TSTP Solution File: SET056+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 Apr 30 20:38:51 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 101 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 41 ~; 41 |; 19 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 45 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(X,Y)
& subclass(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X,Y] :
( X = Y
| ? [U] :
( member(U,X)
& ~ member(U,Y) )
| ? [W] :
( member(W,Y)
& ~ member(W,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y] :
( X = Y
| ? [U] :
( member(U,X)
& ~ member(U,Y) )
| ? [W] :
( member(W,Y)
& ~ member(W,X) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( ~ member(U,X)
| member(U,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ( member(sk0_0(Y,X),X)
& ~ member(sk0_0(Y,X),Y) ) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f54,plain,
! [X,Y] :
( ( X != Y
| ( subclass(X,Y)
& subclass(Y,X) ) )
& ( X = Y
| ~ subclass(X,Y)
| ~ subclass(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
( ! [X,Y] :
( X != Y
| ( subclass(X,Y)
& subclass(Y,X) ) )
& ! [X,Y] :
( X = Y
| ~ subclass(X,Y)
| ~ subclass(Y,X) ) ),
inference(miniscoping,[status(esa)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f191,plain,
? [X,Y] :
( X != Y
& ! [U] :
( ~ member(U,X)
| member(U,Y) )
& ! [W] :
( ~ member(W,Y)
| member(W,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f192,plain,
( sk0_7 != sk0_8
& ! [U] :
( ~ member(U,sk0_7)
| member(U,sk0_8) )
& ! [W] :
( ~ member(W,sk0_8)
| member(W,sk0_7) ) ),
inference(skolemization,[status(esa)],[f191]) ).
fof(f193,plain,
sk0_7 != sk0_8,
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
! [X0] :
( ~ member(X0,sk0_7)
| member(X0,sk0_8) ),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f195,plain,
! [X0] :
( ~ member(X0,sk0_8)
| member(X0,sk0_7) ),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f206,plain,
! [X0] :
( subclass(sk0_8,X0)
| member(sk0_0(X0,sk0_8),sk0_7) ),
inference(resolution,[status(thm)],[f51,f195]) ).
fof(f207,plain,
! [X0] :
( subclass(sk0_7,X0)
| member(sk0_0(X0,sk0_7),sk0_8) ),
inference(resolution,[status(thm)],[f51,f194]) ).
fof(f259,plain,
( spl0_8
<=> subclass(sk0_8,sk0_7) ),
introduced(split_symbol_definition) ).
fof(f260,plain,
( subclass(sk0_8,sk0_7)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( subclass(sk0_8,sk0_7)
| subclass(sk0_8,sk0_7) ),
inference(resolution,[status(thm)],[f52,f206]) ).
fof(f263,plain,
spl0_8,
inference(split_clause,[status(thm)],[f262,f259]) ).
fof(f279,plain,
( spl0_9
<=> sk0_8 = sk0_7 ),
introduced(split_symbol_definition) ).
fof(f280,plain,
( sk0_8 = sk0_7
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( spl0_10
<=> subclass(sk0_7,sk0_8) ),
introduced(split_symbol_definition) ).
fof(f285,plain,
( sk0_8 = sk0_7
| ~ subclass(sk0_7,sk0_8)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f260,f58]) ).
fof(f286,plain,
( spl0_9
| ~ spl0_10
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f285,f279,f282,f259]) ).
fof(f314,plain,
( subclass(sk0_7,sk0_8)
| subclass(sk0_7,sk0_8) ),
inference(resolution,[status(thm)],[f207,f52]) ).
fof(f315,plain,
spl0_10,
inference(split_clause,[status(thm)],[f314,f282]) ).
fof(f318,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f193]) ).
fof(f319,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f320,plain,
$false,
inference(sat_refutation,[status(thm)],[f263,f286,f315,f319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n031.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 22:18:13 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35 % Elapsed time: 0.017920 seconds
% 0.11/0.35 % CPU time: 0.033335 seconds
% 0.11/0.35 % Total memory used: 13.555 MB
% 0.11/0.35 % Net memory used: 13.535 MB
%------------------------------------------------------------------------------