%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP701-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:44:44 AM UTC 2025
% Result : Unsatisfiable 62.40s 62.53s
% Output : CNFRefutation 62.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of clauses : 165 ( 165 unt; 0 nHn; 3 RR)
% Number of literals : 165 ( 164 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 319 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(a,i(mult(b,a))) != i(b),
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(X,i(X)) = unit,
file('theBenchmark.p',c09) ).
cnf(c5,axiom,
mult(i(X),X) = unit,
file('theBenchmark.p',c10) ).
cnf(c6,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c9,plain,
rd(unit,X) = i(X),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c10,plain,
i(i(X)) = X,
inference(equational,[status(thm)],[c3,c6,c9]) ).
cnf(c11,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c12,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c14,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c15,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c16,plain,
ld(X,unit) = i(X),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c17,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c11,c14]) ).
cnf(c18,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c19,axiom,
mult(mult(mult(X,Y),X),mult(X,Z)) = mult(X,mult(mult(mult(Y,X),X),Z)),
file('theBenchmark.p',c07) ).
cnf(c20,plain,
mult(mult(X,X),mult(X,Y)) = mult(X,mult(mult(X,X),Y)),
inference(equational,[status(thm)],[c1,c2,c19]) ).
cnf(c21,plain,
mult(mult(X,X),X) = mult(X,mult(X,X)),
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c22,plain,
mult(mult(mult(X,Y),X),X) = mult(X,mult(mult(Y,X),X)),
inference(equational,[status(thm)],[c1,c19]) ).
cnf(c24,plain,
mult(X,mult(mult(X,X),i(X))) = mult(X,X),
inference(equational,[status(thm)],[c1,c3,c20]) ).
cnf(c25,plain,
mult(mult(X,X),i(X)) = X,
inference(equational,[status(thm)],[c14,c24]) ).
cnf(c26,plain,
rd(X,i(X)) = mult(X,X),
inference(equational,[status(thm)],[c6,c25]) ).
cnf(c28,plain,
mult(i(X),i(X)) = rd(i(X),X),
inference(equational,[status(thm)],[c10,c26]) ).
cnf(c31,axiom,
mult(mult(X,Y),mult(Y,mult(Z,Y))) = mult(mult(X,mult(Y,mult(Y,Z))),Y),
file('theBenchmark.p',c08) ).
cnf(c32,plain,
mult(mult(X,mult(Y,mult(Y,Z))),Y) = mult(mult(X,Y),mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c31]) ).
cnf(c33,plain,
mult(mult(X,mult(X,Y)),X) = mult(X,mult(X,mult(Y,X))),
inference(equational,[status(thm)],[c2,c32]) ).
cnf(c34,plain,
mult(mult(X,mult(Y,Y)),Y) = mult(mult(X,Y),mult(Y,Y)),
inference(equational,[status(thm)],[c1,c2,c32]) ).
cnf(c37,plain,
mult(X,mult(mult(ld(X,Y),X),X)) = mult(mult(Y,X),X),
inference(equational,[status(thm)],[c12,c22]) ).
cnf(c38,plain,
mult(mult(ld(X,Y),X),X) = ld(X,mult(mult(Y,X),X)),
inference(equational,[status(thm)],[c14,c37]) ).
cnf(c39,plain,
rd(mult(X,mult(mult(Y,X),X)),X) = mult(mult(X,Y),X),
inference(equational,[status(thm)],[c6,c22]) ).
cnf(c40,plain,
mult(mult(X,rd(Y,X)),X) = rd(mult(X,mult(Y,X)),X),
inference(equational,[status(thm)],[c11,c39]) ).
cnf(c41,plain,
mult(X,mult(X,mult(ld(X,Y),X))) = mult(mult(X,Y),X),
inference(equational,[status(thm)],[c12,c33]) ).
cnf(c42,plain,
mult(X,mult(ld(X,Y),X)) = ld(X,mult(mult(X,Y),X)),
inference(equational,[status(thm)],[c14,c41]) ).
cnf(c43,plain,
rd(mult(X,mult(X,mult(Y,X))),X) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c6,c33]) ).
cnf(c44,plain,
mult(X,mult(X,rd(Y,X))) = rd(mult(X,mult(X,Y)),X),
inference(equational,[status(thm)],[c11,c43]) ).
cnf(c45,plain,
mult(X,mult(mult(X,X),ld(X,Y))) = mult(mult(X,X),Y),
inference(equational,[status(thm)],[c12,c20]) ).
cnf(c46,plain,
mult(mult(X,X),ld(X,Y)) = ld(X,mult(mult(X,X),Y)),
inference(equational,[status(thm)],[c14,c45]) ).
cnf(c47,plain,
rd(mult(mult(X,Y),mult(Y,Y)),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c6,c34]) ).
cnf(c48,plain,
mult(i(X),mult(X,X)) = X,
inference(equational,[status(thm)],[c2,c5,c6,c47]) ).
cnf(c49,plain,
ld(i(X),X) = mult(X,X),
inference(equational,[status(thm)],[c14,c48]) ).
cnf(c51,plain,
rd(i(X),X) = ld(X,i(X)),
inference(equational,[status(thm)],[c10,c28,c49]) ).
cnf(c53,plain,
mult(mult(X,mult(Y,X)),X) = mult(mult(X,Y),mult(X,X)),
inference(equational,[status(thm)],[c19,c39,c47]) ).
cnf(c54,plain,
mult(rd(X,Y),mult(Y,Y)) = rd(mult(X,mult(Y,Y)),Y),
inference(equational,[status(thm)],[c11,c47]) ).
cnf(c56,plain,
mult(ld(X,i(X)),mult(X,X)) = unit,
inference(equational,[status(thm)],[c11,c15,c28,c46,c49,c51]) ).
cnf(c58,plain,
i(ld(X,i(X))) = mult(X,X),
inference(equational,[status(thm)],[c14,c16,c56]) ).
cnf(c59,plain,
mult(X,mult(mult(mult(Y,X),X),i(X))) = mult(mult(X,Y),X),
inference(equational,[status(thm)],[c1,c3,c19]) ).
cnf(c60,plain,
mult(mult(mult(X,Y),Y),i(Y)) = ld(Y,mult(mult(Y,X),Y)),
inference(equational,[status(thm)],[c14,c59]) ).
cnf(c61,plain,
mult(mult(X,mult(X,X)),i(X)) = mult(X,X),
inference(equational,[status(thm)],[c14,c21,c60]) ).
cnf(c63,plain,
mult(X,mult(mult(Y,X),i(X))) = rd(mult(X,mult(Y,X)),X),
inference(equational,[status(thm)],[c11,c40,c59]) ).
cnf(c64,plain,
mult(X,mult(Y,i(X))) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c11,c63]) ).
cnf(c65,plain,
ld(X,rd(mult(X,Y),X)) = mult(Y,i(X)),
inference(equational,[status(thm)],[c14,c64]) ).
cnf(c66,plain,
mult(ld(X,Y),i(X)) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c12,c65]) ).
cnf(c68,plain,
rd(mult(i(X),Y),i(X)) = mult(i(X),mult(Y,X)),
inference(equational,[status(thm)],[c10,c64]) ).
cnf(c70,plain,
rd(mult(X,rd(Y,i(X))),X) = mult(X,Y),
inference(equational,[status(thm)],[c11,c64]) ).
cnf(c71,plain,
mult(X,rd(Y,i(X))) = mult(mult(X,Y),X),
inference(equational,[status(thm)],[c11,c70]) ).
cnf(c72,plain,
mult(i(X),mult(X,mult(X,X))) = mult(X,X),
inference(equational,[status(thm)],[c10,c21,c26,c48,c61,c63]) ).
cnf(c73,plain,
mult(mult(X,i(Y)),Y) = mult(mult(X,Y),i(Y)),
inference(equational,[status(thm)],[c32,c48,c61,c72]) ).
cnf(c74,plain,
mult(i(X),mult(X,Y)) = mult(X,mult(i(X),Y)),
inference(equational,[status(thm)],[c19,c25,c61,c72]) ).
cnf(c75,plain,
mult(mult(X,mult(Y,X)),i(X)) = mult(X,Y),
inference(equational,[status(thm)],[c11,c14,c40,c44,c60]) ).
cnf(c76,plain,
rd(mult(X,Y),i(X)) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c6,c75]) ).
cnf(c77,plain,
mult(mult(X,Y),i(X)) = mult(X,rd(Y,X)),
inference(equational,[status(thm)],[c11,c75]) ).
cnf(c81,plain,
mult(X,rd(ld(X,Y),X)) = mult(Y,i(X)),
inference(equational,[status(thm)],[c12,c77]) ).
cnf(c82,plain,
ld(X,mult(Y,i(X))) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c14,c81]) ).
cnf(c83,plain,
ld(X,mult(mult(X,Y),X)) = rd(Y,i(X)),
inference(equational,[status(thm)],[c12,c42,c76]) ).
cnf(c87,plain,
mult(mult(X,Y),i(Y)) = rd(rd(X,Y),i(Y)),
inference(equational,[status(thm)],[c40,c65,c83]) ).
cnf(c92,plain,
ld(i(X),rd(Y,i(X))) = mult(ld(i(X),Y),X),
inference(equational,[status(thm)],[c10,c66]) ).
cnf(c93,plain,
mult(mult(i(X),Y),i(X)) = mult(i(X),rd(Y,X)),
inference(equational,[status(thm)],[c10,c71]) ).
cnf(c96,plain,
mult(X,mult(mult(X,X),mult(Y,X))) = mult(X,mult(X,mult(mult(X,Y),X))),
inference(equational,[status(thm)],[c20,c32,c33]) ).
cnf(c97,plain,
mult(mult(X,X),mult(Y,X)) = mult(X,mult(mult(X,Y),X)),
inference(equational,[status(thm)],[c14,c96]) ).
cnf(c100,plain,
rd(rd(X,i(Y)),Y) = rd(rd(X,Y),i(Y)),
inference(equational,[status(thm)],[c10,c73,c87]) ).
cnf(c105,plain,
mult(X,rd(mult(X,mult(Y,X)),X)) = mult(mult(X,X),Y),
inference(equational,[status(thm)],[c11,c40,c97]) ).
cnf(c106,plain,
rd(mult(X,mult(Y,X)),X) = ld(X,mult(mult(X,X),Y)),
inference(equational,[status(thm)],[c14,c105]) ).
cnf(c110,plain,
ld(X,rd(Y,i(X))) = mult(ld(X,Y),X),
inference(equational,[status(thm)],[c14,c42,c83]) ).
cnf(c111,plain,
mult(ld(i(X),Y),i(X)) = ld(i(X),rd(Y,X)),
inference(equational,[status(thm)],[c10,c110]) ).
cnf(c112,plain,
mult(rd(X,Y),i(Y)) = mult(X,ld(Y,i(Y))),
inference(equational,[status(thm)],[c12,c28,c51,c53,c111]) ).
cnf(c113,plain,
mult(rd(X,i(Y)),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c10,c49,c112]) ).
cnf(c114,plain,
rd(mult(mult(X,Y),mult(X,X)),X) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c6,c53]) ).
cnf(c115,plain,
rd(mult(X,mult(Y,Y)),Y) = rd(X,i(Y)),
inference(equational,[status(thm)],[c12,c42,c83,c114]) ).
cnf(c116,plain,
rd(mult(X,Y),i(Y)) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c47,c115]) ).
cnf(c117,plain,
mult(mult(X,Y),mult(X,X)) = mult(X,mult(Y,mult(X,X))),
inference(equational,[status(thm)],[c14,c19,c53,c59,c60,c83,c97,c106,c113,c114]) ).
cnf(c118,plain,
mult(X,ld(Y,i(Y))) = rd(mult(X,i(Y)),Y),
inference(equational,[status(thm)],[c10,c28,c51,c116]) ).
cnf(c119,plain,
rd(rd(X,mult(Y,Y)),i(Y)) = rd(X,Y),
inference(equational,[status(thm)],[c11,c115]) ).
cnf(c120,plain,
rd(mult(X,i(Y)),Y) = rd(X,mult(Y,Y)),
inference(equational,[status(thm)],[c11,c112,c118,c119]) ).
cnf(c121,plain,
rd(X,ld(Y,i(Y))) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c10,c28,c51,c116,c120]) ).
cnf(c122,plain,
rd(ld(X,mult(mult(Y,X),X)),X) = mult(ld(X,Y),X),
inference(equational,[status(thm)],[c6,c38]) ).
cnf(c123,plain,
rd(ld(i(X),Y),i(X)) = ld(i(X),mult(Y,X)),
inference(equational,[status(thm)],[c6,c11,c60,c83,c111,c122]) ).
cnf(c128,plain,
rd(rd(rd(X,Y),Y),i(Y)) = mult(X,i(Y)),
inference(equational,[status(thm)],[c12,c39,c111]) ).
cnf(c129,plain,
mult(rd(X,mult(Y,Y)),Y) = mult(X,i(Y)),
inference(equational,[status(thm)],[c10,c100,c119,c128]) ).
cnf(c130,plain,
mult(X,mult(i(X),ld(X,Y))) = mult(i(X),Y),
inference(equational,[status(thm)],[c12,c74]) ).
cnf(c131,plain,
mult(i(X),ld(X,Y)) = ld(X,mult(i(X),Y)),
inference(equational,[status(thm)],[c14,c130]) ).
cnf(c132,plain,
mult(X,ld(i(X),Y)) = ld(i(X),mult(X,Y)),
inference(equational,[status(thm)],[c10,c131]) ).
cnf(c140,plain,
mult(mult(X,i(Y)),mult(Y,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c11,c34,c129]) ).
cnf(c141,plain,
rd(mult(X,Y),mult(Y,Y)) = mult(X,i(Y)),
inference(equational,[status(thm)],[c6,c140]) ).
cnf(c142,plain,
ld(mult(X,i(Y)),mult(X,Y)) = mult(Y,Y),
inference(equational,[status(thm)],[c14,c140]) ).
cnf(c143,plain,
mult(mult(X,mult(Y,Y)),i(Y)) = mult(X,Y),
inference(equational,[status(thm)],[c6,c34,c141]) ).
cnf(c144,plain,
ld(mult(X,Y),mult(X,i(Y))) = ld(Y,i(Y)),
inference(equational,[status(thm)],[c10,c28,c51,c142]) ).
cnf(c145,plain,
ld(X,rd(X,mult(Y,Y))) = ld(Y,i(Y)),
inference(equational,[status(thm)],[c11,c112,c118,c120,c144]) ).
cnf(c152,plain,
ld(mult(X,mult(Y,Y)),mult(X,Y)) = i(Y),
inference(equational,[status(thm)],[c14,c143]) ).
cnf(c159,plain,
ld(mult(X,X),mult(X,mult(mult(X,X),Y))) = mult(X,Y),
inference(equational,[status(thm)],[c14,c20]) ).
cnf(c160,plain,
mult(X,ld(mult(X,X),Y)) = ld(mult(X,X),mult(X,Y)),
inference(equational,[status(thm)],[c12,c159]) ).
cnf(c168,plain,
mult(mult(X,mult(mult(Y,Z),Y)),Y) = mult(mult(X,Y),mult(mult(Z,Y),Y)),
inference(equational,[status(thm)],[c12,c32,c38,c41]) ).
cnf(c169,plain,
mult(mult(X,Y),rd(Z,i(Y))) = mult(mult(X,mult(Y,Z)),Y),
inference(equational,[status(thm)],[c11,c54,c64,c73,c87,c113,c115,c168]) ).
cnf(c170,plain,
mult(X,rd(mult(i(X),Y),X)) = rd(Y,X),
inference(equational,[status(thm)],[c2,c3,c10,c77,c169]) ).
cnf(c171,plain,
rd(mult(i(X),Y),X) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c14,c170]) ).
cnf(c172,plain,
rd(ld(i(X),Y),X) = mult(X,rd(Y,X)),
inference(equational,[status(thm)],[c12,c170]) ).
cnf(c173,plain,
mult(X,mult(i(X),Y)) = rd(rd(Y,X),i(X)),
inference(equational,[status(thm)],[c11,c54,c100,c114,c115,c170]) ).
cnf(c174,plain,
mult(i(X),mult(Y,X)) = mult(ld(X,Y),X),
inference(equational,[status(thm)],[c54,c68,c83,c110,c113,c115,c173]) ).
cnf(c175,plain,
mult(i(X),rd(Y,X)) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c65,c82,c93,c100,c128,c173]) ).
cnf(c177,plain,
ld(i(X),mult(Y,X)) = mult(mult(X,Y),X),
inference(equational,[status(thm)],[c54,c71,c115,c117,c123,c172]) ).
cnf(c178,plain,
mult(ld(i(X),Y),X) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c10,c76,c92,c171]) ).
cnf(c179,plain,
ld(i(X),mult(X,Y)) = mult(mult(X,X),Y),
inference(equational,[status(thm)],[c12,c75,c77,c106,c132,c178]) ).
cnf(c180,plain,
ld(i(X),rd(Y,X)) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c11,c38,c87,c177]) ).
cnf(c182,plain,
ld(X,mult(mult(X,X),Y)) = ld(i(X),Y),
inference(equational,[status(thm)],[c11,c40,c106,c172]) ).
cnf(c183,plain,
ld(i(X),ld(X,Y)) = ld(X,ld(i(X),Y)),
inference(equational,[status(thm)],[c46,c182]) ).
cnf(c185,plain,
mult(ld(X,i(X)),Y) = ld(X,mult(i(X),Y)),
inference(equational,[status(thm)],[c10,c28,c51,c179]) ).
cnf(c188,plain,
rd(rd(mult(X,Y),X),i(X)) = ld(i(X),Y),
inference(equational,[status(thm)],[c40,c42,c65,c71,c73,c87,c106,c182]) ).
cnf(c189,plain,
rd(rd(X,Y),i(Y)) = ld(Y,ld(i(Y),X)),
inference(equational,[status(thm)],[c65,c73,c87,c110,c188]) ).
cnf(c190,plain,
ld(X,mult(i(X),Y)) = ld(mult(X,X),Y),
inference(equational,[status(thm)],[c6,c58,c121,c185,c188]) ).
cnf(c192,plain,
ld(i(X),ld(i(X),Y)) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c11,c92,c180,c188]) ).
cnf(c193,plain,
ld(X,ld(X,ld(i(X),Y))) = mult(i(X),Y),
inference(equational,[status(thm)],[c12,c14,c44,c175,c183,c188,c189]) ).
cnf(c196,plain,
ld(mult(X,X),mult(X,Y)) = mult(i(X),Y),
inference(equational,[status(thm)],[c12,c160,c190]) ).
cnf(c207,plain,
mult(ld(X,ld(i(X),Y)),X) = rd(Y,i(X)),
inference(equational,[status(thm)],[c10,c42,c74,c75,c83,c173,c174,c189]) ).
cnf(c220,plain,
rd(mult(mult(X,Y),mult(Y,mult(Z,Y))),Y) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c221,plain,
mult(rd(X,Y),mult(Y,mult(Y,Z))) = rd(mult(X,mult(Y,mult(Z,Y))),Y),
inference(equational,[status(thm)],[c11,c220]) ).
cnf(c222,plain,
rd(mult(X,rd(Y,i(Z))),Z) = mult(rd(X,Z),mult(Z,Y)),
inference(equational,[status(thm)],[c12,c42,c83,c221]) ).
cnf(c223,plain,
mult(mult(rd(X,Y),mult(Y,Z)),Y) = mult(X,rd(Z,i(Y))),
inference(equational,[status(thm)],[c11,c222]) ).
cnf(c235,plain,
mult(X,mult(ld(X,mult(mult(Y,X),X)),Z)) = mult(mult(Y,X),mult(X,Z)),
inference(equational,[status(thm)],[c12,c19,c38]) ).
cnf(c236,plain,
mult(X,mult(ld(X,mult(Y,X)),Z)) = mult(Y,mult(X,Z)),
inference(equational,[status(thm)],[c11,c235]) ).
cnf(c237,plain,
mult(ld(X,mult(Y,X)),Z) = ld(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c14,c236]) ).
cnf(c238,plain,
mult(rd(X,Y),mult(Y,Z)) = mult(Y,mult(ld(Y,X),Z)),
inference(equational,[status(thm)],[c11,c236]) ).
cnf(c240,plain,
mult(X,mult(Y,i(ld(Y,mult(X,Y))))) = Y,
inference(equational,[status(thm)],[c1,c3,c236]) ).
cnf(c241,plain,
mult(X,i(ld(X,mult(Y,X)))) = ld(Y,X),
inference(equational,[status(thm)],[c14,c240]) ).
cnf(c242,plain,
i(ld(X,mult(Y,X))) = ld(X,ld(Y,X)),
inference(equational,[status(thm)],[c14,c241]) ).
cnf(c243,plain,
mult(X,i(ld(X,Y))) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c11,c241]) ).
cnf(c244,plain,
i(ld(X,ld(Y,X))) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c10,c242]) ).
cnf(c246,plain,
ld(rd(mult(X,Y),X),X) = mult(X,i(Y)),
inference(equational,[status(thm)],[c14,c243]) ).
cnf(c249,plain,
mult(X,i(mult(Y,X))) = ld(ld(i(X),Y),X),
inference(equational,[status(thm)],[c106,c182,c246]) ).
cnf(c250,plain,
ld(rd(ld(X,Y),Y),Y) = mult(X,Y),
inference(equational,[status(thm)],[c12,c241,c242,c244,c246]) ).
cnf(c251,plain,
rd(ld(X,Y),Y) = rd(Y,mult(X,Y)),
inference(equational,[status(thm)],[c18,c250]) ).
cnf(c252,plain,
mult(rd(X,Y),X) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c17,c250]) ).
cnf(c255,plain,
mult(X,i(mult(i(X),Y))) = ld(mult(Y,i(X)),X),
inference(equational,[status(thm)],[c73,c87,c189,c193,c241]) ).
cnf(c260,plain,
mult(X,i(rd(Y,i(X)))) = ld(mult(X,Y),X),
inference(equational,[status(thm)],[c6,c83,c243]) ).
cnf(c261,plain,
rd(ld(X,mult(Y,mult(X,Z))),Z) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c6,c237]) ).
cnf(c262,plain,
ld(X,mult(i(mult(X,Y)),X)) = rd(i(X),Y),
inference(equational,[status(thm)],[c5,c16,c261]) ).
cnf(c264,plain,
rd(rd(X,Y),i(X)) = ld(mult(Y,i(X)),X),
inference(equational,[status(thm)],[c10,c14,c73,c87,c123,c183,c189,c192,c255,c262]) ).
cnf(c268,plain,
mult(ld(X,rd(X,Y)),X) = i(mult(i(X),Y)),
inference(equational,[status(thm)],[c6,c10,c207,c262]) ).
cnf(c271,plain,
mult(X,mult(ld(X,Y),ld(X,Z))) = mult(rd(Y,X),Z),
inference(equational,[status(thm)],[c12,c238]) ).
cnf(c272,plain,
ld(ld(rd(X,Y),Y),Y) = i(ld(X,Y)),
inference(equational,[status(thm)],[c12,c152,c252,c271]) ).
cnf(c280,plain,
i(mult(i(X),mult(Y,Y))) = ld(mult(Y,Y),X),
inference(equational,[status(thm)],[c145,c185,c190,c268]) ).
cnf(c282,plain,
i(mult(X,mult(Y,Y))) = ld(mult(Y,Y),i(X)),
inference(equational,[status(thm)],[c10,c280]) ).
cnf(c287,plain,
ld(mult(X,mult(Y,X)),X) = mult(i(X),i(Y)),
inference(equational,[status(thm)],[c14,c53,c117,c160,c196,c241,c282]) ).
cnf(c288,plain,
ld(ld(i(X),Y),X) = ld(ld(X,Y),i(X)),
inference(equational,[status(thm)],[c10,c12,c73,c87,c189,c249,c287]) ).
cnf(c292,plain,
mult(i(X),i(rd(Y,X))) = ld(mult(X,Y),X),
inference(equational,[status(thm)],[c11,c287]) ).
cnf(c293,plain,
ld(ld(X,Y),i(X)) = ld(X,i(rd(Y,X))),
inference(equational,[status(thm)],[c10,c87,c100,c188,c251,c264,c288,c292]) ).
cnf(c296,plain,
mult(i(X),i(ld(X,Y))) = ld(rd(Y,i(X)),X),
inference(equational,[status(thm)],[c42,c83,c287]) ).
cnf(c297,plain,
ld(X,i(ld(X,Y))) = ld(mult(Y,X),X),
inference(equational,[status(thm)],[c10,c100,c113,c143,c188,c251,c264,c296]) ).
cnf(c298,plain,
i(ld(mult(X,X),Y)) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c58,c145,c252,c272,c297]) ).
cnf(c310,plain,
i(ld(X,mult(Y,Y))) = ld(mult(Y,Y),X),
inference(equational,[status(thm)],[c10,c298]) ).
cnf(c323,plain,
mult(X,rd(i(ld(Y,X)),i(Y))) = mult(Y,Y),
inference(equational,[status(thm)],[c11,c223,c240]) ).
cnf(c324,plain,
rd(i(ld(X,Y)),i(X)) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c14,c323]) ).
cnf(c325,plain,
mult(i(X),Y) = i(ld(Y,X)),
inference(equational,[status(thm)],[c160,c196,c243,c260,c272,c310,c324]) ).
cnf(c327,plain,
rd(i(X),Y) = ld(X,i(Y)),
inference(equational,[status(thm)],[c14,c262,c325]) ).
cnf(c336,plain,
ld(X,i(rd(Y,X))) = i(Y),
inference(equational,[status(thm)],[c6,c293,c325,c327]) ).
cnf(g1,plain,
mult(a,i(mult(b,a))) = i(b),
inference(equational,[status(thm)],[c249,c288,c293,c336]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP701-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:54:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 62.40/62.53 % SZS status Unsatisfiable
% 62.40/62.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------