TSTP Solution File: SET924+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET924+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 0.14s 0.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 2 unt; 0 def)
% Number of atoms : 62 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 24 |; 4 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 (; 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
? [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<~> ~ in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f14,plain,
? [A,B] :
( ( set_difference(singleton(A),B) = singleton(A)
| ~ in(A,B) )
& ( set_difference(singleton(A),B) != singleton(A)
| in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f15,plain,
( ( set_difference(singleton(sk0_2),sk0_3) = singleton(sk0_2)
| ~ in(sk0_2,sk0_3) )
& ( set_difference(singleton(sk0_2),sk0_3) != singleton(sk0_2)
| in(sk0_2,sk0_3) ) ),
inference(skolemization,[status(esa)],[f14]) ).
fof(f16,plain,
( set_difference(singleton(sk0_2),sk0_3) = singleton(sk0_2)
| ~ in(sk0_2,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
( set_difference(singleton(sk0_2),sk0_3) != singleton(sk0_2)
| in(sk0_2,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f18,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) )
& ( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f19,plain,
( ! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) )
& ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) != singleton(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f22,plain,
( spl0_0
<=> set_difference(singleton(sk0_2),sk0_3) = singleton(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f23,plain,
( set_difference(singleton(sk0_2),sk0_3) = singleton(sk0_2)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
( spl0_1
<=> in(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f27,plain,
( ~ in(sk0_2,sk0_3)
| spl0_1 ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f16,f22,f25]) ).
fof(f29,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f17,f22,f25]) ).
fof(f48,plain,
( set_difference(singleton(sk0_2),sk0_3) = singleton(sk0_2)
| spl0_1 ),
inference(resolution,[status(thm)],[f27,f21]) ).
fof(f51,plain,
( spl0_2
<=> singleton(sk0_2) = singleton(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f53,plain,
( singleton(sk0_2) != singleton(sk0_2)
| spl0_2 ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f74,plain,
( singleton(sk0_2) != singleton(sk0_2)
| ~ in(sk0_2,sk0_3)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f23,f20]) ).
fof(f75,plain,
( ~ spl0_2
| ~ spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f74,f51,f25,f22]) ).
fof(f76,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f53]) ).
fof(f77,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f48,f22,f25]) ).
fof(f79,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f29,f75,f77,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET924+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32 % Computer : n032.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Tue May 30 10:18:01 EDT 2023
% 0.09/0.32 % CPUTime :
% 0.09/0.33 % Drodi V3.5.1
% 0.14/0.56 % Refutation found
% 0.14/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.56 % Elapsed time: 0.011587 seconds
% 0.14/0.56 % CPU time: 0.010679 seconds
% 0.14/0.56 % Memory used: 2.865 MB
%------------------------------------------------------------------------------