%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP658-10 : 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 13.48s 13.67s
% Output : CNFRefutation 13.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 25 unt; 0 def)
% Number of atoms : 28 ( 27 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 : 48 ( 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(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(c8,axiom,
mult(mult(X,mult(Y,Y)),Z) = mult(mult(X,Y),mult(Y,Z)),
file('theBenchmark.p',f05) ).
cnf(c13,plain,
mult(mult(rd(X,mult(Y,Y)),Y),mult(Y,Z)) = mult(X,Z),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c14,plain,
rd(mult(X,Y),mult(Z,Y)) = mult(rd(X,mult(Z,Z)),Z),
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c15,plain,
rd(X,mult(Y,ld(Z,X))) = mult(rd(Z,mult(Y,Y)),Y),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c16,plain,
rd(X,X) = mult(rd(Y,mult(Y,Y)),Y),
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c17,plain,
rd(X,X) = rd(Y,Y),
inference(equational,[status(thm)],[c2,c15,c16]) ).
cnf(c19,plain,
mult(rd(X,X),Y) = Y,
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c24,plain,
mult(mult(rd(X,mult(Y,Y)),Y),Z) = mult(X,ld(Y,Z)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c25,plain,
mult(mult(rd(X,mult(X,X)),X),Y) = Y,
inference(equational,[status(thm)],[c2,c24]) ).
cnf(c30,plain,
mult(rd(rd(X,Y),mult(Z,Z)),Z) = rd(X,mult(Z,Y)),
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c36,plain,
mult(rd(X,mult(Y,Z)),W) = mult(rd(X,Z),ld(Y,W)),
inference(equational,[status(thm)],[c24,c30]) ).
cnf(c37,plain,
ld(X,X) = rd(Y,Y),
inference(equational,[status(thm)],[c16,c19,c36]) ).
cnf(c39,plain,
mult(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c19,c25,c36]) ).
cnf(c40,plain,
mult(X,rd(Y,Y)) = X,
inference(equational,[status(thm)],[c2,c37]) ).
cnf(c42,plain,
mult(X,ld(Y,Y)) = X,
inference(equational,[status(thm)],[c37,c40]) ).
cnf(c227,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(c228,plain,
true = false,
inference(equational,[status(thm)],[c1,c39,c42,c227]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c228]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP658-10 : TPTP v9.0.0. Released v8.1.0.
% 0.07/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:45:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 13.48/13.67 % SZS status Unsatisfiable
% 13.48/13.67 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------