TSTP Solution File: SET925+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 12:35:33 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 1 unt; 0 def)
% Number of atoms : 58 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 23 |; 4 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 (; 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
? [A,B] :
( set_difference(singleton(A),B) = empty_set
<~> in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f16,plain,
? [A,B] :
( ( set_difference(singleton(A),B) = empty_set
| in(A,B) )
& ( set_difference(singleton(A),B) != empty_set
| ~ in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
( ( set_difference(singleton(sk0_2),sk0_3) = empty_set
| in(sk0_2,sk0_3) )
& ( set_difference(singleton(sk0_2),sk0_3) != empty_set
| ~ in(sk0_2,sk0_3) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
( set_difference(singleton(sk0_2),sk0_3) = empty_set
| in(sk0_2,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
( set_difference(singleton(sk0_2),sk0_3) != empty_set
| ~ in(sk0_2,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f21,plain,
( ! [A,B] :
( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ! [A,B] :
( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) != empty_set
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
( spl0_0
<=> set_difference(singleton(sk0_2),sk0_3) = empty_set ),
introduced(split_symbol_definition) ).
fof(f25,plain,
( set_difference(singleton(sk0_2),sk0_3) = empty_set
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f26,plain,
( set_difference(singleton(sk0_2),sk0_3) != empty_set
| spl0_0 ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( spl0_1
<=> in(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f28,plain,
( in(sk0_2,sk0_3)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f18,f24,f27]) ).
fof(f31,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f19,f24,f27]) ).
fof(f32,plain,
( set_difference(singleton(sk0_2),sk0_3) = empty_set
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f28,f23]) ).
fof(f34,plain,
( $false
| spl0_0
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f26]) ).
fof(f35,plain,
( spl0_0
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f36,plain,
( in(sk0_2,sk0_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f25,f22]) ).
fof(f37,plain,
( spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f36,f27,f24]) ).
fof(f43,plain,
$false,
inference(sat_refutation,[status(thm)],[f30,f31,f35,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:18:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.58 % Refutation found
% 0.20/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58 % Elapsed time: 0.017377 seconds
% 0.20/0.58 % CPU time: 0.018644 seconds
% 0.20/0.58 % Memory used: 2.859 MB
%------------------------------------------------------------------------------