%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP660-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:44:37 AM UTC 2025
% Result : Unsatisfiable 91.12s 91.25s
% Output : CNFRefutation 91.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 99 ( 98 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 214 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('theBenchmark.p',goal) ).
fof(e,plain,
! [X0] :
( true != false
& eq(X0,X0) = true
& eq(tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)),tuple(x1(X0),x1_2(X0))) = false ),
inference(encode_existential,[status(esa)],[g0]) ).
cnf(g1,plain,
true != false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c1,plain,
eq(X,X) = true,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c2,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c3,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c4,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c6,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c8,axiom,
mult(mult(mult(X,Y),Z),X) = mult(X,mult(Y,mult(Z,X))),
file('theBenchmark.p',f05) ).
cnf(c9,plain,
rd(mult(X,mult(Y,mult(Z,X))),X) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
mult(mult(X,Y),rd(Z,X)) = rd(mult(X,mult(Y,Z)),X),
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c11,plain,
mult(X,mult(ld(X,Y),mult(Z,X))) = mult(mult(Y,Z),X),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c13,plain,
mult(mult(X,rd(Y,Z)),Z) = mult(Z,mult(ld(Z,X),Y)),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c14,plain,
mult(mult(X,rd(Y,mult(Z,X))),Z) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c15,plain,
mult(X,rd(Y,mult(Z,X))) = rd(rd(mult(X,Y),X),Z),
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c16,plain,
rd(mult(X,mult(ld(X,Y),Z)),X) = mult(Y,rd(Z,X)),
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c17,plain,
mult(X,mult(Y,mult(ld(mult(X,Y),Z),X))) = mult(Z,X),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c18,plain,
mult(X,mult(ld(mult(Y,X),Z),Y)) = ld(Y,mult(Z,Y)),
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c19,plain,
mult(ld(mult(X,Y),Z),X) = ld(Y,ld(X,mult(Z,X))),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c20,plain,
rd(ld(X,ld(Y,mult(Z,Y))),Y) = ld(mult(Y,X),Z),
inference(equational,[status(thm)],[c5,c19]) ).
cnf(c21,plain,
rd(ld(X,Y),Y) = ld(mult(Y,X),Y),
inference(equational,[status(thm)],[c3,c20]) ).
cnf(c22,plain,
ld(mult(X,rd(X,Y)),X) = rd(Y,X),
inference(equational,[status(thm)],[c7,c21]) ).
cnf(c23,plain,
mult(X,rd(X,Y)) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c6,c22]) ).
cnf(c24,plain,
rd(ld(X,ld(Y,Z)),Y) = ld(mult(Y,X),rd(Z,Y)),
inference(equational,[status(thm)],[c4,c20]) ).
cnf(c25,plain,
ld(X,rd(X,rd(Y,X))) = rd(X,Y),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c27,plain,
ld(ld(X,Y),ld(X,mult(Z,X))) = mult(ld(Y,Z),X),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c28,plain,
mult(ld(X,Y),Y) = ld(ld(Y,X),Y),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c29,plain,
ld(ld(X,rd(X,Y)),X) = mult(Y,X),
inference(equational,[status(thm)],[c7,c28]) ).
cnf(c30,plain,
mult(ld(X,rd(Y,Z)),Z) = ld(ld(Z,X),ld(Z,Y)),
inference(equational,[status(thm)],[c4,c27]) ).
cnf(c31,plain,
mult(X,rd(ld(ld(Y,X),Z),Y)) = rd(mult(Y,Z),Y),
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c32,plain,
rd(ld(ld(X,Y),Z),X) = ld(Y,rd(mult(X,Z),X)),
inference(equational,[status(thm)],[c3,c31]) ).
cnf(c33,plain,
ld(X,rd(rd(mult(X,Y),X),Z)) = rd(Y,mult(Z,X)),
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c34,plain,
rd(ld(X,Y),mult(Z,X)) = ld(X,rd(rd(Y,X),Z)),
inference(equational,[status(thm)],[c2,c33]) ).
cnf(c35,plain,
rd(rd(mult(X,Y),X),rd(Z,X)) = mult(X,rd(Y,Z)),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c36,plain,
mult(X,rd(ld(X,Y),Z)) = rd(rd(Y,X),rd(Z,X)),
inference(equational,[status(thm)],[c2,c35]) ).
cnf(c40,plain,
mult(X,mult(ld(Y,Z),rd(Y,X))) = ld(rd(Y,X),mult(Z,rd(Y,X))),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c42,plain,
mult(mult(X,mult(ld(X,Y),Z)),Y) = mult(Y,mult(rd(Z,X),mult(X,Y))),
inference(equational,[status(thm)],[c8,c13]) ).
cnf(c44,plain,
mult(X,mult(ld(X,rd(Y,rd(Z,X))),Z)) = mult(Y,X),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c45,plain,
mult(ld(X,rd(Y,rd(Z,X))),Z) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c3,c44]) ).
cnf(c46,plain,
rd(ld(X,mult(Y,X)),Z) = ld(X,rd(Y,rd(Z,X))),
inference(equational,[status(thm)],[c5,c45]) ).
cnf(c47,plain,
ld(mult(X,Y),rd(mult(X,mult(Y,Z)),X)) = rd(Z,X),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c49,plain,
ld(mult(X,Y),rd(mult(X,Z),X)) = rd(ld(Y,Z),X),
inference(equational,[status(thm)],[c2,c47]) ).
cnf(c55,plain,
ld(X,rd(rd(Y,X),rd(Z,X))) = rd(ld(X,Y),Z),
inference(equational,[status(thm)],[c4,c34]) ).
cnf(c56,plain,
ld(mult(mult(X,Y),Y),mult(X,Y)) = ld(Y,rd(X,X)),
inference(equational,[status(thm)],[c5,c21,c34]) ).
cnf(c57,plain,
ld(mult(X,ld(Y,X)),X) = ld(ld(Y,X),rd(Y,Y)),
inference(equational,[status(thm)],[c2,c56]) ).
cnf(c58,plain,
ld(ld(X,X),rd(X,X)) = ld(X,X),
inference(equational,[status(thm)],[c2,c57]) ).
cnf(c59,plain,
rd(rd(X,X),ld(X,X)) = ld(X,X),
inference(equational,[status(thm)],[c6,c58]) ).
cnf(c60,plain,
mult(ld(X,X),ld(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c2,c58]) ).
cnf(c65,plain,
mult(ld(X,Y),mult(ld(ld(X,Y),Z),Y)) = mult(mult(Z,X),ld(X,Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c66,plain,
mult(mult(X,ld(ld(X,X),Y)),X) = mult(X,mult(mult(Y,X),ld(X,X))),
inference(equational,[status(thm)],[c11,c65]) ).
cnf(c73,plain,
rd(ld(X,mult(ld(Y,Z),W)),Y) = ld(mult(Y,X),mult(Z,rd(W,Y))),
inference(equational,[status(thm)],[c16,c49]) ).
cnf(c77,plain,
rd(mult(ld(X,Y),Z),mult(W,X)) = ld(X,rd(mult(Y,rd(Z,X)),W)),
inference(equational,[status(thm)],[c16,c33]) ).
cnf(c78,plain,
mult(X,rd(ld(Y,Z),rd(X,Y))) = rd(mult(rd(X,Y),Z),rd(X,Y)),
inference(equational,[status(thm)],[c7,c31]) ).
cnf(c81,plain,
mult(ld(ld(X,Y),rd(Z,X)),Y) = ld(ld(X,Y),mult(Z,ld(X,Y))),
inference(equational,[status(thm)],[c6,c45]) ).
cnf(c84,plain,
ld(rd(ld(X,X),Y),mult(Y,X)) = mult(Y,mult(Y,X)),
inference(equational,[status(thm)],[c29,c49]) ).
cnf(c96,plain,
rd(mult(rd(X,X),Y),rd(X,X)) = rd(rd(Y,X),rd(rd(X,X),X)),
inference(equational,[status(thm)],[c36,c78]) ).
cnf(c97,plain,
rd(rd(X,X),rd(rd(X,X),X)) = rd(X,rd(X,X)),
inference(equational,[status(thm)],[c4,c96]) ).
cnf(c98,plain,
rd(ld(X,X),rd(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c25,c55,c97]) ).
cnf(c99,plain,
mult(rd(X,X),rd(X,X)) = ld(X,X),
inference(equational,[status(thm)],[c4,c25,c45,c97]) ).
cnf(c100,plain,
ld(rd(X,X),ld(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c3,c99]) ).
cnf(c101,plain,
ld(ld(X,X),ld(X,X)) = ld(X,ld(ld(X,X),X)),
inference(equational,[status(thm)],[c28,c30,c45,c98]) ).
cnf(c102,plain,
ld(ld(ld(X,X),X),X) = rd(X,X),
inference(equational,[status(thm)],[c6,c21,c24,c28,c60,c100,c101]) ).
cnf(c103,plain,
rd(X,rd(X,X)) = ld(ld(X,X),X),
inference(equational,[status(thm)],[c6,c102]) ).
cnf(c107,plain,
ld(ld(X,ld(X,X)),ld(X,Y)) = ld(ld(X,X),mult(Y,ld(X,X))),
inference(equational,[status(thm)],[c30,c81]) ).
cnf(c119,plain,
mult(rd(rd(X,Y),rd(Z,Y)),Z) = mult(Z,mult(ld(Z,Y),ld(Y,X))),
inference(equational,[status(thm)],[c13,c36]) ).
cnf(c120,plain,
mult(ld(ld(X,X),X),rd(X,X)) = X,
inference(equational,[status(thm)],[c2,c4,c7,c97,c103,c119]) ).
cnf(c121,plain,
ld(ld(X,ld(X,X)),X) = mult(X,X),
inference(equational,[status(thm)],[c2,c28,c42,c59,c120]) ).
cnf(c122,plain,
ld(ld(X,X),X) = X,
inference(equational,[status(thm)],[c5,c32,c121]) ).
cnf(c123,plain,
rd(X,X) = ld(X,X),
inference(equational,[status(thm)],[c102,c122]) ).
cnf(c124,plain,
rd(X,mult(Y,ld(X,X))) = ld(ld(X,X),rd(X,Y)),
inference(equational,[status(thm)],[c2,c59,c77,c120]) ).
cnf(c125,plain,
rd(ld(X,Y),ld(Y,Y)) = ld(mult(ld(Y,Y),X),Y),
inference(equational,[status(thm)],[c2,c59,c73,c120]) ).
cnf(c128,plain,
ld(mult(X,Y),mult(Z,rd(Y,X))) = ld(Y,rd(ld(X,Z),rd(X,Y))),
inference(equational,[status(thm)],[c46,c73]) ).
cnf(c129,plain,
ld(mult(X,X),X) = ld(X,ld(X,X)),
inference(equational,[status(thm)],[c28,c120,c122,c123,c125,c128]) ).
cnf(c160,plain,
ld(rd(ld(X,X),rd(Y,X)),Y) = mult(rd(Y,X),Y),
inference(equational,[status(thm)],[c4,c84]) ).
cnf(c163,plain,
rd(mult(X,mult(mult(Y,X),ld(X,X))),X) = mult(X,ld(ld(X,X),Y)),
inference(equational,[status(thm)],[c5,c66]) ).
cnf(c168,plain,
ld(X,rd(mult(X,mult(Y,ld(X,X))),X)) = mult(Y,ld(X,ld(X,X))),
inference(equational,[status(thm)],[c16,c21,c32,c40,c123,c129]) ).
cnf(c169,plain,
mult(mult(X,Y),ld(Y,ld(Y,Y))) = ld(ld(Y,Y),X),
inference(equational,[status(thm)],[c3,c163,c168]) ).
cnf(c170,plain,
mult(ld(ld(X,X),Y),X) = ld(ld(X,X),mult(Y,X)),
inference(equational,[status(thm)],[c2,c60,c101,c107,c122,c123,c169]) ).
cnf(c171,plain,
mult(X,ld(Y,Y)) = X,
inference(equational,[status(thm)],[c2,c4,c6,c44,c170]) ).
cnf(c172,plain,
ld(X,X) = ld(Y,Y),
inference(equational,[status(thm)],[c3,c171]) ).
cnf(c173,plain,
ld(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c101,c122,c169,c171]) ).
cnf(c174,plain,
mult(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c2,c66,c101,c122,c171]) ).
cnf(c175,plain,
rd(X,ld(Y,Y)) = X,
inference(equational,[status(thm)],[c4,c171]) ).
cnf(c177,plain,
rd(ld(X,X),Y) = ld(Y,ld(Y,Y)),
inference(equational,[status(thm)],[c21,c129,c172]) ).
cnf(c188,plain,
rd(ld(X,X),Y) = ld(Y,ld(X,X)),
inference(equational,[status(thm)],[c6,c160,c171,c177]) ).
cnf(c195,plain,
mult(X,ld(Y,ld(Y,Y))) = rd(X,Y),
inference(equational,[status(thm)],[c4,c169,c173]) ).
cnf(c196,plain,
rd(X,ld(Y,ld(Y,Y))) = mult(X,Y),
inference(equational,[status(thm)],[c60,c101,c107,c123,c171,c173,c195]) ).
cnf(c199,plain,
rd(X,ld(Y,ld(Z,Z))) = mult(X,Y),
inference(equational,[status(thm)],[c2,c44,c171,c188]) ).
cnf(c200,plain,
mult(ld(X,ld(X,X)),Y) = ld(X,Y),
inference(equational,[status(thm)],[c3,c29,c196]) ).
cnf(c204,plain,
rd(ld(X,rd(X,Y)),Z) = rd(ld(Y,ld(Y,Y)),Z),
inference(equational,[status(thm)],[c47,c49,c195]) ).
cnf(c205,plain,
mult(ld(X,rd(X,Y)),Z) = ld(Y,Z),
inference(equational,[status(thm)],[c196,c199,c200,c204]) ).
cnf(c207,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c6,c205]) ).
cnf(c209,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c124,c173,c199,c207]) ).
cnf(c708,plain,
eq(tuple(mult(X,x1(X)),mult(x1_2(X),X)),tuple(x1(X),x1_2(X))) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c709,plain,
true = false,
inference(equational,[status(thm)],[c1,c174,c175,c209,c708]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c709]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP660-10 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n009.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 08:46:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 91.12/91.25 % SZS status Unsatisfiable
% 91.12/91.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------