TSTP Solution File: SET016+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET016+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 20:38:39 EDT 2024
% Result : Theorem 3.85s 0.88s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 124 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 113 ( 44 ~; 46 |; 15 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [W,X,Y,Z] :
( ( ordered_pair(W,X) = ordered_pair(Y,Z)
& member(W,universal_class) )
=> W = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [W,X,Y,Z] :
( ( ordered_pair(W,X) = ordered_pair(Y,Z)
& member(W,universal_class) )
=> W = Y ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f59,plain,
! [U,X,Y] :
( ( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f60,plain,
( ! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ! [U,X,Y] :
( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f65,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f66,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f67,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f191,plain,
? [W,X,Y,Z] :
( ordered_pair(W,X) = ordered_pair(Y,Z)
& member(W,universal_class)
& W != Y ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f192,plain,
? [W,Y] :
( ? [X,Z] : ordered_pair(W,X) = ordered_pair(Y,Z)
& member(W,universal_class)
& W != Y ),
inference(miniscoping,[status(esa)],[f191]) ).
fof(f193,plain,
( ordered_pair(sk0_7,sk0_9) = ordered_pair(sk0_8,sk0_10)
& member(sk0_7,universal_class)
& sk0_7 != sk0_8 ),
inference(skolemization,[status(esa)],[f192]) ).
fof(f194,plain,
ordered_pair(sk0_7,sk0_9) = ordered_pair(sk0_8,sk0_10),
inference(cnf_transformation,[status(esa)],[f193]) ).
fof(f195,plain,
member(sk0_7,universal_class),
inference(cnf_transformation,[status(esa)],[f193]) ).
fof(f196,plain,
sk0_7 != sk0_8,
inference(cnf_transformation,[status(esa)],[f193]) ).
fof(f199,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(destructive_equality_resolution,[status(esa)],[f63]) ).
fof(f207,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f66,f65]) ).
fof(f218,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f66,f62]) ).
fof(f219,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f218]) ).
fof(f291,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f66,f199]) ).
fof(f300,plain,
! [X0,X1,X2] :
( ~ member(X0,ordered_pair(X1,X2))
| X0 = singleton(X1)
| X0 = unordered_pair(X1,singleton(X2)) ),
inference(paramodulation,[status(thm)],[f67,f62]) ).
fof(f424,plain,
( spl0_25
<=> member(sk0_7,universal_class) ),
introduced(split_symbol_definition) ).
fof(f426,plain,
( ~ member(sk0_7,universal_class)
| spl0_25 ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f454,plain,
( $false
| spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f195]) ).
fof(f455,plain,
spl0_25,
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f558,plain,
( spl0_41
<=> member(sk0_7,singleton(sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f559,plain,
( member(sk0_7,singleton(sk0_8))
| ~ spl0_41 ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f560,plain,
( ~ member(sk0_7,singleton(sk0_8))
| spl0_41 ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f996,plain,
( spl0_72
<=> member(singleton(sk0_8),ordered_pair(sk0_7,sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f997,plain,
( member(singleton(sk0_8),ordered_pair(sk0_7,sk0_9))
| ~ spl0_72 ),
inference(component_clause,[status(thm)],[f996]) ).
fof(f998,plain,
( ~ member(singleton(sk0_8),ordered_pair(sk0_7,sk0_9))
| spl0_72 ),
inference(component_clause,[status(thm)],[f996]) ).
fof(f1026,plain,
( spl0_75
<=> singleton(sk0_8) = singleton(sk0_7) ),
introduced(split_symbol_definition) ).
fof(f1027,plain,
( singleton(sk0_8) = singleton(sk0_7)
| ~ spl0_75 ),
inference(component_clause,[status(thm)],[f1026]) ).
fof(f1029,plain,
( spl0_76
<=> singleton(sk0_8) = unordered_pair(sk0_7,singleton(sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f1030,plain,
( singleton(sk0_8) = unordered_pair(sk0_7,singleton(sk0_9))
| ~ spl0_76 ),
inference(component_clause,[status(thm)],[f1029]) ).
fof(f1032,plain,
( singleton(sk0_8) = singleton(sk0_7)
| singleton(sk0_8) = unordered_pair(sk0_7,singleton(sk0_9))
| ~ spl0_72 ),
inference(resolution,[status(thm)],[f997,f300]) ).
fof(f1033,plain,
( spl0_75
| spl0_76
| ~ spl0_72 ),
inference(split_clause,[status(thm)],[f1032,f1026,f1029,f996]) ).
fof(f1261,plain,
( member(sk0_7,singleton(sk0_8))
| ~ member(sk0_7,universal_class)
| ~ spl0_76 ),
inference(paramodulation,[status(thm)],[f1030,f199]) ).
fof(f1262,plain,
( spl0_41
| ~ spl0_25
| ~ spl0_76 ),
inference(split_clause,[status(thm)],[f1261,f558,f424,f1029]) ).
fof(f1505,plain,
( sk0_7 = sk0_8
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f219,f559]) ).
fof(f1506,plain,
( $false
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[status(thm)],[f1505,f196]) ).
fof(f1507,plain,
~ spl0_41,
inference(contradiction_clause,[status(thm)],[f1506]) ).
fof(f3070,plain,
! [X0,X1] :
( member(singleton(X0),ordered_pair(X0,X1))
| ~ member(singleton(X0),universal_class) ),
inference(paramodulation,[status(thm)],[f67,f199]) ).
fof(f3071,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f3070,f207]) ).
fof(f3790,plain,
( ~ member(sk0_7,singleton(sk0_7))
| ~ spl0_75
| spl0_41 ),
inference(backward_demodulation,[status(thm)],[f1027,f560]) ).
fof(f3955,plain,
( ~ member(sk0_7,universal_class)
| ~ spl0_75
| spl0_41 ),
inference(resolution,[status(thm)],[f3790,f291]) ).
fof(f3956,plain,
( ~ spl0_25
| ~ spl0_75
| spl0_41 ),
inference(split_clause,[status(thm)],[f3955,f424,f1026,f558]) ).
fof(f5492,plain,
member(singleton(sk0_8),ordered_pair(sk0_7,sk0_9)),
inference(paramodulation,[status(thm)],[f194,f3071]) ).
fof(f5493,plain,
( $false
| spl0_72 ),
inference(forward_subsumption_resolution,[status(thm)],[f5492,f998]) ).
fof(f5494,plain,
spl0_72,
inference(contradiction_clause,[status(thm)],[f5493]) ).
fof(f5495,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f1033,f1262,f1507,f3956,f5494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET016+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 21:35:55 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 3.85/0.88 % Refutation found
% 3.85/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.85/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.85/0.89 % Elapsed time: 0.543130 seconds
% 3.85/0.89 % CPU time: 4.186548 seconds
% 3.85/0.89 % Total memory used: 112.126 MB
% 3.85/0.89 % Net memory used: 108.068 MB
%------------------------------------------------------------------------------