TSTP Solution File: NUM535+2 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n014.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 Aug 31 18:05:41 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 140 ( 9 unt; 0 def)
% Number of atoms : 608 ( 68 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 707 ( 239 ~; 247 |; 154 &)
% ( 45 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 27 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 70 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f656,plain,
$false,
inference(avatar_sat_refutation,[],[f215,f240,f251,f261,f262,f267,f271,f277,f291,f299,f311,f323,f328,f349,f352,f611,f624,f630,f636,f649,f654,f655]) ).
fof(f655,plain,
( spl17_26
| ~ spl17_18 ),
inference(avatar_split_clause,[],[f575,f275,f335]) ).
fof(f335,plain,
( spl17_26
<=> ! [X0] :
( aElementOf0(X0,sF15)
| xx = X0
| ~ aElementOf0(X0,sF16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f275,plain,
( spl17_18
<=> ! [X0] :
( xx = X0
| aElementOf0(X0,sF15)
| ~ aElementOf0(X0,sdtpldt0(sF15,xx)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f575,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF16)
| aElementOf0(X0,sF15)
| xx = X0 )
| ~ spl17_18 ),
inference(forward_demodulation,[],[f276,f181]) ).
fof(f181,plain,
sdtpldt0(sF15,xx) = sF16,
introduced(function_definition,[]) ).
fof(f276,plain,
( ! [X0] :
( xx = X0
| ~ aElementOf0(X0,sdtpldt0(sF15,xx))
| aElementOf0(X0,sF15) )
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f654,plain,
( spl17_14
| ~ spl17_19
| ~ spl17_45 ),
inference(avatar_contradiction_clause,[],[f653]) ).
fof(f653,plain,
( $false
| spl17_14
| ~ spl17_19
| ~ spl17_45 ),
inference(subsumption_resolution,[],[f650,f283]) ).
fof(f283,plain,
( aElementOf0(xx,sF16)
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f281,plain,
( spl17_19
<=> aElementOf0(xx,sF16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f650,plain,
( ~ aElementOf0(xx,sF16)
| spl17_14
| ~ spl17_45 ),
inference(superposition,[],[f612,f606]) ).
fof(f606,plain,
( xx = sK9
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f604,plain,
( spl17_45
<=> xx = sK9 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f612,plain,
( ~ aElementOf0(sK9,sF16)
| spl17_14 ),
inference(forward_demodulation,[],[f250,f181]) ).
fof(f250,plain,
( ~ aElementOf0(sK9,sdtpldt0(sF15,xx))
| spl17_14 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f248,plain,
( spl17_14
<=> aElementOf0(sK9,sdtpldt0(sF15,xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f649,plain,
( ~ spl17_12
| spl17_14
| ~ spl17_16
| ~ spl17_46 ),
inference(avatar_contradiction_clause,[],[f648]) ).
fof(f648,plain,
( $false
| ~ spl17_12
| spl17_14
| ~ spl17_16
| ~ spl17_46 ),
inference(subsumption_resolution,[],[f647,f612]) ).
fof(f647,plain,
( aElementOf0(sK9,sF16)
| ~ spl17_12
| ~ spl17_16
| ~ spl17_46 ),
inference(subsumption_resolution,[],[f643,f348]) ).
fof(f348,plain,
( aElement0(sK9)
| ~ spl17_16 ),
inference(subsumption_resolution,[],[f344,f151]) ).
fof(f151,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
fof(f344,plain,
( aElement0(sK9)
| ~ aSet0(xS)
| ~ spl17_16 ),
inference(resolution,[],[f165,f260]) ).
fof(f260,plain,
( aElementOf0(sK9,xS)
| ~ spl17_16 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f258,plain,
( spl17_16
<=> aElementOf0(sK9,xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f165,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f643,plain,
( ~ aElement0(sK9)
| aElementOf0(sK9,sF16)
| ~ spl17_12
| ~ spl17_46 ),
inference(resolution,[],[f610,f338]) ).
fof(f338,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF15)
| aElementOf0(X0,sF16)
| ~ aElement0(X0) )
| ~ spl17_12 ),
inference(forward_demodulation,[],[f239,f181]) ).
fof(f239,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,sF15)
| aElementOf0(X0,sdtpldt0(sF15,xx)) )
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f238,plain,
( spl17_12
<=> ! [X0] :
( ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sF15,xx))
| ~ aElementOf0(X0,sF15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f610,plain,
( aElementOf0(sK9,sF15)
| ~ spl17_46 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f608,plain,
( spl17_46
<=> aElementOf0(sK9,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f636,plain,
( spl17_25
| ~ spl17_48 ),
inference(avatar_contradiction_clause,[],[f635]) ).
fof(f635,plain,
( $false
| spl17_25
| ~ spl17_48 ),
inference(subsumption_resolution,[],[f633,f102]) ).
fof(f102,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(f633,plain,
( ~ aElementOf0(xx,xS)
| spl17_25
| ~ spl17_48 ),
inference(superposition,[],[f322,f623]) ).
fof(f623,plain,
( xx = sK10
| ~ spl17_48 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f621,plain,
( spl17_48
<=> xx = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f322,plain,
( ~ aElementOf0(sK10,xS)
| spl17_25 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f320,plain,
( spl17_25
<=> aElementOf0(sK10,xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f630,plain,
( ~ spl17_17
| spl17_25
| ~ spl17_47 ),
inference(avatar_contradiction_clause,[],[f629]) ).
fof(f629,plain,
( $false
| ~ spl17_17
| spl17_25
| ~ spl17_47 ),
inference(subsumption_resolution,[],[f626,f322]) ).
fof(f626,plain,
( aElementOf0(sK10,xS)
| ~ spl17_17
| ~ spl17_47 ),
inference(resolution,[],[f619,f266]) ).
fof(f266,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF15)
| aElementOf0(X0,xS) )
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f265,plain,
( spl17_17
<=> ! [X0] :
( ~ aElementOf0(X0,sF15)
| aElementOf0(X0,xS) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f619,plain,
( aElementOf0(sK10,sF15)
| ~ spl17_47 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f617,plain,
( spl17_47
<=> aElementOf0(sK10,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f624,plain,
( spl17_47
| spl17_48
| ~ spl17_23
| ~ spl17_26 ),
inference(avatar_split_clause,[],[f614,f335,f308,f621,f617]) ).
fof(f308,plain,
( spl17_23
<=> aElementOf0(sK10,sF16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f614,plain,
( xx = sK10
| aElementOf0(sK10,sF15)
| ~ spl17_23
| ~ spl17_26 ),
inference(resolution,[],[f336,f310]) ).
fof(f310,plain,
( aElementOf0(sK10,sF16)
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f336,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF16)
| aElementOf0(X0,sF15)
| xx = X0 )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f611,plain,
( spl17_45
| spl17_46
| ~ spl17_16
| ~ spl17_20 ),
inference(avatar_split_clause,[],[f544,f289,f258,f608,f604]) ).
fof(f289,plain,
( spl17_20
<=> ! [X0] :
( aElementOf0(X0,sF15)
| xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f544,plain,
( aElementOf0(sK9,sF15)
| xx = sK9
| ~ spl17_16
| ~ spl17_20 ),
inference(subsumption_resolution,[],[f526,f348]) ).
fof(f526,plain,
( ~ aElement0(sK9)
| aElementOf0(sK9,sF15)
| xx = sK9
| ~ spl17_16
| ~ spl17_20 ),
inference(resolution,[],[f290,f260]) ).
fof(f290,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| xx = X0
| aElementOf0(X0,sF15)
| ~ aElement0(X0) )
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f352,plain,
( spl17_19
| ~ spl17_5 ),
inference(avatar_split_clause,[],[f351,f204,f281]) ).
fof(f204,plain,
( spl17_5
<=> aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f351,plain,
( aElementOf0(xx,sF16)
| ~ spl17_5 ),
inference(forward_demodulation,[],[f350,f181]) ).
fof(f350,plain,
( aElementOf0(xx,sdtpldt0(sF15,xx))
| ~ spl17_5 ),
inference(forward_demodulation,[],[f206,f180]) ).
fof(f180,plain,
sdtmndt0(xS,xx) = sF15,
introduced(function_definition,[]) ).
fof(f206,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f349,plain,
spl17_6,
inference(avatar_split_clause,[],[f345,f208]) ).
fof(f208,plain,
( spl17_6
<=> aElement0(xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f345,plain,
aElement0(xx),
inference(subsumption_resolution,[],[f343,f151]) ).
fof(f343,plain,
( ~ aSet0(xS)
| aElement0(xx) ),
inference(resolution,[],[f165,f102]) ).
fof(f328,plain,
( spl17_7
| ~ spl17_9 ),
inference(avatar_split_clause,[],[f103,f221,f212]) ).
fof(f212,plain,
( spl17_7
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f221,plain,
( spl17_9
<=> sP4 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f103,plain,
( ~ sP4
| sP0 ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ( aSet0(sdtmndt0(xS,xx))
& sP1
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sK9,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK9,xS)
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& sP0 )
| ~ sP4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f59,f60]) ).
fof(f60,plain,
( ? [X0] :
( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X0,xS) )
=> ( ~ aElementOf0(sK9,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK9,xS) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ( aSet0(sdtmndt0(xS,xx))
& sP1
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X0] :
( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X0,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& sP0 )
| ~ sP4 ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
( ( aSet0(sdtmndt0(xS,xx))
& sP1
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& sP0 )
| ~ sP4 ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
( ( aSet0(sdtmndt0(xS,xx))
& sP1
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& sP0 )
| ~ sP4 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f323,plain,
( ~ spl17_25
| spl17_9 ),
inference(avatar_split_clause,[],[f130,f221,f320]) ).
fof(f130,plain,
( sP4
| ~ aElementOf0(sK10,xS) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ( sP3
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sK10,xS)
& aElementOf0(sK10,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(xS,xx))
& sP2 )
| sP4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f73,f74]) ).
fof(f74,plain,
( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( ~ aElementOf0(sK10,xS)
& aElementOf0(sK10,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
( ( sP3
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(xS,xx))
& sP2 )
| sP4 ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
( ( sP3
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(xS,xx))
& sP2 )
| sP4 ),
inference(definition_folding,[],[f42,f50,f49,f48,f47,f46]) ).
fof(f46,plain,
( ! [X1] :
( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 )
& aElement0(X1) )
<=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f47,plain,
( ! [X0] :
( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
<=> aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f48,plain,
( ! [X3] :
( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
<=> aElementOf0(X3,sdtmndt0(xS,xx)) )
| ~ sP2 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f49,plain,
( ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) )
| ~ sP3 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f42,plain,
( ( ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X3] :
( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
<=> aElementOf0(X3,sdtmndt0(xS,xx)) ) )
| ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
<=> aElementOf0(X0,sdtmndt0(xS,xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 )
& aElement0(X1) )
<=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
( ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X3] :
( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
<=> aElementOf0(X3,sdtmndt0(xS,xx)) ) )
| ( ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 )
& aElement0(X1) )
<=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
<=> aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
~ ( ( ( aSet0(sdtmndt0(xS,xx))
& ! [X3] :
( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
<=> aElementOf0(X3,sdtmndt0(xS,xx)) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) ) )
=> ( ! [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X5,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) )
& ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
<=> aElementOf0(X0,sdtmndt0(xS,xx)) ) )
=> ( ( ! [X1] :
( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 )
& aElement0(X1) )
<=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
<=> aElementOf0(X0,sdtmndt0(xS,xx)) ) )
=> ( ( ! [X0] :
( ( ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0 )
& aElement0(X0) )
<=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X0] :
( ( aElement0(X0)
& ( xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) ) )
<=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
<=> aElementOf0(X0,sdtmndt0(xS,xx)) ) )
=> ( ( ! [X0] :
( ( ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0 )
& aElement0(X0) )
<=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X0] :
( ( aElement0(X0)
& ( xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) ) )
<=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f311,plain,
( spl17_23
| spl17_9 ),
inference(avatar_split_clause,[],[f183,f221,f308]) ).
fof(f183,plain,
( sP4
| aElementOf0(sK10,sF16) ),
inference(definition_folding,[],[f129,f181,f180]) ).
fof(f129,plain,
( aElementOf0(sK10,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP4 ),
inference(cnf_transformation,[],[f75]) ).
fof(f299,plain,
( spl17_9
| spl17_1 ),
inference(avatar_split_clause,[],[f132,f187,f221]) ).
fof(f187,plain,
( spl17_1
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f132,plain,
( sP3
| sP4 ),
inference(cnf_transformation,[],[f75]) ).
fof(f291,plain,
( ~ spl17_10
| spl17_20 ),
inference(avatar_split_clause,[],[f287,f289,f227]) ).
fof(f227,plain,
( spl17_10
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f287,plain,
! [X0] :
( aElementOf0(X0,sF15)
| ~ sP1
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 ),
inference(forward_demodulation,[],[f118,f180]) ).
fof(f118,plain,
! [X0] :
( ~ sP1
| ~ aElement0(X0)
| xx = X0
| ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ! [X0] :
( ( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ) )
| ~ sP1 ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
( ! [X0] :
( ( ( xx != X0
& aElement0(X0)
& aElementOf0(X0,xS) )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f47]) ).
fof(f277,plain,
( ~ spl17_1
| spl17_18 ),
inference(avatar_split_clause,[],[f273,f275,f187]) ).
fof(f273,plain,
! [X0] :
( xx = X0
| ~ aElementOf0(X0,sdtpldt0(sF15,xx))
| ~ sP3
| aElementOf0(X0,sF15) ),
inference(forward_demodulation,[],[f272,f180]) ).
fof(f272,plain,
! [X0] :
( aElementOf0(X0,sF15)
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP3
| xx = X0 ),
inference(forward_demodulation,[],[f110,f180]) ).
fof(f110,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP3
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = X0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
& xx != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP3 ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
( ! [X4] :
( ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X4)
| ( ~ aElementOf0(X4,sdtmndt0(xS,xx))
& xx != X4 ) )
& ( ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) )
| ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP3 ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
( ! [X4] :
( ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X4)
| ( ~ aElementOf0(X4,sdtmndt0(xS,xx))
& xx != X4 ) )
& ( ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) )
| ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP3 ),
inference(nnf_transformation,[],[f49]) ).
fof(f271,plain,
( spl17_10
| ~ spl17_9 ),
inference(avatar_split_clause,[],[f108,f221,f227]) ).
fof(f108,plain,
( ~ sP4
| sP1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f267,plain,
( spl17_17
| ~ spl17_4 ),
inference(avatar_split_clause,[],[f263,f199,f265]) ).
fof(f199,plain,
( spl17_4
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f263,plain,
! [X0] :
( ~ sP2
| ~ aElementOf0(X0,sF15)
| aElementOf0(X0,xS) ),
inference(forward_demodulation,[],[f116,f180]) ).
fof(f116,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ sP2
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0] :
( ( ( aElement0(X0)
& aElementOf0(X0,xS)
& xx != X0 )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 ) )
| ~ sP2 ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
( ! [X3] :
( ( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
| ~ aElementOf0(X3,sdtmndt0(xS,xx)) )
& ( aElementOf0(X3,sdtmndt0(xS,xx))
| ~ aElement0(X3)
| ~ aElementOf0(X3,xS)
| xx = X3 ) )
| ~ sP2 ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
( ! [X3] :
( ( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
| ~ aElementOf0(X3,sdtmndt0(xS,xx)) )
& ( aElementOf0(X3,sdtmndt0(xS,xx))
| ~ aElement0(X3)
| ~ aElementOf0(X3,xS)
| xx = X3 ) )
| ~ sP2 ),
inference(nnf_transformation,[],[f48]) ).
fof(f262,plain,
( spl17_4
| spl17_9 ),
inference(avatar_split_clause,[],[f126,f221,f199]) ).
fof(f126,plain,
( sP4
| sP2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f261,plain,
( ~ spl17_9
| spl17_16 ),
inference(avatar_split_clause,[],[f105,f258,f221]) ).
fof(f105,plain,
( aElementOf0(sK9,xS)
| ~ sP4 ),
inference(cnf_transformation,[],[f61]) ).
fof(f251,plain,
( ~ spl17_9
| ~ spl17_14 ),
inference(avatar_split_clause,[],[f246,f248,f221]) ).
fof(f246,plain,
( ~ aElementOf0(sK9,sdtpldt0(sF15,xx))
| ~ sP4 ),
inference(forward_demodulation,[],[f106,f180]) ).
fof(f106,plain,
( ~ aElementOf0(sK9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP4 ),
inference(cnf_transformation,[],[f61]) ).
fof(f240,plain,
( ~ spl17_7
| spl17_12 ),
inference(avatar_split_clause,[],[f236,f238,f212]) ).
fof(f236,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,sF15)
| ~ sP0
| aElementOf0(X0,sdtpldt0(sF15,xx)) ),
inference(forward_demodulation,[],[f235,f180]) ).
fof(f235,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sF15,xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP0
| ~ aElement0(X0) ),
inference(forward_demodulation,[],[f123,f180]) ).
fof(f123,plain,
! [X0] :
( ~ sP0
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ! [X0] :
( ( ( ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0 )
& aElement0(X0) )
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
& xx != X0 )
| ~ aElement0(X0) ) )
| ~ sP0 ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
( ! [X1] :
( ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 )
& aElement0(X1) )
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
& xx != X1 )
| ~ aElement0(X1) ) )
| ~ sP0 ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
( ! [X1] :
( ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 )
& aElement0(X1) )
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
& xx != X1 )
| ~ aElement0(X1) ) )
| ~ sP0 ),
inference(nnf_transformation,[],[f46]) ).
fof(f215,plain,
( spl17_5
| ~ spl17_6
| ~ spl17_7 ),
inference(avatar_split_clause,[],[f173,f212,f208,f204]) ).
fof(f173,plain,
( ~ sP0
| ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(equality_resolution,[],[f122]) ).
fof(f122,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx != X0
| ~ aElement0(X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 07:09:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.48 % (12847)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48 % (12838)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.49 % (12834)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.49 % (12834)Refutation not found, incomplete strategy% (12834)------------------------------
% 0.20/0.49 % (12834)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (12855)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.51 % (12834)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (12834)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (12834)Memory used [KB]: 5628
% 0.20/0.51 % (12834)Time elapsed: 0.103 s
% 0.20/0.51 % (12834)Instructions burned: 6 (million)
% 0.20/0.51 % (12834)------------------------------
% 0.20/0.51 % (12834)------------------------------
% 0.20/0.51 % (12847)First to succeed.
% 0.20/0.51 % (12847)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (12847)------------------------------
% 0.20/0.51 % (12847)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (12847)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (12847)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (12847)Memory used [KB]: 5756
% 0.20/0.51 % (12847)Time elapsed: 0.099 s
% 0.20/0.51 % (12847)Instructions burned: 12 (million)
% 0.20/0.51 % (12847)------------------------------
% 0.20/0.51 % (12847)------------------------------
% 0.20/0.51 % (12830)Success in time 0.152 s
%------------------------------------------------------------------------------