TSTP Solution File: SEU298+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.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 : Sun May 5 09:22:02 EDT 2024
% Result : Theorem 0.56s 0.76s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 103 ( 5 unt; 0 def)
% Number of atoms : 532 ( 130 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 640 ( 211 ~; 238 |; 153 &)
% ( 19 <=>; 17 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 233 ( 136 !; 97 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f485,plain,
$false,
inference(avatar_sat_refutation,[],[f320,f324,f347,f360,f362,f397,f402,f407,f412,f445,f478,f481,f484]) ).
fof(f484,plain,
( ~ spl29_9
| spl29_27 ),
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f482,plain,
( $false
| ~ spl29_9
| spl29_27 ),
inference(resolution,[],[f477,f371]) ).
fof(f371,plain,
( in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2))
| ~ spl29_9 ),
inference(factoring,[],[f365]) ).
fof(f365,plain,
( ! [X0] :
( in(sK3(X0),sK26(sK1,sK2))
| in(sK3(X0),X0) )
| ~ spl29_9 ),
inference(duplicate_literal_removal,[],[f363]) ).
fof(f363,plain,
( ! [X0] :
( in(sK3(X0),X0)
| in(sK3(X0),sK26(sK1,sK2))
| in(sK3(X0),X0) )
| ~ spl29_9 ),
inference(resolution,[],[f346,f129]) ).
fof(f129,plain,
! [X2] :
( in(sK3(X2),powerset(sK1))
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( ! [X2] :
( ( ! [X4] :
( set_difference(X4,singleton(sK1)) != sK3(X2)
| ~ in(X4,sK2) )
| ~ in(sK3(X2),powerset(sK1))
| ~ in(sK3(X2),X2) )
& ( ( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
& in(sK4(X2),sK2)
& in(sK3(X2),powerset(sK1)) )
| in(sK3(X2),X2) ) )
& element(sK2,powerset(powerset(succ(sK1))))
& ordinal(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f79,f82,f81,f80]) ).
fof(f80,plain,
( ? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(sK1)) != X3
| ~ in(X4,sK2) )
| ~ in(X3,powerset(sK1))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(sK1)) = X3
& in(X5,sK2) )
& in(X3,powerset(sK1)) )
| in(X3,X2) ) )
& element(sK2,powerset(powerset(succ(sK1))))
& ordinal(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X2] :
( ? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(sK1)) != X3
| ~ in(X4,sK2) )
| ~ in(X3,powerset(sK1))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(sK1)) = X3
& in(X5,sK2) )
& in(X3,powerset(sK1)) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( set_difference(X4,singleton(sK1)) != sK3(X2)
| ~ in(X4,sK2) )
| ~ in(sK3(X2),powerset(sK1))
| ~ in(sK3(X2),X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(sK1)) = sK3(X2)
& in(X5,sK2) )
& in(sK3(X2),powerset(sK1)) )
| in(sK3(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X2] :
( ? [X5] :
( set_difference(X5,singleton(sK1)) = sK3(X2)
& in(X5,sK2) )
=> ( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
& in(sK4(X2),sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PxwB9m59L4/Vampire---4.8_8293',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(f346,plain,
( ! [X0] :
( ~ in(sK3(X0),powerset(sK1))
| in(sK3(X0),X0)
| in(sK3(X0),sK26(sK1,sK2)) )
| ~ spl29_9 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f345,plain,
( spl29_9
<=> ! [X0] :
( in(sK3(X0),X0)
| ~ in(sK3(X0),powerset(sK1))
| in(sK3(X0),sK26(sK1,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_9])]) ).
fof(f477,plain,
( ~ in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2))
| spl29_27 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f475,plain,
( spl29_27
<=> in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_27])]) ).
fof(f481,plain,
( ~ spl29_15
| ~ spl29_17
| spl29_22 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f479,plain,
( $false
| ~ spl29_15
| ~ spl29_17
| spl29_22 ),
inference(resolution,[],[f452,f413]) ).
fof(f413,plain,
( in(sK3(sK26(sK1,sK2)),powerset(sK1))
| ~ spl29_15
| ~ spl29_17 ),
inference(forward_demodulation,[],[f401,f411]) ).
fof(f411,plain,
( sK3(sK26(sK1,sK2)) = sK27(sK1,sK2,sK3(sK26(sK1,sK2)))
| ~ spl29_17 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f409,plain,
( spl29_17
<=> sK3(sK26(sK1,sK2)) = sK27(sK1,sK2,sK3(sK26(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).
fof(f401,plain,
( in(sK27(sK1,sK2,sK3(sK26(sK1,sK2))),powerset(sK1))
| ~ spl29_15 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f399,plain,
( spl29_15
<=> in(sK27(sK1,sK2,sK3(sK26(sK1,sK2))),powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).
fof(f452,plain,
( ~ in(sK3(sK26(sK1,sK2)),powerset(sK1))
| spl29_22 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f450,plain,
( spl29_22
<=> in(sK3(sK26(sK1,sK2)),powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).
fof(f478,plain,
( ~ spl29_22
| ~ spl29_27
| ~ spl29_20 ),
inference(avatar_split_clause,[],[f473,f443,f475,f450]) ).
fof(f443,plain,
( spl29_20
<=> ! [X0] :
( sK3(X0) != sK3(sK26(sK1,sK2))
| ~ in(sK3(X0),X0)
| ~ in(sK3(X0),powerset(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).
fof(f473,plain,
( ~ in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2))
| ~ in(sK3(sK26(sK1,sK2)),powerset(sK1))
| ~ spl29_20 ),
inference(equality_resolution,[],[f444]) ).
fof(f444,plain,
( ! [X0] :
( sK3(X0) != sK3(sK26(sK1,sK2))
| ~ in(sK3(X0),X0)
| ~ in(sK3(X0),powerset(sK1)) )
| ~ spl29_20 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( ~ spl29_16
| spl29_20
| ~ spl29_14 ),
inference(avatar_split_clause,[],[f438,f394,f443,f404]) ).
fof(f404,plain,
( spl29_16
<=> in(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).
fof(f394,plain,
( spl29_14
<=> sK3(sK26(sK1,sK2)) = set_difference(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),singleton(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).
fof(f438,plain,
( ! [X0] :
( sK3(X0) != sK3(sK26(sK1,sK2))
| ~ in(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),sK2)
| ~ in(sK3(X0),powerset(sK1))
| ~ in(sK3(X0),X0) )
| ~ spl29_14 ),
inference(superposition,[],[f132,f396]) ).
fof(f396,plain,
( sK3(sK26(sK1,sK2)) = set_difference(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),singleton(sK1))
| ~ spl29_14 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f132,plain,
! [X2,X4] :
( set_difference(X4,singleton(sK1)) != sK3(X2)
| ~ in(X4,sK2)
| ~ in(sK3(X2),powerset(sK1))
| ~ in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f412,plain,
( ~ spl29_3
| ~ spl29_8
| spl29_7
| spl29_17
| ~ spl29_9 ),
inference(avatar_split_clause,[],[f391,f345,f409,f337,f341,f314]) ).
fof(f314,plain,
( spl29_3
<=> ordinal(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).
fof(f341,plain,
( spl29_8
<=> element(sK2,powerset(powerset(succ(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_8])]) ).
fof(f337,plain,
( spl29_7
<=> sP0(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).
fof(f391,plain,
( sK3(sK26(sK1,sK2)) = sK27(sK1,sK2,sK3(sK26(sK1,sK2)))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1)
| ~ spl29_9 ),
inference(resolution,[],[f371,f226]) ).
fof(f226,plain,
! [X3,X0,X1] :
( ~ in(X3,sK26(X0,X1))
| sK27(X0,X1,X3) = X3
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK26(X0,X1))
| ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) ) )
& ( ( set_difference(sK28(X0,X1,X3),singleton(X0)) = X3
& in(sK28(X0,X1,X3),X1)
& sK27(X0,X1,X3) = X3
& in(sK27(X0,X1,X3),powerset(X0)) )
| ~ in(X3,sK26(X0,X1)) ) )
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28])],[f122,f125,f124,f123]) ).
fof(f123,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) ) )
& ( ? [X6] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X6
& in(X6,powerset(X0)) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK26(X0,X1))
| ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) ) )
& ( ? [X6] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X6
& in(X6,powerset(X0)) )
| ~ in(X3,sK26(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0,X1,X3] :
( ? [X6] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X6
& in(X6,powerset(X0)) )
=> ( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& sK27(X0,X1,X3) = X3
& in(sK27(X0,X1,X3),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0,X1,X3] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
=> ( set_difference(sK28(X0,X1,X3),singleton(X0)) = X3
& in(sK28(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) ) )
& ( ? [X6] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X6
& in(X6,powerset(X0)) )
| ~ in(X3,X2) ) )
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(rectify,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ! [X10] :
( set_difference(X10,singleton(X0)) != X8
| ~ in(X10,X1) )
| X8 != X9
| ~ in(X9,powerset(X0)) ) )
& ( ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) )
| ~ in(X8,X7) ) )
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) )
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(definition_folding,[],[f74,f75]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( set_difference(X6,singleton(X0)) = X4
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X4
& in(X4,powerset(X0)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PxwB9m59L4/Vampire---4.8_8293',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(f407,plain,
( ~ spl29_3
| ~ spl29_8
| spl29_7
| spl29_16
| ~ spl29_9 ),
inference(avatar_split_clause,[],[f390,f345,f404,f337,f341,f314]) ).
fof(f390,plain,
( in(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),sK2)
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1)
| ~ spl29_9 ),
inference(resolution,[],[f371,f227]) ).
fof(f227,plain,
! [X3,X0,X1] :
( ~ in(X3,sK26(X0,X1))
| in(sK28(X0,X1,X3),X1)
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f402,plain,
( ~ spl29_3
| ~ spl29_8
| spl29_7
| spl29_15
| ~ spl29_9 ),
inference(avatar_split_clause,[],[f389,f345,f399,f337,f341,f314]) ).
fof(f389,plain,
( in(sK27(sK1,sK2,sK3(sK26(sK1,sK2))),powerset(sK1))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1)
| ~ spl29_9 ),
inference(resolution,[],[f371,f225]) ).
fof(f225,plain,
! [X3,X0,X1] :
( ~ in(X3,sK26(X0,X1))
| in(sK27(X0,X1,X3),powerset(X0))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f397,plain,
( ~ spl29_3
| ~ spl29_8
| spl29_7
| spl29_14
| ~ spl29_9 ),
inference(avatar_split_clause,[],[f388,f345,f394,f337,f341,f314]) ).
fof(f388,plain,
( sK3(sK26(sK1,sK2)) = set_difference(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),singleton(sK1))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1)
| ~ spl29_9 ),
inference(resolution,[],[f371,f228]) ).
fof(f228,plain,
! [X3,X0,X1] :
( ~ in(X3,sK26(X0,X1))
| set_difference(sK28(X0,X1,X3),singleton(X0)) = X3
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f362,plain,
spl29_8,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f361,plain,
( $false
| spl29_8 ),
inference(resolution,[],[f343,f128]) ).
fof(f128,plain,
element(sK2,powerset(powerset(succ(sK1)))),
inference(cnf_transformation,[],[f83]) ).
fof(f343,plain,
( ~ element(sK2,powerset(powerset(succ(sK1))))
| spl29_8 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f360,plain,
( ~ spl29_7
| ~ spl29_7 ),
inference(avatar_split_clause,[],[f359,f337,f337]) ).
fof(f359,plain,
( ~ sP0(sK1,sK2)
| ~ spl29_7 ),
inference(trivial_inequality_removal,[],[f358]) ).
fof(f358,plain,
( sK22(sK1,sK2) != sK22(sK1,sK2)
| ~ sP0(sK1,sK2)
| ~ spl29_7 ),
inference(superposition,[],[f224,f356]) ).
fof(f356,plain,
( sK23(sK1,sK2) = sK22(sK1,sK2)
| ~ spl29_7 ),
inference(superposition,[],[f351,f350]) ).
fof(f350,plain,
( sK23(sK1,sK2) = sK21(sK1,sK2)
| ~ spl29_7 ),
inference(resolution,[],[f339,f221]) ).
fof(f221,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK23(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ( sK22(X0,X1) != sK23(X0,X1)
& sK23(X0,X1) = set_difference(sK24(X0,X1),singleton(X0))
& in(sK24(X0,X1),X1)
& sK21(X0,X1) = sK23(X0,X1)
& sK22(X0,X1) = set_difference(sK25(X0,X1),singleton(X0))
& in(sK25(X0,X1),X1)
& sK21(X0,X1) = sK22(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25])],[f116,f119,f118,f117]) ).
fof(f117,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
=> ( sK22(X0,X1) != sK23(X0,X1)
& ? [X5] :
( set_difference(X5,singleton(X0)) = sK23(X0,X1)
& in(X5,X1) )
& sK21(X0,X1) = sK23(X0,X1)
& ? [X6] :
( set_difference(X6,singleton(X0)) = sK22(X0,X1)
& in(X6,X1) )
& sK21(X0,X1) = sK22(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X5] :
( set_difference(X5,singleton(X0)) = sK23(X0,X1)
& in(X5,X1) )
=> ( sK23(X0,X1) = set_difference(sK24(X0,X1),singleton(X0))
& in(sK24(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X1] :
( ? [X6] :
( set_difference(X6,singleton(X0)) = sK22(X0,X1)
& in(X6,X1) )
=> ( sK22(X0,X1) = set_difference(sK25(X0,X1),singleton(X0))
& in(sK25(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f75]) ).
fof(f339,plain,
( sP0(sK1,sK2)
| ~ spl29_7 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f351,plain,
( sK22(sK1,sK2) = sK21(sK1,sK2)
| ~ spl29_7 ),
inference(resolution,[],[f339,f218]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK22(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f224,plain,
! [X0,X1] :
( sK22(X0,X1) != sK23(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f347,plain,
( spl29_7
| ~ spl29_8
| spl29_9
| ~ spl29_4 ),
inference(avatar_split_clause,[],[f335,f318,f345,f341,f337]) ).
fof(f318,plain,
( spl29_4
<=> ! [X0,X1] :
( ~ in(sK3(X0),powerset(sK1))
| in(sK3(X0),X0)
| ~ element(X1,powerset(powerset(succ(sK1))))
| sP0(sK1,X1)
| in(sK3(X0),sK26(sK1,X1))
| ~ in(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).
fof(f335,plain,
( ! [X0] :
( in(sK3(X0),X0)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| sP0(sK1,sK2)
| in(sK3(X0),sK26(sK1,sK2))
| ~ in(sK3(X0),powerset(sK1)) )
| ~ spl29_4 ),
inference(duplicate_literal_removal,[],[f334]) ).
fof(f334,plain,
( ! [X0] :
( in(sK3(X0),X0)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| sP0(sK1,sK2)
| in(sK3(X0),sK26(sK1,sK2))
| ~ in(sK3(X0),powerset(sK1))
| in(sK3(X0),X0) )
| ~ spl29_4 ),
inference(resolution,[],[f319,f130]) ).
fof(f130,plain,
! [X2] :
( in(sK4(X2),sK2)
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f319,plain,
( ! [X0,X1] :
( ~ in(sK4(X0),X1)
| in(sK3(X0),X0)
| ~ element(X1,powerset(powerset(succ(sK1))))
| sP0(sK1,X1)
| in(sK3(X0),sK26(sK1,X1))
| ~ in(sK3(X0),powerset(sK1)) )
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f324,plain,
spl29_3,
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f321,plain,
( $false
| spl29_3 ),
inference(resolution,[],[f316,f127]) ).
fof(f127,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f83]) ).
fof(f316,plain,
( ~ ordinal(sK1)
| spl29_3 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f320,plain,
( ~ spl29_3
| spl29_4 ),
inference(avatar_split_clause,[],[f312,f318,f314]) ).
fof(f312,plain,
! [X0,X1] :
( ~ in(sK3(X0),powerset(sK1))
| ~ in(sK4(X0),X1)
| in(sK3(X0),sK26(sK1,X1))
| sP0(sK1,X1)
| ~ element(X1,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1)
| in(sK3(X0),X0) ),
inference(superposition,[],[f231,f131]) ).
fof(f131,plain,
! [X2] :
( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f231,plain,
! [X0,X1,X5] :
( ~ in(set_difference(X5,singleton(X0)),powerset(X0))
| ~ in(X5,X1)
| in(set_difference(X5,singleton(X0)),sK26(X0,X1))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(equality_resolution,[],[f230]) ).
fof(f230,plain,
! [X0,X1,X4,X5] :
( in(set_difference(X5,singleton(X0)),sK26(X0,X1))
| ~ in(X5,X1)
| set_difference(X5,singleton(X0)) != X4
| ~ in(X4,powerset(X0))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(equality_resolution,[],[f229]) ).
fof(f229,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK26(X0,X1))
| set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1)
| X3 != X4
| ~ in(X4,powerset(X0))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:36:34 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.PxwB9m59L4/Vampire---4.8_8293
% 0.56/0.74 % (8408)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.56/0.74 % (8401)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.74 % (8403)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.74 % (8404)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.56/0.74 % (8402)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.56/0.74 % (8406)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.56/0.74 % (8405)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.74 % (8407)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.56/0.74 % (8408)Refutation not found, incomplete strategy% (8408)------------------------------
% 0.56/0.74 % (8408)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (8408)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (8408)Memory used [KB]: 1153
% 0.56/0.74 % (8408)Time elapsed: 0.003 s
% 0.56/0.74 % (8408)Instructions burned: 6 (million)
% 0.56/0.75 % (8408)------------------------------
% 0.56/0.75 % (8408)------------------------------
% 0.56/0.75 % (8409)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.56/0.75 % (8405)Refutation not found, incomplete strategy% (8405)------------------------------
% 0.56/0.75 % (8405)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75 % (8405)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75
% 0.56/0.75 % (8405)Memory used [KB]: 1146
% 0.56/0.75 % (8405)Time elapsed: 0.006 s
% 0.56/0.75 % (8405)Instructions burned: 7 (million)
% 0.56/0.75 % (8401)Refutation not found, incomplete strategy% (8401)------------------------------
% 0.56/0.75 % (8401)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75 % (8401)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75
% 0.56/0.75 % (8401)Memory used [KB]: 1143
% 0.56/0.75 % (8401)Time elapsed: 0.006 s
% 0.56/0.75 % (8401)Instructions burned: 8 (million)
% 0.56/0.75 % (8406)Refutation not found, incomplete strategy% (8406)------------------------------
% 0.56/0.75 % (8406)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75 % (8406)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75 % (8405)------------------------------
% 0.56/0.75 % (8405)------------------------------
% 0.56/0.75
% 0.56/0.75 % (8406)Memory used [KB]: 1144
% 0.56/0.75 % (8406)Time elapsed: 0.006 s
% 0.56/0.75 % (8406)Instructions burned: 7 (million)
% 0.56/0.75 % (8401)------------------------------
% 0.56/0.75 % (8401)------------------------------
% 0.56/0.75 % (8406)------------------------------
% 0.56/0.75 % (8406)------------------------------
% 0.56/0.75 % (8410)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.56/0.75 % (8402)First to succeed.
% 0.56/0.75 % (8411)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.56/0.75 % (8412)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.56/0.76 % (8402)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8400"
% 0.56/0.76 % (8402)Refutation found. Thanks to Tanya!
% 0.56/0.76 % SZS status Theorem for Vampire---4
% 0.56/0.76 % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.76 % (8402)------------------------------
% 0.56/0.76 % (8402)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.76 % (8402)Termination reason: Refutation
% 0.56/0.76
% 0.56/0.76 % (8402)Memory used [KB]: 1204
% 0.56/0.76 % (8402)Time elapsed: 0.013 s
% 0.56/0.76 % (8402)Instructions burned: 18 (million)
% 0.56/0.76 % (8400)Success in time 0.387 s
% 0.56/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------