TSTP Solution File: SET047+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 : Wed May 31 12:33:43 EDT 2023
% Result : Theorem 0.10s 0.33s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 1 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 142 ( 54 ~; 68 |; 11 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 44 (; 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( set_equal(X,Y)
<=> ! [Z] :
( element(Z,X)
<=> element(Z,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [X,Y] :
( ( ~ set_equal(X,Y)
| ! [Z] :
( ( ~ element(Z,X)
| element(Z,Y) )
& ( element(Z,X)
| ~ element(Z,Y) ) ) )
& ( set_equal(X,Y)
| ? [Z] :
( ( ~ element(Z,X)
| ~ element(Z,Y) )
& ( element(Z,X)
| element(Z,Y) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f5,plain,
( ! [X,Y] :
( ~ set_equal(X,Y)
| ( ! [Z] :
( ~ element(Z,X)
| element(Z,Y) )
& ! [Z] :
( element(Z,X)
| ~ element(Z,Y) ) ) )
& ! [X,Y] :
( set_equal(X,Y)
| ? [Z] :
( ( ~ element(Z,X)
| ~ element(Z,Y) )
& ( element(Z,X)
| element(Z,Y) ) ) ) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f6,plain,
( ! [X,Y] :
( ~ set_equal(X,Y)
| ( ! [Z] :
( ~ element(Z,X)
| element(Z,Y) )
& ! [Z] :
( element(Z,X)
| ~ element(Z,Y) ) ) )
& ! [X,Y] :
( set_equal(X,Y)
| ( ( ~ element(sk0_0(Y,X),X)
| ~ element(sk0_0(Y,X),Y) )
& ( element(sk0_0(Y,X),X)
| element(sk0_0(Y,X),Y) ) ) ) ),
inference(skolemization,[status(esa)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( ~ set_equal(X0,X1)
| ~ element(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ set_equal(X0,X1)
| element(X2,X0)
| ~ element(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( set_equal(X0,X1)
| ~ element(sk0_0(X1,X0),X0)
| ~ element(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( set_equal(X0,X1)
| element(sk0_0(X1,X0),X0)
| element(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f11,plain,
? [X,Y] :
( set_equal(X,Y)
<~> set_equal(Y,X) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f12,plain,
? [X,Y] :
( ( set_equal(X,Y)
| set_equal(Y,X) )
& ( ~ set_equal(X,Y)
| ~ set_equal(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
( ( set_equal(sk0_1,sk0_2)
| set_equal(sk0_2,sk0_1) )
& ( ~ set_equal(sk0_1,sk0_2)
| ~ set_equal(sk0_2,sk0_1) ) ),
inference(skolemization,[status(esa)],[f12]) ).
fof(f14,plain,
( set_equal(sk0_1,sk0_2)
| set_equal(sk0_2,sk0_1) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f15,plain,
( ~ set_equal(sk0_1,sk0_2)
| ~ set_equal(sk0_2,sk0_1) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f16,plain,
( spl0_0
<=> set_equal(sk0_1,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f17,plain,
( set_equal(sk0_1,sk0_2)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,plain,
( spl0_1
<=> set_equal(sk0_2,sk0_1) ),
introduced(split_symbol_definition) ).
fof(f20,plain,
( set_equal(sk0_2,sk0_1)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f14,f16,f19]) ).
fof(f23,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f15,f16,f19]) ).
fof(f34,plain,
! [X0] :
( element(X0,sk0_2)
| ~ element(X0,sk0_1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f20,f8]) ).
fof(f35,plain,
! [X0] :
( ~ element(X0,sk0_2)
| element(X0,sk0_1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f20,f7]) ).
fof(f56,plain,
! [X0] :
( element(sk0_0(sk0_2,X0),sk0_1)
| set_equal(X0,sk0_2)
| element(sk0_0(sk0_2,X0),X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f35,f10]) ).
fof(f60,plain,
( spl0_6
<=> element(sk0_0(sk0_1,sk0_2),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f90,plain,
( spl0_10
<=> element(sk0_0(sk0_2,sk0_1),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( set_equal(sk0_1,sk0_2)
| set_equal(sk0_1,sk0_2)
| ~ element(sk0_0(sk0_2,sk0_1),sk0_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f56,f9]) ).
fof(f98,plain,
( spl0_0
| ~ spl0_10
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f97,f16,f90,f19]) ).
fof(f101,plain,
( set_equal(sk0_1,sk0_2)
| element(sk0_0(sk0_2,sk0_1),sk0_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f56,f34]) ).
fof(f102,plain,
( spl0_0
| spl0_10
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f101,f16,f90,f19]) ).
fof(f110,plain,
! [X0] :
( element(X0,sk0_1)
| ~ element(X0,sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f17,f8]) ).
fof(f111,plain,
! [X0] :
( ~ element(X0,sk0_1)
| element(X0,sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f17,f7]) ).
fof(f120,plain,
! [X0] :
( element(sk0_0(sk0_1,X0),sk0_2)
| set_equal(X0,sk0_1)
| element(sk0_0(sk0_1,X0),X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f111,f10]) ).
fof(f149,plain,
( set_equal(sk0_2,sk0_1)
| set_equal(sk0_2,sk0_1)
| ~ element(sk0_0(sk0_1,sk0_2),sk0_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f120,f9]) ).
fof(f150,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f149,f19,f60,f16]) ).
fof(f153,plain,
( set_equal(sk0_2,sk0_1)
| element(sk0_0(sk0_1,sk0_2),sk0_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f120,f110]) ).
fof(f154,plain,
( spl0_1
| spl0_6
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f153,f19,f60,f16]) ).
fof(f162,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f23,f98,f102,f150,f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n024.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 10:17:48 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 0.10/0.33 % Refutation found
% 0.10/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58 % Elapsed time: 0.033968 seconds
% 0.17/0.58 % CPU time: 0.018158 seconds
% 0.17/0.58 % Memory used: 520.728 KB
%------------------------------------------------------------------------------