105]) ).
cnf(c197,plain,
mult(X,mult(ld(X,Y),mult(X,Z))) = ld(rd(i(X),Y),Z),
inference(equational,[status(thm)],[c7,c110]) ).
cnf(c199,plain,
rd(ld(X,rd(X,Y)),mult(X,Y)) = ld(mult(X,Y),i(Y)),
inference(equational,[status(thm)],[c9,c86,c93]) ).
cnf(c208,plain,
rd(ld(rd(X,Y),mult(Z,Y)),X) = ld(rd(X,Y),mult(Z,rd(Y,X))),
inference(equational,[status(thm)],[c3,c40,c85]) ).
cnf(c209,plain,
ld(rd(X,Y),ld(Y,rd(Y,X))) = rd(rd(Y,X),X),
inference(equational,[status(thm)],[c19,c23,c24,c28,c208]) ).
cnf(c215,plain,
ld(rd(X,op_d),mult(op_d,rd(op_d,X))) = ld(X,i(X)),
inference(equational,[status(thm)],[c12,c18,c42,c56,c208]) ).
cnf(c216,plain,
ld(X,mult(mult(X,op_d),X)) = ld(op_d,rd(X,op_d)),
inference(equational,[status(thm)],[c28,c30,c35,c46,c103,c215]) ).
cnf(c217,plain,
mult(X,ld(op_d,rd(X,op_d))) = mult(mult(X,op_d),X),
inference(equational,[status(thm)],[c7,c216]) ).
cnf(c219,plain,
ld(rd(op_d,X),ld(X,i(X))) = mult(op_d,rd(op_d,X)),
inference(equational,[status(thm)],[c114,c215]) ).
cnf(c220,plain,
ld(X,ld(X,rd(X,op_d))) = ld(rd(X,op_d),op_d),
inference(equational,[status(thm)],[c5,c28,c30,c40,c49,c60,c94,c219]) ).
cnf(c221,plain,
mult(X,mult(X,rd(op_d,X))) = ld(rd(op_d,X),i(op_d)),
inference(equational,[status(thm)],[c27,c49,c60,c96,c219]) ).
cnf(c222,plain,
ld(X,ld(ld(X,op_d),X)) = mult(op_d,rd(op_d,i(X))),
inference(equational,[status(thm)],[c21,c25,c185,c219]) ).
cnf(c223,plain,
ld(rd(op_d,op_c),mult(op_c,op_c)) = mult(op_d,rd(op_d,op_c)),
inference(equational,[status(thm)],[c38,c219]) ).
cnf(c232,plain,
i(ld(X,mult(mult(X,Y),Z))) = ld(rd(Y,X),ld(X,i(Z))),
inference(equational,[status(thm)],[c30,c64,c103]) ).
cnf(c235,plain,
i(ld(op_d,ld(ld(op_d,X),op_d))) = ld(rd(i(op_d),X),op_d),
inference(equational,[status(thm)],[c12,c18,c34,c197]) ).
cnf(c242,plain,
ld(rd(X,Y),rd(rd(X,Y),Y)) = ld(X,rd(X,Y)),
inference(equational,[status(thm)],[c7,c40,c209]) ).
cnf(c243,plain,
ld(rd(X,Y),rd(X,rd(Y,X))) = mult(Y,rd(X,Y)),
inference(equational,[status(thm)],[c28,c46,c67,c209]) ).
cnf(c246,plain,
mult(mult(X,op_d),rd(ld(X,op_d),X)) = ld(X,i(op_d)),
inference(equational,[status(thm)],[c4,c8,c10,c14,c30,c60,c61,c106,c155,c199]) ).
cnf(c247,plain,
ld(rd(op_d,X),ld(op_d,X)) = mult(X,mult(X,op_d)),
inference(equational,[status(thm)],[c28,c84,c96,c232,c246]) ).
cnf(c261,plain,
ld(op_d,ld(ld(op_d,X),op_d)) = ld(X,mult(ld(X,op_d),X)),
inference(equational,[status(thm)],[c23,c102,c160,c221]) ).
cnf(c262,plain,
ld(op_c,ld(op_c,rd(op_d,op_c))) = ld(rd(op_d,op_c),i(op_d)),
inference(equational,[status(thm)],[c27,c58,c96,c223]) ).
cnf(c263,plain,
ld(mult(X,Y),ld(X,rd(X,Y))) = ld(X,ld(Y,i(Y))),
inference(equational,[status(thm)],[c9,c30,c55,c56,c58,c71,c93,c137]) ).
cnf(c264,plain,
ld(X,ld(X,rd(X,Y))) = ld(rd(X,Y),ld(Y,i(Y))),
inference(equational,[status(thm)],[c3,c242,c263]) ).
cnf(c271,plain,
ld(op_c,mult(mult(op_c,X),mult(op_c,op_c))) = ld(rd(op_c,X),i(op_c)),
inference(equational,[status(thm)],[c37,c103]) ).
cnf(c299,plain,
rd(i(op_c),ld(op_c,ld(op_c,X))) = ld(op_c,ld(mult(op_c,X),i(op_c))),
inference(equational,[status(thm)],[c53,c91]) ).
cnf(c350,plain,
i(ld(X,mult(ld(X,op_d),X))) = ld(rd(i(X),op_d),op_d),
inference(equational,[status(thm)],[c25,c71,c100,c220]) ).
cnf(c384,plain,
ld(ld(op_d,X),ld(op_d,mult(X,X))) = mult(ld(op_d,X),op_d),
inference(equational,[status(thm)],[c21,c25,c50,c98,c195,c219]) ).
cnf(c420,plain,
i(ld(X,mult(ld(X,Y),X))) = i(ld(Y,ld(ld(Y,X),Y))),
inference(equational,[status(thm)],[c25,c34,c71,c100,c188,c264]) ).
cnf(c443,plain,
rd(i(op_c),ld(op_c,ld(X,mult(op_c,op_c)))) = mult(op_c,mult(X,op_c)),
inference(equational,[status(thm)],[c38,c170]) ).
cnf(c448,plain,
rd(ld(X,mult(op_c,op_c)),i(Y)) = rd(Y,mult(X,mult(op_c,op_c))),
inference(equational,[status(thm)],[c44,c83]) ).
cnf(c449,plain,
i(ld(X,ld(Y,mult(op_c,op_c)))) = mult(X,mult(Y,mult(op_c,op_c))),
inference(equational,[status(thm)],[c34,c83]) ).
cnf(c450,plain,
ld(op_d,rd(mult(op_c,op_c),op_d)) = rd(op_d,mult(op_c,op_c)),
inference(equational,[status(thm)],[c7,c28,c30,c38,c49,c58,c139,c197,c222,c449]) ).
cnf(c452,plain,
i(ld(X,mult(Y,mult(op_c,op_c)))) = mult(X,ld(Y,mult(op_c,op_c))),
inference(equational,[status(thm)],[c35,c83]) ).
cnf(c453,plain,
ld(rd(mult(op_c,op_c),op_d),op_d) = rd(mult(op_c,op_c),op_d),
inference(equational,[status(thm)],[c7,c30,c38,c49,c58,c72,c104,c137,c350,c452]) ).
cnf(c454,plain,
rd(mult(op_c,op_c),op_d) = ld(op_d,mult(op_c,op_c)),
inference(equational,[status(thm)],[c14,c40,c114,c261,c450,c453]) ).
cnf(c455,plain,
mult(op_d,mult(op_c,op_c)) = rd(op_d,mult(op_c,op_c)),
inference(equational,[status(thm)],[c14,c28,c40,c83,c114,c420,c450,c453]) ).
cnf(c456,plain,
ld(ld(op_d,mult(op_c,op_c)),op_d) = ld(op_d,mult(op_c,op_c)),
inference(equational,[status(thm)],[c7,c49,c58,c72,c104,c133,c137,c235,c261,c452,c454]) ).
cnf(c457,plain,
rd(op_d,rd(op_d,mult(op_c,op_c))) = mult(op_c,op_c),
inference(equational,[status(thm)],[c10,c14,c18,c20,c24,c32,c34,c53,c99,c162,c187,c192,c448,c455,c456]) ).
cnf(c458,plain,
rd(op_d,mult(op_c,op_c)) = ld(op_c,ld(op_c,op_d)),
inference(equational,[status(thm)],[c6,c7,c8,c28,c49,c53,c58,c105,c219,c247,c454,c455,c457]) ).
cnf(c459,plain,
rd(ld(op_d,mult(op_c,op_c)),op_d) = ld(op_c,ld(op_c,op_d)),
inference(equational,[status(thm)],[c14,c51,c73,c115,c192,c454,c455,c456,c458]) ).
cnf(c460,plain,
rd(op_d,ld(op_d,mult(op_c,op_c))) = ld(op_d,mult(op_c,op_c)),
inference(equational,[status(thm)],[c13,c456]) ).
cnf(c461,plain,
ld(op_c,ld(op_c,i(op_d))) = ld(op_d,mult(op_c,op_c)),
inference(equational,[status(thm)],[c6,c24,c75,c161,c243,c459,c460]) ).
cnf(c462,plain,
mult(op_c,mult(op_d,op_c)) = rd(ld(op_c,op_d),op_c),
inference(equational,[status(thm)],[c9,c25,c34,c71,c86,c299,c443,c461]) ).
cnf(c515,plain,
ld(X,mult(mult(X,op_d),mult(X,Y))) = ld(op_d,ld(rd(op_d,X),Y)),
inference(equational,[status(thm)],[c5,c40,c49,c60,c103,c176,c219]) ).
cnf(c516,plain,
ld(op_d,ld(rd(op_d,op_c),op_c)) = ld(rd(op_c,op_d),i(op_c)),
inference(equational,[status(thm)],[c271,c515]) ).
cnf(c517,plain,
ld(ld(rd(op_d,op_c),op_c),op_d) = ld(rd(op_d,op_c),op_c),
inference(equational,[status(thm)],[c1,c5,c10,c40,c60,c61,c162,c223,c384,c516]) ).
cnf(c518,plain,
ld(rd(op_c,op_d),rd(op_d,op_c)) = ld(rd(op_d,op_c),op_c),
inference(equational,[status(thm)],[c13,c80,c517]) ).
cnf(c519,plain,
rd(op_c,rd(op_c,op_d)) = op_d,
inference(equational,[status(thm)],[c5,c40,c114,c162,c223,c518]) ).
cnf(c520,plain,
rd(op_c,op_d) = ld(op_d,op_c),
inference(equational,[status(thm)],[c14,c519]) ).
cnf(c522,plain,
ld(op_d,rd(op_d,op_c)) = i(op_c),
inference(equational,[status(thm)],[c168,c519]) ).
cnf(c528,plain,
rd(ld(op_c,op_d),op_c) = ld(op_c,rd(op_d,op_c)),
inference(equational,[status(thm)],[c28,c92,c519]) ).
cnf(c529,plain,
mult(op_d,rd(op_d,op_c)) = ld(op_d,i(op_c)),
inference(equational,[status(thm)],[c51,c522]) ).
cnf(c532,plain,
mult(mult(op_c,op_d),op_c) = ld(op_c,rd(op_d,op_c)),
inference(equational,[status(thm)],[c51,c217,c462,c520,c528]) ).
cnf(c535,plain,
ld(ld(op_d,op_c),op_d) = ld(op_d,i(op_c)),
inference(equational,[status(thm)],[c21,c38,c64,c223,c232,c262,c520,c529,c532]) ).
cnf(c536,plain,
rd(mult(op_d,op_c),op_d) = op_c,
inference(equational,[status(thm)],[c9,c35,c51,c86,c535]) ).
cnf(c538,plain,
mult(op_c,op_d) = mult(op_d,op_c),
inference(equational,[status(thm)],[c3,c536]) ).
cnf(g1,plain,
mult(op_c,op_d) = mult(op_d,op_c),
inference(equational,[status(thm)],[c538]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP688-1 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:52:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 74.47/74.60 % SZS status Unsatisfiable
% 74.47/74.60 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------