%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP681-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 06:44:42 AM UTC 2025
% Result : Unsatisfiable 145.62s 145.60s
% Output : CNFRefutation 145.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of clauses : 114 ( 114 unt; 0 nHn; 3 RR)
% Number of literals : 114 ( 113 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; 4 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(mult(op_c,op_c),op_d),a) != mult(a,mult(mult(op_c,op_c),op_d)),
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(op_c,X) = mult(X,op_c),
file('theBenchmark.p',c08) ).
cnf(c4,axiom,
mult(op_d,X) = mult(X,op_d),
file('theBenchmark.p',c09) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c7,plain,
rd(X,unit) = X,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c8,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c9,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c10,plain,
ld(unit,X) = X,
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c11,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c13,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c14,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c15,plain,
ld(X,mult(op_c,X)) = op_c,
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c16,plain,
ld(X,mult(op_d,X)) = op_d,
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c19,plain,
mult(op_d,rd(X,op_d)) = X,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c20,plain,
rd(X,op_d) = ld(op_d,X),
inference(equational,[status(thm)],[c11,c19]) ).
cnf(c21,plain,
mult(op_c,rd(X,op_c)) = X,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c22,plain,
rd(X,op_c) = ld(op_c,X),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c23,plain,
ld(op_d,mult(X,op_d)) = X,
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c24,plain,
ld(op_c,mult(X,op_c)) = X,
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c25,plain,
ld(ld(op_c,X),X) = op_c,
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c26,plain,
ld(ld(op_d,X),X) = op_d,
inference(equational,[status(thm)],[c9,c16]) ).
cnf(c27,axiom,
mult(X,mult(Y,mult(X,Z))) = mult(mult(X,mult(Y,X)),Z),
file('theBenchmark.p',c07) ).
cnf(c28,plain,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c27]) ).
cnf(c29,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c2,c28]) ).
cnf(c31,plain,
mult(X,mult(X,op_d)) = mult(op_d,mult(X,X)),
inference(equational,[status(thm)],[c4,c29]) ).
cnf(c36,plain,
rd(mult(X,mult(X,Y)),Y) = mult(X,X),
inference(equational,[status(thm)],[c5,c29]) ).
cnf(c37,plain,
ld(op_d,mult(X,mult(X,op_d))) = mult(X,X),
inference(equational,[status(thm)],[c23,c29]) ).
cnf(c40,plain,
mult(X,mult(Y,mult(X,op_d))) = mult(op_d,mult(X,mult(Y,X))),
inference(equational,[status(thm)],[c4,c28]) ).
cnf(c42,plain,
mult(mult(X,mult(X,op_d)),Y) = mult(X,mult(op_d,mult(X,Y))),
inference(equational,[status(thm)],[c4,c28]) ).
cnf(c43,plain,
rd(mult(X,Y),ld(X,Y)) = mult(X,X),
inference(equational,[status(thm)],[c9,c36]) ).
cnf(c46,plain,
mult(mult(op_c,mult(op_c,X)),Y) = mult(op_c,mult(X,mult(op_c,Y))),
inference(equational,[status(thm)],[c3,c28]) ).
cnf(c47,plain,
mult(X,mult(op_c,op_c)) = mult(op_c,mult(op_c,X)),
inference(equational,[status(thm)],[c11,c24,c46]) ).
cnf(c48,plain,
mult(op_c,mult(X,op_c)) = mult(X,mult(op_c,op_c)),
inference(equational,[status(thm)],[c3,c47]) ).
cnf(c50,plain,
mult(mult(op_d,mult(op_d,X)),Y) = mult(op_d,mult(X,mult(op_d,Y))),
inference(equational,[status(thm)],[c4,c28]) ).
cnf(c51,plain,
mult(X,mult(op_d,op_d)) = mult(op_d,mult(op_d,X)),
inference(equational,[status(thm)],[c11,c23,c50]) ).
cnf(c52,plain,
mult(op_d,mult(X,op_d)) = mult(X,mult(op_d,op_d)),
inference(equational,[status(thm)],[c4,c51]) ).
cnf(c62,plain,
ld(X,mult(op_d,mult(op_d,X))) = mult(op_d,op_d),
inference(equational,[status(thm)],[c11,c51]) ).
cnf(c63,plain,
rd(mult(X,mult(op_d,op_d)),X) = mult(op_d,op_d),
inference(equational,[status(thm)],[c36,c51]) ).
cnf(c68,plain,
ld(mult(X,X),mult(X,Y)) = ld(X,Y),
inference(equational,[status(thm)],[c13,c43]) ).
cnf(c69,plain,
ld(mult(X,X),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c9,c68]) ).
cnf(c78,plain,
mult(op_c,mult(op_d,mult(op_d,X))) = mult(op_d,mult(X,mult(op_d,op_c))),
inference(equational,[status(thm)],[c3,c50]) ).
cnf(c84,plain,
rd(X,rd(X,mult(op_d,op_d))) = mult(op_d,op_d),
inference(equational,[status(thm)],[c8,c63]) ).
cnf(c85,plain,
rd(X,mult(op_d,op_d)) = ld(op_d,ld(op_d,X)),
inference(equational,[status(thm)],[c13,c69,c84]) ).
cnf(c86,plain,
ld(X,mult(op_d,mult(X,op_d))) = mult(op_d,op_d),
inference(equational,[status(thm)],[c4,c62]) ).
cnf(c99,plain,
mult(mult(op_d,mult(X,X)),Y) = mult(X,mult(op_d,mult(X,Y))),
inference(equational,[status(thm)],[c31,c42]) ).
cnf(c102,plain,
mult(X,mult(rd(Y,X),mult(X,Z))) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c8,c28]) ).
cnf(c103,plain,
mult(mult(X,Y),ld(X,Z)) = mult(X,mult(rd(Y,X),Z)),
inference(equational,[status(thm)],[c9,c102]) ).
cnf(c104,plain,
mult(X,mult(rd(unit,X),Y)) = Y,
inference(equational,[status(thm)],[c1,c9,c103]) ).
cnf(c105,plain,
mult(X,rd(unit,X)) = unit,
inference(equational,[status(thm)],[c1,c104]) ).
cnf(c106,plain,
rd(unit,X) = ld(X,unit),
inference(equational,[status(thm)],[c11,c105]) ).
cnf(c107,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c11,c104,c106]) ).
cnf(c108,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c9,c104,c106]) ).
cnf(c109,plain,
rd(X,mult(Y,X)) = ld(Y,unit),
inference(equational,[status(thm)],[c14,c108]) ).
cnf(c110,plain,
rd(ld(X,Y),Y) = ld(X,unit),
inference(equational,[status(thm)],[c5,c107]) ).
cnf(c113,plain,
mult(op_c,ld(X,unit)) = ld(X,op_c),
inference(equational,[status(thm)],[c3,c107]) ).
cnf(c116,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c13,c110]) ).
cnf(c119,plain,
mult(op_d,ld(X,op_d)) = ld(X,mult(op_d,op_d)),
inference(equational,[status(thm)],[c52,c107]) ).
cnf(c120,plain,
mult(op_c,ld(X,op_c)) = ld(X,mult(op_c,op_c)),
inference(equational,[status(thm)],[c48,c107]) ).
cnf(c123,plain,
ld(ld(op_d,X),unit) = rd(op_d,X),
inference(equational,[status(thm)],[c26,c110]) ).
cnf(c124,plain,
ld(ld(op_c,X),unit) = rd(op_c,X),
inference(equational,[status(thm)],[c25,c110]) ).
cnf(c125,plain,
mult(rd(X,Y),mult(Y,Z)) = ld(Y,mult(mult(Y,X),Z)),
inference(equational,[status(thm)],[c11,c102]) ).
cnf(c126,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c107,c116]) ).
cnf(c129,plain,
mult(ld(op_c,X),Y) = ld(rd(op_c,X),Y),
inference(equational,[status(thm)],[c108,c124]) ).
cnf(c130,plain,
mult(ld(op_d,X),Y) = ld(rd(op_d,X),Y),
inference(equational,[status(thm)],[c108,c123]) ).
cnf(c135,plain,
ld(rd(X,Y),mult(op_d,X)) = ld(X,mult(op_d,mult(X,Y))),
inference(equational,[status(thm)],[c4,c125,c126]) ).
cnf(c140,plain,
ld(rd(X,Y),mult(op_c,X)) = ld(X,mult(op_c,mult(X,Y))),
inference(equational,[status(thm)],[c3,c125,c126]) ).
cnf(c141,plain,
rd(X,ld(op_c,unit)) = mult(op_c,X),
inference(equational,[status(thm)],[c7,c9,c105,c106,c108,c116,c129,c140]) ).
cnf(c142,plain,
ld(mult(op_c,X),X) = ld(op_c,unit),
inference(equational,[status(thm)],[c13,c141]) ).
cnf(c143,plain,
ld(X,ld(op_c,X)) = ld(op_c,unit),
inference(equational,[status(thm)],[c21,c22,c142]) ).
cnf(c145,plain,
rd(mult(X,mult(Y,mult(X,Z))),Z) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c150,plain,
mult(mult(X,op_c),ld(op_c,Y)) = mult(op_c,ld(rd(op_c,X),Y)),
inference(equational,[status(thm)],[c3,c22,c103,c129]) ).
cnf(c151,plain,
mult(op_d,mult(X,op_c)) = mult(op_d,mult(op_c,X)),
inference(equational,[status(thm)],[c4,c9,c16,c135,c150]) ).
cnf(c157,plain,
ld(rd(op_d,X),mult(op_d,Y)) = ld(op_d,mult(mult(op_d,X),Y)),
inference(equational,[status(thm)],[c20,c125,c130]) ).
cnf(c168,plain,
mult(mult(X,mult(op_c,op_c)),Y) = mult(op_c,mult(X,mult(op_c,Y))),
inference(equational,[status(thm)],[c46,c47]) ).
cnf(c170,plain,
mult(mult(X,mult(op_d,op_d)),Y) = mult(op_d,mult(X,mult(op_d,Y))),
inference(equational,[status(thm)],[c50,c51]) ).
cnf(c177,plain,
mult(X,ld(op_c,unit)) = ld(op_c,X),
inference(equational,[status(thm)],[c9,c143]) ).
cnf(c184,plain,
mult(op_c,mult(X,mult(op_d,op_d))) = mult(op_d,mult(X,mult(op_d,op_c))),
inference(equational,[status(thm)],[c51,c78]) ).
cnf(c201,plain,
rd(mult(op_d,mult(X,X)),mult(X,op_d)) = X,
inference(equational,[status(thm)],[c5,c31]) ).
cnf(c210,plain,
mult(X,ld(rd(mult(X,Y),Z),X)) = rd(mult(X,Z),Y),
inference(equational,[status(thm)],[c8,c126,c145]) ).
cnf(c213,plain,
mult(X,ld(mult(X,Y),X)) = rd(X,Y),
inference(equational,[status(thm)],[c1,c7,c210]) ).
cnf(c215,plain,
mult(X,ld(Y,X)) = rd(X,ld(X,Y)),
inference(equational,[status(thm)],[c9,c213]) ).
cnf(c217,plain,
rd(op_d,ld(op_d,X)) = ld(X,mult(op_d,op_d)),
inference(equational,[status(thm)],[c19,c20,c119,c213]) ).
cnf(c224,plain,
ld(rd(mult(X,Y),Z),X) = ld(X,rd(mult(X,Z),Y)),
inference(equational,[status(thm)],[c11,c210]) ).
cnf(c249,plain,
ld(rd(mult(op_d,X),Y),X) = ld(X,ld(op_d,mult(X,Y))),
inference(equational,[status(thm)],[c4,c20,c224]) ).
cnf(c250,plain,
mult(op_c,ld(op_d,X)) = ld(rd(op_d,X),op_c),
inference(equational,[status(thm)],[c1,c2,c10,c113,c249]) ).
cnf(c338,plain,
mult(X,ld(Y,mult(X,Z))) = ld(rd(ld(X,Y),X),Z),
inference(equational,[status(thm)],[c28,c107,c126,c215]) ).
cnf(c344,plain,
rd(mult(X,mult(op_d,mult(X,op_d))),X) = mult(op_d,mult(X,op_d)),
inference(equational,[status(thm)],[c40,c145]) ).
cnf(c384,plain,
mult(X,ld(rd(X,ld(X,Y)),Z)) = mult(Y,ld(X,Z)),
inference(equational,[status(thm)],[c9,c103,c126]) ).
cnf(c385,plain,
ld(rd(X,ld(X,Y)),Z) = ld(X,mult(Y,ld(X,Z))),
inference(equational,[status(thm)],[c11,c384]) ).
cnf(c388,plain,
ld(ld(X,mult(op_d,op_d)),Y) = ld(op_d,mult(X,ld(op_d,Y))),
inference(equational,[status(thm)],[c217,c385]) ).
cnf(c435,plain,
mult(ld(X,mult(op_d,op_d)),Y) = ld(ld(op_d,ld(op_d,X)),Y),
inference(equational,[status(thm)],[c20,c107,c170,c338]) ).
cnf(c470,plain,
mult(op_c,ld(X,mult(op_d,op_d))) = ld(ld(op_d,ld(op_d,X)),op_c),
inference(equational,[status(thm)],[c20,c107,c184,c338]) ).
cnf(c497,plain,
rd(mult(X,X),mult(op_d,mult(X,op_d))) = ld(op_d,ld(op_d,X)),
inference(equational,[status(thm)],[c85,c86,c210,c215,c344]) ).
cnf(c501,plain,
rd(ld(rd(X,Y),mult(Z,Y)),X) = ld(rd(X,Y),mult(Z,rd(Y,X))),
inference(equational,[status(thm)],[c8,c126,c145]) ).
cnf(c502,plain,
ld(X,mult(Y,ld(X,unit))) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c1,c7,c106,c501]) ).
cnf(c503,plain,
mult(X,rd(ld(X,Y),X)) = mult(Y,ld(X,unit)),
inference(equational,[status(thm)],[c9,c502]) ).
cnf(c534,plain,
rd(ld(X,mult(Y,Z)),mult(X,Z)) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c5,c109,c501,c502]) ).
cnf(c535,plain,
rd(ld(X,rd(Y,Z)),X) = rd(ld(X,Y),mult(X,Z)),
inference(equational,[status(thm)],[c8,c534]) ).
cnf(c548,plain,
rd(ld(X,mult(op_c,Y)),X) = rd(ld(X,Y),ld(op_c,X)),
inference(equational,[status(thm)],[c141,c177,c535]) ).
cnf(c685,plain,
rd(ld(X,mult(op_d,Y)),mult(X,op_d)) = rd(ld(X,Y),X),
inference(equational,[status(thm)],[c4,c534]) ).
cnf(c686,plain,
rd(ld(X,mult(Y,op_c)),X) = rd(ld(X,Y),ld(op_c,X)),
inference(equational,[status(thm)],[c151,c548,c685]) ).
cnf(c689,plain,
rd(ld(op_d,X),ld(op_c,op_d)) = ld(op_d,ld(op_d,mult(X,op_c))),
inference(equational,[status(thm)],[c20,c686]) ).
cnf(c720,plain,
mult(X,ld(rd(mult(X,Y),Z),W)) = ld(rd(Y,mult(X,Z)),ld(X,W)),
inference(equational,[status(thm)],[c103,c110,c116,c126,c210]) ).
cnf(c754,plain,
ld(op_d,ld(ld(op_d,ld(op_d,X)),Y)) = ld(X,mult(op_d,Y)),
inference(equational,[status(thm)],[c14,c119,c157,c435]) ).
cnf(c758,plain,
ld(ld(op_d,ld(op_d,X)),ld(op_d,Y)) = mult(op_d,ld(X,Y)),
inference(equational,[status(thm)],[c201,c497,c720]) ).
cnf(c969,plain,
ld(rd(X,Y),mult(op_c,mult(op_c,X))) = ld(X,mult(op_c,mult(op_c,mult(X,Y)))),
inference(equational,[status(thm)],[c3,c47,c48,c125,c126]) ).
cnf(c970,plain,
ld(op_d,mult(X,mult(op_c,op_c))) = ld(op_d,mult(op_c,mult(op_c,X))),
inference(equational,[status(thm)],[c9,c37,c217,c388,c969]) ).
cnf(c971,plain,
mult(op_c,mult(X,ld(op_d,op_c))) = ld(op_d,mult(op_c,mult(op_c,X))),
inference(equational,[status(thm)],[c3,c7,c9,c168,c250,c503,c548,c689,c970]) ).
cnf(c1034,plain,
mult(op_c,mult(op_d,ld(X,op_c))) = ld(X,mult(op_d,mult(op_c,op_c))),
inference(equational,[status(thm)],[c120,c435,c470,c754,c758,c971]) ).
cnf(c1630,plain,
mult(op_c,mult(op_d,mult(X,op_c))) = mult(X,mult(op_d,mult(op_c,op_c))),
inference(equational,[status(thm)],[c108,c1034]) ).
cnf(g1,plain,
mult(mult(mult(op_c,op_c),op_d),a) = mult(a,mult(mult(op_c,op_c),op_d)),
inference(equational,[status(thm)],[c3,c4,c99,c1630]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP681-1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n011.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 08:52:19 EDT 2025
% 0.12/0.32 % CPUTime :
% 145.62/145.60 % SZS status Unsatisfiable
% 145.62/145.60 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------