TSTP Solution File: RNG106+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : RNG106+1 : 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_uns --cores 0 -t %d %s
% Computer : n019.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 18:15:01 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 98 ( 7 unt; 0 def)
% Number of atoms : 527 ( 75 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 674 ( 245 ~; 245 |; 150 &)
% ( 15 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 161 ( 115 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f505,plain,
$false,
inference(avatar_sat_refutation,[],[f337,f344,f346,f353,f365,f435,f440,f445,f473,f504]) ).
fof(f504,plain,
( ~ spl25_1
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_10
| ~ spl25_11 ),
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f503,plain,
( $false
| ~ spl25_1
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_10
| ~ spl25_11 ),
inference(subsumption_resolution,[],[f502,f433]) ).
fof(f433,plain,
( aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_11 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f432,plain,
( spl25_11
<=> aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_11])]) ).
fof(f502,plain,
( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_10
| ~ spl25_11 ),
inference(subsumption_resolution,[],[f500,f429]) ).
fof(f429,plain,
( aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_10 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f428,plain,
( spl25_10
<=> aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_10])]) ).
fof(f500,plain,
( ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_4
| ~ spl25_5
| ~ spl25_7
| ~ spl25_11 ),
inference(resolution,[],[f499,f343]) ).
fof(f343,plain,
( ! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) )
| ~ spl25_4 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f342,plain,
( spl25_4
<=> ! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_4])]) ).
fof(f499,plain,
( ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_5
| ~ spl25_7
| ~ spl25_11 ),
inference(subsumption_resolution,[],[f498,f433]) ).
fof(f498,plain,
( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_5
| ~ spl25_7 ),
inference(subsumption_resolution,[],[f497,f207]) ).
fof(f207,plain,
~ aIdeal0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( ! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ( sdtasdt0(xc,sK5(X0,X1,X2)) = X1
& aElement0(sK5(X0,X1,X2))
& aElement0(sK6(X0,X1,X2))
& sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)))
& sdtasdt0(xc,sK6(X0,X1,X2)) = X0
& aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
& sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) ) )
& ~ aIdeal0(slsdtgt0(xc)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f128,f130,f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ? [X3] :
( sdtasdt0(xc,X3) = X1
& aElement0(X3)
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X0
& aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
& sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) )
=> ( sdtasdt0(xc,sK5(X0,X1,X2)) = X1
& aElement0(sK5(X0,X1,X2))
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),X4))
& sdtasdt0(xc,X4) = X0
& aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
& sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ? [X4] :
( aElement0(X4)
& sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),X4))
& sdtasdt0(xc,X4) = X0
& aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
& sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) )
=> ( aElement0(sK6(X0,X1,X2))
& sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)))
& sdtasdt0(xc,sK6(X0,X1,X2)) = X0
& aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
& sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
( ! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X1
& aElement0(X3)
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X0
& aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
& sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
& ~ aIdeal0(slsdtgt0(xc)) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
( ! [X1,X0,X2] :
( ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X0
& aElement0(X3)
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
& ~ aIdeal0(slsdtgt0(xc)) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ! [X1,X0,X2] :
( ? [X3] :
( sdtasdt0(xc,X3) = X0
& aElement0(X3)
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) )
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,negated_conjecture,
~ ( ! [X1,X0,X2] :
( ( aElementOf0(X0,slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc))
& aElement0(X2) )
=> ? [X3] :
( sdtasdt0(xc,X3) = X0
& aElement0(X3)
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
=> aIdeal0(slsdtgt0(xc)) ),
inference(negated_conjecture,[],[f39]) ).
fof(f39,conjecture,
( ! [X1,X0,X2] :
( ( aElementOf0(X0,slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc))
& aElement0(X2) )
=> ? [X3] :
( sdtasdt0(xc,X3) = X0
& aElement0(X3)
& ? [X4] :
( aElement0(X4)
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
=> aIdeal0(slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f497,plain,
( ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_5
| ~ spl25_7 ),
inference(subsumption_resolution,[],[f496,f401]) ).
fof(f401,plain,
( aElement0(sK13(slsdtgt0(xc)))
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f399,plain,
( spl25_7
<=> aElement0(sK13(slsdtgt0(xc))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).
fof(f496,plain,
( ~ aElement0(sK13(slsdtgt0(xc)))
| ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_5 ),
inference(subsumption_resolution,[],[f494,f357]) ).
fof(f357,plain,
( aSet0(slsdtgt0(xc))
| ~ spl25_5 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f356,plain,
( spl25_5
<=> aSet0(slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_5])]) ).
fof(f494,plain,
( ~ aSet0(slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
| ~ aElement0(sK13(slsdtgt0(xc)))
| ~ spl25_1 ),
inference(resolution,[],[f239,f333]) ).
fof(f333,plain,
( ! [X2,X1] :
( aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) )
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f332,plain,
( spl25_1
<=> ! [X2,X1] :
( aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).
fof(f239,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0)
| ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0)
& aElementOf0(sK12(X0),X0) )
| ( aElement0(sK13(X0))
& ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0) ) )
& aElementOf0(sK11(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) ) )
| ~ aElementOf0(X4,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f149,f152,f151,f150]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
& aElementOf0(X1,X0) )
=> ( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(sK11(X0),X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,sK11(X0)),X0) ) )
& aElementOf0(sK11(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f151,plain,
! [X0] :
( ? [X2] :
( ~ aElementOf0(sdtpldt0(sK11(X0),X2),X0)
& aElementOf0(X2,X0) )
=> ( ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0)
& aElementOf0(sK12(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
! [X0] :
( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,sK11(X0)),X0) )
=> ( aElement0(sK13(X0))
& ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) ) )
| ~ aElementOf0(X4,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) )
<=> aIdeal0(X0) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f473,plain,
( ~ spl25_5
| spl25_11 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f472,plain,
( $false
| ~ spl25_5
| spl25_11 ),
inference(subsumption_resolution,[],[f471,f357]) ).
fof(f471,plain,
( ~ aSet0(slsdtgt0(xc))
| spl25_11 ),
inference(subsumption_resolution,[],[f470,f207]) ).
fof(f470,plain,
( aIdeal0(slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| spl25_11 ),
inference(resolution,[],[f434,f236]) ).
fof(f236,plain,
! [X0] :
( aElementOf0(sK11(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f434,plain,
( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| spl25_11 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f445,plain,
( ~ spl25_5
| spl25_7
| spl25_10 ),
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f444,plain,
( $false
| ~ spl25_5
| spl25_7
| spl25_10 ),
inference(subsumption_resolution,[],[f443,f400]) ).
fof(f400,plain,
( ~ aElement0(sK13(slsdtgt0(xc)))
| spl25_7 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f443,plain,
( aElement0(sK13(slsdtgt0(xc)))
| ~ spl25_5
| spl25_10 ),
inference(subsumption_resolution,[],[f442,f207]) ).
fof(f442,plain,
( aIdeal0(slsdtgt0(xc))
| aElement0(sK13(slsdtgt0(xc)))
| ~ spl25_5
| spl25_10 ),
inference(subsumption_resolution,[],[f441,f357]) ).
fof(f441,plain,
( ~ aSet0(slsdtgt0(xc))
| aElement0(sK13(slsdtgt0(xc)))
| aIdeal0(slsdtgt0(xc))
| spl25_10 ),
inference(resolution,[],[f430,f238]) ).
fof(f238,plain,
! [X0] :
( aElementOf0(sK12(X0),X0)
| aElement0(sK13(X0))
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f430,plain,
( ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| spl25_10 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f440,plain,
( ~ spl25_11
| ~ spl25_7
| spl25_10
| ~ spl25_1
| ~ spl25_5 ),
inference(avatar_split_clause,[],[f439,f356,f332,f428,f399,f432]) ).
fof(f439,plain,
( aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElement0(sK13(slsdtgt0(xc)))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_1
| ~ spl25_5 ),
inference(subsumption_resolution,[],[f438,f207]) ).
fof(f438,plain,
( aIdeal0(slsdtgt0(xc))
| aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElement0(sK13(slsdtgt0(xc)))
| ~ spl25_1
| ~ spl25_5 ),
inference(subsumption_resolution,[],[f436,f357]) ).
fof(f436,plain,
( ~ aSet0(slsdtgt0(xc))
| aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ aElement0(sK13(slsdtgt0(xc)))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_1 ),
inference(resolution,[],[f237,f333]) ).
fof(f237,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0)
| ~ aSet0(X0)
| aElementOf0(sK12(X0),X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f435,plain,
( ~ spl25_10
| spl25_7
| ~ spl25_11
| ~ spl25_4
| ~ spl25_5 ),
inference(avatar_split_clause,[],[f426,f356,f342,f432,f399,f428]) ).
fof(f426,plain,
( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| aElement0(sK13(slsdtgt0(xc)))
| ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_4
| ~ spl25_5 ),
inference(subsumption_resolution,[],[f425,f357]) ).
fof(f425,plain,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| aElement0(sK13(slsdtgt0(xc)))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl25_4 ),
inference(subsumption_resolution,[],[f423,f207]) ).
fof(f423,plain,
( aElement0(sK13(slsdtgt0(xc)))
| ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| ~ spl25_4 ),
inference(resolution,[],[f240,f343]) ).
fof(f240,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0)
| aElement0(sK13(X0))
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f365,plain,
spl25_5,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| spl25_5 ),
inference(subsumption_resolution,[],[f363,f206]) ).
fof(f206,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f363,plain,
( ~ aElement0(xc)
| spl25_5 ),
inference(resolution,[],[f358,f279]) ).
fof(f279,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f199]) ).
fof(f199,plain,
! [X0,X1] :
( ~ aElement0(X0)
| aSet0(X1)
| slsdtgt0(X0) != X1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) = X1
| ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK2(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK2(X0,X1),X1) )
& ( ( sdtasdt0(X0,sK3(X0,X1)) = sK2(X0,X1)
& aElement0(sK3(X0,X1)) )
| aElementOf0(sK2(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(X0,sK4(X0,X5)) = X5
& aElement0(sK4(X0,X5)) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f123,f126,f125,f124]) ).
fof(f124,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
=> ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK2(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK2(X0,X1),X1) )
& ( ? [X4] :
( sK2(X0,X1) = sdtasdt0(X0,X4)
& aElement0(X4) )
| aElementOf0(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0,X1] :
( ? [X4] :
( sK2(X0,X1) = sdtasdt0(X0,X4)
& aElement0(X4) )
=> ( sdtasdt0(X0,sK3(X0,X1)) = sK2(X0,X1)
& aElement0(sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f126,plain,
! [X0,X5] :
( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(X0,sK4(X0,X5)) = X5
& aElement0(sK4(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) = X1
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) = X1
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) = X1
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f358,plain,
( ~ aSet0(slsdtgt0(xc))
| spl25_5 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f353,plain,
~ spl25_2,
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f352,plain,
( $false
| ~ spl25_2 ),
inference(subsumption_resolution,[],[f351,f206]) ).
fof(f351,plain,
( ~ aElement0(xc)
| ~ spl25_2 ),
inference(resolution,[],[f350,f279]) ).
fof(f350,plain,
( ~ aSet0(slsdtgt0(xc))
| ~ spl25_2 ),
inference(subsumption_resolution,[],[f347,f207]) ).
fof(f347,plain,
( ~ aSet0(slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl25_2 ),
inference(resolution,[],[f236,f336]) ).
fof(f336,plain,
( ! [X0] : ~ aElementOf0(X0,slsdtgt0(xc))
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f335,plain,
( spl25_2
<=> ! [X0] : ~ aElementOf0(X0,slsdtgt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).
fof(f346,plain,
~ spl25_3,
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f345,plain,
( $false
| ~ spl25_3 ),
inference(subsumption_resolution,[],[f206,f340]) ).
fof(f340,plain,
( ! [X2] : ~ aElement0(X2)
| ~ spl25_3 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f339,plain,
( spl25_3
<=> ! [X2] : ~ aElement0(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).
fof(f344,plain,
( spl25_3
| spl25_4 ),
inference(avatar_split_clause,[],[f209,f342,f339]) ).
fof(f209,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f337,plain,
( spl25_1
| spl25_2 ),
inference(avatar_split_clause,[],[f210,f335,f332]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
| ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG106+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 12:12:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % (23285)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.44 % (23301)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.44 % (23293)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.47 % (23301)First to succeed.
% 0.19/0.48 % (23301)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (23301)------------------------------
% 0.19/0.48 % (23301)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (23301)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (23301)Termination reason: Refutation
% 0.19/0.48
% 0.19/0.48 % (23301)Memory used [KB]: 6268
% 0.19/0.48 % (23301)Time elapsed: 0.088 s
% 0.19/0.48 % (23301)Instructions burned: 11 (million)
% 0.19/0.48 % (23301)------------------------------
% 0.19/0.48 % (23301)------------------------------
% 0.19/0.48 % (23276)Success in time 0.132 s
%------------------------------------------------------------------------------