%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG109+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:33 PM UTC 2026
% Result : Theorem 5.19s 1.68s
% Output : Refutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 89 ( 15 unt; 7 def)
% Number of atoms : 368 ( 88 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 449 ( 170 ~; 175 |; 83 &)
% ( 18 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 160 ( 0 sgn 124 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aSet0(X1) )
=> ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f40,axiom,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f43,axiom,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(f44,conjecture,
? [X0] :
( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f51,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X0 ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f99,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f100,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f101,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(definition_folding,[],[f88,f100,f99]) ).
fof(f115,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtpldt1(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtpldt1(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X0) )
& ( ? [X6,X7] :
( aElementOf0(X6,X1)
& aElementOf0(X7,X2)
& sdtpldt0(X6,X7) = X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( aElementOf0(X11,X1)
& aElementOf0(X12,X2)
& sdtpldt0(X11,X12) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != sK10(X0,X1,X2) )
| ~ aElementOf0(sK10(X0,X1,X2),X0) )
& ( ( aElementOf0(sK11(X0,X1,X2),X1)
& aElementOf0(sK12(X0,X1,X2),X2)
& sK10(X0,X1,X2) = sdtpldt0(sK11(X0,X1,X2),sK12(X0,X1,X2)) )
| aElementOf0(sK10(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ( aElementOf0(sK13(X1,X2,X8),X1)
& aElementOf0(sK14(X1,X2,X8),X2)
& sdtpldt0(sK13(X1,X2,X8),sK14(X1,X2,X8)) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14]),skolemize(X3,sK10(X0,X1,X2)),skolemize(X6,sK11(X0,X1,X2)),skolemize(X7,sK12(X0,X1,X2)),skolemize(X11,sK13(X1,X2,X8)),skolemize(X12,sK14(X1,X2,X8))],[f119]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f89]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK15(X0,X1) )
| ~ aElementOf0(sK15(X0,X1),X1) )
& ( ( aElement0(sK16(X0,X1))
& sK15(X0,X1) = sdtasdt0(X0,sK16(X0,X1)) )
| aElementOf0(sK15(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK17(X0,X5))
& sdtasdt0(X0,sK17(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X2,sK15(X0,X1)),skolemize(X4,sK16(X0,X1)),skolemize(X7,sK17(X0,X5))],[f123]) ).
fof(f134,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
( sz00 != xa
| sz00 != xb ),
inference(cnf_transformation,[],[f40]) ).
fof(f140,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f43]) ).
fof(f141,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f43]) ).
fof(f142,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f43]) ).
fof(f143,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f43]) ).
fof(f144,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f152,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f153,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f193,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f198,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X0)
| ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f204,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f208,plain,
! [X0,X1] :
( aSet0(X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f232,plain,
! [X0,X1] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f193]) ).
fof(f233,plain,
! [X2,X10,X0,X1,X9] :
( aElementOf0(sdtpldt0(X9,X10),X0)
| ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| ~ sP0(X0,X1,X2) ),
inference(equality_resolution,[],[f198]) ).
fof(f234,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f208]) ).
fof(f246,definition,
( spl20_1
<=> sz00 = xb ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f248,plain,
( sz00 != xb
| spl20_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl20_2
<=> sz00 = xa ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f252,plain,
( sz00 != xa
| spl20_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl20_1
| ~ spl20_2 ),
inference(avatar_split_clause,[],[f136,f250,f246]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ~ sP0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),X2,X3)
| ~ aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| sz00 = sdtpldt0(X0,X1) ),
inference(resolution,[],[f144,f233]) ).
fof(f272,definition,
( spl20_3
<=> sP1(slsdtgt0(xb),slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f273,plain,
( sP1(slsdtgt0(xb),slsdtgt0(xa))
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f274,plain,
( ~ sP1(slsdtgt0(xb),slsdtgt0(xa))
| spl20_3 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f310,plain,
( ~ aSet0(slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xb))
| spl20_3 ),
inference(resolution,[],[f274,f204]) ).
fof(f312,definition,
( spl20_12
<=> aSet0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition]) ).
fof(f314,plain,
( ~ aSet0(slsdtgt0(xb))
| spl20_12 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f316,definition,
( spl20_13
<=> aSet0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition]) ).
fof(f318,plain,
( ~ aSet0(slsdtgt0(xa))
| spl20_13 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f319,plain,
( ~ spl20_12
| ~ spl20_13
| spl20_3 ),
inference(avatar_split_clause,[],[f310,f272,f316,f312]) ).
fof(f320,plain,
( ~ aElement0(xb)
| spl20_12 ),
inference(resolution,[],[f314,f234]) ).
fof(f321,plain,
( $false
| spl20_12 ),
inference(forward_subsumption_resolution,[],[f320,f134]) ).
fof(f322,plain,
spl20_12,
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f323,plain,
( ~ aElement0(xa)
| spl20_13 ),
inference(resolution,[],[f318,f234]) ).
fof(f324,plain,
( $false
| spl20_13 ),
inference(forward_subsumption_resolution,[],[f323,f135]) ).
fof(f325,plain,
spl20_13,
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f432,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sz00 = sdtpldt0(X0,X1)
| ~ sP1(slsdtgt0(xb),slsdtgt0(xa)) ),
inference(resolution,[],[f255,f232]) ).
fof(f435,plain,
( ! [X0,X1] :
( sz00 = sdtpldt0(X0,X1)
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) )
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f432,f273]) ).
fof(f454,plain,
( ! [X0] :
( sz00 = X0
| ~ aElement0(X0)
| ~ aElementOf0(X0,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
| ~ spl20_3 ),
inference(superposition,[],[f152,f435]) ).
fof(f463,plain,
( ! [X0] :
( sz00 = X0
| ~ aElement0(X0)
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) )
| ~ spl20_3 ),
inference(superposition,[],[f153,f435]) ).
fof(f471,plain,
( ! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElement0(X0)
| sz00 = X0 )
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f463,f141]) ).
fof(f472,plain,
( ! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xb))
| ~ aElement0(X0)
| sz00 = X0 )
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f454,f143]) ).
fof(f508,plain,
( ~ aElement0(xa)
| sz00 = xa
| ~ spl20_3 ),
inference(resolution,[],[f471,f142]) ).
fof(f529,plain,
( sz00 = xa
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f508,f135]) ).
fof(f569,plain,
( $false
| spl20_2
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f529,f252]) ).
fof(f570,plain,
( spl20_2
| ~ spl20_3 ),
inference(avatar_contradiction_clause,[],[f569]) ).
fof(f1012,plain,
( ~ aElement0(xb)
| sz00 = xb
| ~ spl20_3 ),
inference(resolution,[],[f472,f140]) ).
fof(f1045,plain,
( sz00 = xb
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f1012,f134]) ).
fof(f1090,plain,
( $false
| spl20_1
| ~ spl20_3 ),
inference(forward_subsumption_resolution,[],[f1045,f248]) ).
fof(f1091,plain,
( spl20_1
| ~ spl20_3 ),
inference(avatar_contradiction_clause,[],[f1090]) ).
cnf(s1,plain,
( ~ spl20_1
| ~ spl20_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s9,plain,
( spl20_3
| ~ spl20_12
| ~ spl20_13 ),
inference(sat_conversion,[],[f319]) ).
cnf(s10,plain,
spl20_12,
inference(sat_conversion,[],[f322]) ).
cnf(s11,plain,
spl20_13,
inference(sat_conversion,[],[f325]) ).
cnf(s18,plain,
( spl20_2
| ~ spl20_3 ),
inference(sat_conversion,[],[f570]) ).
cnf(s27,plain,
( spl20_1
| ~ spl20_3 ),
inference(sat_conversion,[],[f1091]) ).
cnf(s29,plain,
spl20_3,
inference(rat,[],[s9,s11,s10]) ).
cnf(s30,plain,
spl20_1,
inference(rat,[],[s27,s29]) ).
cnf(s31,plain,
spl20_2,
inference(rat,[],[s18,s29]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s1,s31,s30]) ).
fof(f1122,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:18:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.68 % (287924)Detected formulas, will run a generic FOF schedule.
% 5.19/1.68 % (287931)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=278952198:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.19/1.68 % (287935)dis-21_1_sil=8000:lcm=predicate:random_seed=1271983791:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.19/1.68 % (287933)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1876054830:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.19/1.68 % (287930)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=291615306:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.19/1.68 % (287932)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=405153778:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.19/1.68 % (287934)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3862812346:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.19/1.68 % (287929)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1423765466:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.19/1.68 % (287932)Instruction limit reached!
% 5.19/1.68 % (287932)------------------------------
% 5.19/1.68 % (287932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287932)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287932)Termination reason: Instruction limit
% 5.19/1.68 % (287932)Termination phase: Saturation
% 5.19/1.68 % (287932)Time elapsed: 0.068 s
% 5.19/1.68 % (287932)Peak memory usage: 89 MB
% 5.19/1.68 % (287932)Instructions burned: 110 (million)
% 5.19/1.68 % (287933)Instruction limit reached!
% 5.19/1.68 % (287933)------------------------------
% 5.19/1.68 % (287933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287933)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287933)Termination reason: Instruction limit
% 5.19/1.68 % (287933)Termination phase: Saturation
% 5.19/1.68 % (287933)Time elapsed: 0.069 s
% 5.19/1.68 % (287933)Peak memory usage: 88 MB
% 5.19/1.68 % (287933)Instructions burned: 119 (million)
% 5.19/1.68 % (287935)Instruction limit reached!
% 5.19/1.68 % (287935)------------------------------
% 5.19/1.68 % (287935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287935)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287935)Termination reason: Instruction limit
% 5.19/1.68 % (287935)Termination phase: Saturation
% 5.19/1.68 % (287935)Time elapsed: 0.070 s
% 5.19/1.68 % (287935)Peak memory usage: 89 MB
% 5.19/1.68 % (287935)Instructions burned: 130 (million)
% 5.19/1.68 % (287934)Instruction limit reached!
% 5.19/1.68 % (287934)------------------------------
% 5.19/1.68 % (287934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287934)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287934)Termination reason: Instruction limit
% 5.19/1.68 % (287934)Termination phase: Saturation
% 5.19/1.68 % (287934)Time elapsed: 0.092 s
% 5.19/1.68 % (287934)Peak memory usage: 90 MB
% 5.19/1.68 % (287934)Instructions burned: 140 (million)
% 5.19/1.68 % (287944)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2249343913:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.19/1.68 % (287943)lrs+10_1_sil=8000:sp=occurrence:random_seed=3471424851:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.19/1.68 % (287945)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2588077100:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.19/1.68 % (287946)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3006125077:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.19/1.68 % (287944)Instruction limit reached!
% 5.19/1.68 % (287944)------------------------------
% 5.19/1.68 % (287944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287944)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287944)Termination reason: Instruction limit
% 5.19/1.68 % (287944)Termination phase: Saturation
% 5.19/1.68 % (287944)Time elapsed: 0.083 s
% 5.19/1.68 % (287944)Peak memory usage: 91 MB
% 5.19/1.68 % (287944)Instructions burned: 158 (million)
% 5.19/1.68 % (287946)Instruction limit reached!
% 5.19/1.68 % (287946)------------------------------
% 5.19/1.68 % (287946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287946)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287946)Termination reason: Instruction limit
% 5.19/1.68 % (287946)Termination phase: Saturation
% 5.19/1.68 % (287946)Time elapsed: 0.116 s
% 5.19/1.68 % (287946)Peak memory usage: 94 MB
% 5.19/1.68 % (287946)Instructions burned: 248 (million)
% 5.19/1.68 % (287943)Instruction limit reached!
% 5.19/1.68 % (287943)------------------------------
% 5.19/1.68 % (287943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287943)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287943)Termination reason: Instruction limit
% 5.19/1.68 % (287943)Termination phase: Saturation
% 5.19/1.68 % (287943)Time elapsed: 0.167 s
% 5.19/1.68 % (287943)Peak memory usage: 93 MB
% 5.19/1.68 % (287943)Instructions burned: 285 (million)
% 5.19/1.68 % (287951)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1525655966:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.19/1.68 % (287945)Instruction limit reached!
% 5.19/1.68 % (287945)------------------------------
% 5.19/1.68 % (287945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287945)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287945)Termination reason: Instruction limit
% 5.19/1.68 % (287945)Termination phase: Saturation
% 5.19/1.68 % (287945)Time elapsed: 0.200 s
% 5.19/1.68 % (287945)Peak memory usage: 93 MB
% 5.19/1.68 % (287945)Instructions burned: 326 (million)
% 5.19/1.68 % (287951)First to succeed.
% 5.19/1.68 % (287951)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-287924"
% 5.19/1.68 % (287952)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1222134080:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.19/1.68 % (287953)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2290669750:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.19/1.68 % (287955)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2401601389:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.19/1.68 % (287953)Instruction limit reached!
% 5.19/1.68 % (287953)------------------------------
% 5.19/1.68 % (287953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287953)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287953)Termination reason: Instruction limit
% 5.19/1.68 % (287953)Termination phase: Saturation
% 5.19/1.68 % (287953)Time elapsed: 0.075 s
% 5.19/1.68 % (287953)Peak memory usage: 90 MB
% 5.19/1.68 % (287953)Instructions burned: 113 (million)
% 5.19/1.68 % (287955)Instruction limit reached!
% 5.19/1.68 % (287955)------------------------------
% 5.19/1.68 % (287955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.68 % (287955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.68 % (287955)CaDiCaL version: 2.1.3
% 5.19/1.68 % (287955)Termination reason: Instruction limit
% 5.19/1.68 % (287955)Termination phase: Saturation
% 5.19/1.68 % (287955)Time elapsed: 0.065 s
% 5.19/1.68 % (287955)Peak memory usage: 89 MB
% 5.19/1.68 % (287955)Instructions burned: 127 (million)
% 5.19/1.68 % (287931)Also succeeded, but the first one will report.
% 5.19/1.68 % (287951)Refutation found. Thanks to Tanya!
% 5.19/1.68 % SZS status Theorem for theBenchmark
% 5.19/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.46/1.88 % (287951)------------------------------
% 6.46/1.88 % (287951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.88 % (287951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.88 % (287951)CaDiCaL version: 2.1.3
% 6.46/1.88 % (287951)Termination reason: Refutation
% 6.46/1.88 % (287951)Time elapsed: 0.028 s
% 6.46/1.88 % (287951)Peak memory usage: 90 MB
% 6.46/1.88 % (287951)Instructions burned: 46 (million)
% 6.46/1.88 % (287951)------------------------------
% 6.46/1.88 % (287951)------------------------------
% 6.46/1.88 % (287924)Success in time 0.843 s
% 6.46/1.88 % Vampire exiting
%------------------------------------------------------------------------------