%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP657-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 225.87s 226.03s
% Output : CNFRefutation 225.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 52 unt; 0 def)
% Number of atoms : 55 ( 54 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 : 5 ( 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 : 122 ( 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(X,Y),mult(Z,X)) = mult(X,mult(mult(Y,Z),X)),
file('theBenchmark.p',f05) ).
cnf(c9,plain,
mult(X,mult(mult(ld(X,Y),Z),X)) = mult(Y,mult(Z,X)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c10,plain,
mult(mult(ld(X,Y),Z),X) = ld(X,mult(Y,mult(Z,X))),
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c11,plain,
mult(X,mult(mult(Y,rd(Z,X)),X)) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c12,plain,
mult(mult(X,rd(Y,Z)),Z) = ld(Z,mult(mult(Z,X),Y)),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c13,plain,
mult(mult(X,rd(Y,rd(Z,X))),Z) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c14,plain,
mult(X,rd(Y,rd(Z,X))) = rd(mult(X,mult(Y,X)),Z),
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c17,plain,
rd(ld(X,mult(mult(X,Y),Z)),X) = mult(Y,rd(Z,X)),
inference(equational,[status(thm)],[c5,c12]) ).
cnf(c19,plain,
rd(ld(X,mult(Y,mult(Z,X))),X) = mult(ld(X,Y),Z),
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c20,plain,
mult(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c3,c5,c19]) ).
cnf(c21,plain,
rd(X,X) = ld(Y,Y),
inference(equational,[status(thm)],[c5,c20]) ).
cnf(c22,plain,
ld(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c2,c20]) ).
cnf(c23,plain,
ld(rd(X,X),Y) = Y,
inference(equational,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
mult(X,ld(Y,Y)) = X,
inference(equational,[status(thm)],[c4,c5,c14,c21]) ).
cnf(c29,plain,
rd(X,ld(Y,Y)) = X,
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c36,plain,
rd(ld(X,mult(Y,X)),X) = ld(X,Y),
inference(equational,[status(thm)],[c19,c20,c24]) ).
cnf(c37,plain,
rd(ld(X,X),X) = ld(X,ld(Y,Y)),
inference(equational,[status(thm)],[c20,c36]) ).
cnf(c38,plain,
rd(ld(X,Y),X) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c4,c36]) ).
cnf(c39,plain,
ld(X,rd(X,X)) = ld(X,ld(Y,Y)),
inference(equational,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
rd(rd(X,X),Y) = ld(Y,ld(Y,Y)),
inference(equational,[status(thm)],[c21,c38,c39]) ).
cnf(c41,plain,
rd(rd(X,X),Y) = ld(Y,ld(Z,Z)),
inference(equational,[status(thm)],[c21,c37]) ).
cnf(c49,plain,
rd(ld(X,X),Y) = rd(rd(Z,Z),Y),
inference(equational,[status(thm)],[c21,c40,c41]) ).
cnf(c57,plain,
mult(ld(X,ld(Y,Y)),Z) = ld(X,Z),
inference(equational,[status(thm)],[c19,c20,c36]) ).
cnf(c59,plain,
rd(ld(X,Y),Y) = ld(X,ld(Z,Z)),
inference(equational,[status(thm)],[c5,c57]) ).
cnf(c61,plain,
rd(X,mult(Y,X)) = ld(Y,ld(Z,Z)),
inference(equational,[status(thm)],[c3,c59]) ).
cnf(c63,plain,
rd(X,mult(Y,X)) = rd(rd(Z,Z),Y),
inference(equational,[status(thm)],[c41,c61]) ).
cnf(c67,plain,
mult(ld(X,rd(Y,Y)),Z) = ld(X,Z),
inference(equational,[status(thm)],[c21,c57]) ).
cnf(c76,plain,
mult(X,rd(ld(Y,Y),Z)) = rd(X,Z),
inference(equational,[status(thm)],[c3,c17,c24]) ).
cnf(c79,plain,
ld(X,rd(X,Y)) = rd(ld(Z,Z),Y),
inference(equational,[status(thm)],[c3,c76]) ).
cnf(c80,plain,
ld(X,rd(X,Y)) = rd(rd(Z,Z),Y),
inference(equational,[status(thm)],[c49,c79]) ).
cnf(c86,plain,
rd(X,mult(Y,X)) = ld(Z,rd(Z,Y)),
inference(equational,[status(thm)],[c23,c63,c79]) ).
cnf(c89,plain,
ld(ld(X,rd(X,Y)),Z) = mult(Y,Z),
inference(equational,[status(thm)],[c7,c67,c80]) ).
cnf(c90,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c6,c89]) ).
cnf(c97,plain,
ld(mult(X,Y),mult(X,mult(mult(Y,Z),X))) = mult(Z,X),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c98,plain,
ld(mult(X,Y),mult(X,mult(Z,X))) = ld(ld(Z,Y),X),
inference(equational,[status(thm)],[c2,c90,c97]) ).
cnf(c99,plain,
ld(ld(mult(X,Y),X),Z) = mult(Y,Z),
inference(equational,[status(thm)],[c97,c98]) ).
cnf(c100,plain,
ld(X,rd(X,Y)) = ld(mult(Z,Y),Z),
inference(equational,[status(thm)],[c6,c86,c99]) ).
cnf(c106,plain,
mult(X,ld(mult(Y,Z),Y)) = rd(X,Z),
inference(equational,[status(thm)],[c2,c100]) ).
cnf(c107,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c2,c106]) ).
cnf(c1025,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(c1026,plain,
true = false,
inference(equational,[status(thm)],[c1,c20,c29,c107,c1025]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c1026]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP657-10 : TPTP v9.0.0. Released v8.1.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n006.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 08:45:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 225.87/226.03 % SZS status Unsatisfiable
% 225.87/226.03 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------