%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG106+2 : 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 : n015.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 12:35:32 PM UTC 2026
% Result : Theorem 2.80s 1.30s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 105 ( 13 unt; 8 def)
% Number of atoms : 512 ( 84 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 590 ( 183 ~; 169 |; 194 &)
% ( 12 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 232 ( 0 sgn 169 !; 63 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f39,conjecture,
( ! [X0,X1,X2] :
( ( ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0 )
| aElementOf0(X0,slsdtgt0(xc)) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X1 )
| aElementOf0(X1,slsdtgt0(xc)) )
& aElement0(X2) )
=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = sdtpldt0(X0,X1) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = sdtasdt0(X2,X0) )
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) ) )
=> ( ( aSet0(slsdtgt0(xc))
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = X0 ) ) )
=> ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) ) ) )
| aIdeal0(slsdtgt0(xc)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ! [X0,X1,X2] :
( ( ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0 )
| aElementOf0(X0,slsdtgt0(xc)) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X1 )
| aElementOf0(X1,slsdtgt0(xc)) )
& aElement0(X2) )
=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = sdtpldt0(X0,X1) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = sdtasdt0(X2,X0) )
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) ) )
=> ( ( aSet0(slsdtgt0(xc))
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = X0 ) ) )
=> ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) ) ) )
| aIdeal0(slsdtgt0(xc)) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
~ ( ! [X0,X1,X2] :
( ( ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0 )
| aElementOf0(X0,slsdtgt0(xc)) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1 )
| aElementOf0(X1,slsdtgt0(xc)) )
& aElement0(X2) )
=> ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = X0
& ? [X6] :
( aElement0(X6)
& sdtasdt0(xc,X6) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& ? [X7] :
( aElement0(X7)
& sdtpldt0(X0,X1) = sdtasdt0(xc,X7) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X8] :
( aElement0(X8)
& sdtasdt0(X2,X0) = sdtasdt0(xc,X8) )
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) ) )
=> ( ( aSet0(slsdtgt0(xc))
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( aElement0(X10)
& sdtasdt0(xc,X10) = X9 ) ) )
=> ( ! [X11] :
( aElementOf0(X11,slsdtgt0(xc))
=> ( ! [X12] :
( aElementOf0(X12,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X11,X12),slsdtgt0(xc)) )
& ! [X13] :
( aElement0(X13)
=> aElementOf0(sdtasdt0(X13,X11),slsdtgt0(xc)) ) ) )
| aIdeal0(slsdtgt0(xc)) ) ) ),
inference(rectify,[],[f40]) ).
fof(f45,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f46,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(unused_predicate_definition_removal,[],[f45]) ).
fof(f47,plain,
( ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtpldt0(X11,X12),slsdtgt0(xc))
& aElementOf0(X12,slsdtgt0(xc)) )
| ? [X13] :
( ~ aElementOf0(sdtasdt0(X13,X11),slsdtgt0(xc))
& aElement0(X13) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( aElement0(X10)
& sdtasdt0(xc,X10) = X9 ) )
& ! [X0,X1,X2] :
( ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = X0
& ? [X6] :
( aElement0(X6)
& sdtasdt0(xc,X6) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& ? [X7] :
( aElement0(X7)
& sdtpldt0(X0,X1) = sdtasdt0(xc,X7) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X8] :
( aElement0(X8)
& sdtasdt0(X2,X0) = sdtasdt0(xc,X8) )
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) )
| ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xc,X3) != X0 )
& ~ aElementOf0(X0,slsdtgt0(xc)) )
| ( ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X1 )
& ~ aElementOf0(X1,slsdtgt0(xc)) )
| ~ aElement0(X2) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f48,plain,
( ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtpldt0(X11,X12),slsdtgt0(xc))
& aElementOf0(X12,slsdtgt0(xc)) )
| ? [X13] :
( ~ aElementOf0(sdtasdt0(X13,X11),slsdtgt0(xc))
& aElement0(X13) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( aElement0(X10)
& sdtasdt0(xc,X10) = X9 ) )
& ! [X0,X1,X2] :
( ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = X0
& ? [X6] :
( aElement0(X6)
& sdtasdt0(xc,X6) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& ? [X7] :
( aElement0(X7)
& sdtpldt0(X0,X1) = sdtasdt0(xc,X7) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X8] :
( aElement0(X8)
& sdtasdt0(X2,X0) = sdtasdt0(xc,X8) )
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) )
| ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xc,X3) != X0 )
& ~ aElementOf0(X0,slsdtgt0(xc)) )
| ( ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X1 )
& ~ aElementOf0(X1,slsdtgt0(xc)) )
| ~ aElement0(X2) ) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f56]) ).
fof(f60,plain,
! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) ),
inference(flattening,[],[f60]) ).
fof(f66,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f67,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f66]) ).
fof(f69,definition,
! [X0,X2] :
( ? [X8] :
( aElement0(X8)
& sdtasdt0(X2,X0) = sdtasdt0(xc,X8) )
| ~ sP0(X0,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f70,definition,
! [X1,X0] :
( ? [X7] :
( aElement0(X7)
& sdtpldt0(X0,X1) = sdtasdt0(xc,X7) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f71,definition,
! [X1,X5,X0,X2] :
( ? [X6] :
( aElement0(X6)
& sdtasdt0(xc,X6) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sP1(X1,X0)
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sP0(X0,X2)
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) )
| ~ sP2(X1,X5,X0,X2) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f72,definition,
! [X0,X2,X1] :
( ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = X0
& sP2(X1,X5,X0,X2) )
| ~ sP3(X0,X2,X1) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f73,plain,
( ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtpldt0(X11,X12),slsdtgt0(xc))
& aElementOf0(X12,slsdtgt0(xc)) )
| ? [X13] :
( ~ aElementOf0(sdtasdt0(X13,X11),slsdtgt0(xc))
& aElement0(X13) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( aElement0(X10)
& sdtasdt0(xc,X10) = X9 ) )
& ! [X0,X1,X2] :
( sP3(X0,X2,X1)
| ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xc,X3) != X0 )
& ~ aElementOf0(X0,slsdtgt0(xc)) )
| ( ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X1 )
& ~ aElementOf0(X1,slsdtgt0(xc)) )
| ~ aElement0(X2) ) ),
inference(definition_folding,[],[f48,f72,f71,f70,f69]) ).
fof(f74,plain,
! [X0,X2,X1] :
( ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = X0
& sP2(X1,X5,X0,X2) )
| ~ sP3(X0,X2,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& sP2(X2,X3,X0,X1) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( aElement0(sK4(X0,X1,X2))
& sdtasdt0(xc,sK4(X0,X1,X2)) = X0
& sP2(X2,sK4(X0,X1,X2),X0,X1) )
| ~ sP3(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f75]) ).
fof(f77,plain,
! [X1,X5,X0,X2] :
( ? [X6] :
( aElement0(X6)
& sdtasdt0(xc,X6) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sP1(X1,X0)
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sP0(X0,X2)
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) )
| ~ sP2(X1,X5,X0,X2) ),
inference(nnf_transformation,[],[f71]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X0
& sdtpldt0(X2,X0) = sdtasdt0(xc,sdtpldt0(X1,X4))
& sdtasdt0(X3,X2) = sdtasdt0(xc,sdtasdt0(X1,X3))
& sP1(X0,X2)
& aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc))
& sP0(X2,X3)
& aElementOf0(sdtasdt0(X3,X2),slsdtgt0(xc)) )
| ~ sP2(X0,X1,X2,X3) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ( aElement0(sK5(X0,X1,X2,X3))
& sdtasdt0(xc,sK5(X0,X1,X2,X3)) = X0
& sdtpldt0(X2,X0) = sdtasdt0(xc,sdtpldt0(X1,sK5(X0,X1,X2,X3)))
& sdtasdt0(X3,X2) = sdtasdt0(xc,sdtasdt0(X1,X3))
& sP1(X0,X2)
& aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc))
& sP0(X2,X3)
& aElementOf0(sdtasdt0(X3,X2),slsdtgt0(xc)) )
| ~ sP2(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2,X3))],[f78]) ).
fof(f86,plain,
( ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtpldt0(X11,X12),slsdtgt0(xc))
& aElementOf0(X12,slsdtgt0(xc)) )
| ? [X13] :
( ~ aElementOf0(sdtasdt0(X13,X11),slsdtgt0(xc))
& aElement0(X13) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X9] :
( ( aElementOf0(X9,slsdtgt0(xc))
| ! [X10] :
( ~ aElement0(X10)
| sdtasdt0(xc,X10) != X9 ) )
& ( ? [X10] :
( aElement0(X10)
& sdtasdt0(xc,X10) = X9 )
| ~ aElementOf0(X9,slsdtgt0(xc)) ) )
& ! [X0,X1,X2] :
( sP3(X0,X2,X1)
| ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xc,X3) != X0 )
& ~ aElementOf0(X0,slsdtgt0(xc)) )
| ( ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X1 )
& ~ aElementOf0(X1,slsdtgt0(xc)) )
| ~ aElement0(X2) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f87,plain,
( ? [X0] :
( ( ? [X1] :
( ~ aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc)) )
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElement0(X2) ) )
& aElementOf0(X0,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xc))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X3 ) )
& ( ? [X5] :
( aElement0(X5)
& sdtasdt0(xc,X5) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xc)) ) )
& ! [X6,X7,X8] :
( sP3(X6,X8,X7)
| ( ! [X9] :
( ~ aElement0(X9)
| sdtasdt0(xc,X9) != X6 )
& ~ aElementOf0(X6,slsdtgt0(xc)) )
| ( ! [X10] :
( ~ aElement0(X10)
| sdtasdt0(xc,X10) != X7 )
& ~ aElementOf0(X7,slsdtgt0(xc)) )
| ~ aElement0(X8) ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
( ( ( ~ aElementOf0(sdtpldt0(sK8,sK9),slsdtgt0(xc))
& aElementOf0(sK9,slsdtgt0(xc)) )
| ( ~ aElementOf0(sdtasdt0(sK10,sK8),slsdtgt0(xc))
& aElement0(sK10) ) )
& aElementOf0(sK8,slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xc))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X3 ) )
& ( ( aElement0(sK11(X3))
& sdtasdt0(xc,sK11(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xc)) ) )
& ! [X6,X7,X8] :
( sP3(X6,X8,X7)
| ( ! [X9] :
( ~ aElement0(X9)
| sdtasdt0(xc,X9) != X6 )
& ~ aElementOf0(X6,slsdtgt0(xc)) )
| ( ! [X10] :
( ~ aElement0(X10)
| sdtasdt0(xc,X10) != X7 )
& ~ aElementOf0(X7,slsdtgt0(xc)) )
| ~ aElement0(X8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X5,sK11(X3))],[f87]) ).
fof(f90,plain,
! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK14(X0),sK15(X0)),X0)
& aElementOf0(sK15(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK16(X0),sK14(X0)),X0)
& aElement0(sK16(X0)) ) )
& aElementOf0(sK14(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f61]) ).
fof(f95,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f96,plain,
! [X2,X0,X1] :
( sP2(X2,sK4(X0,X1,X2),X0,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( aElementOf0(sdtasdt0(X3,X2),slsdtgt0(xc))
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc))
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f111,plain,
! [X8,X6,X7] :
( ~ aElementOf0(X7,slsdtgt0(xc))
| ~ aElementOf0(X6,slsdtgt0(xc))
| sP3(X6,X8,X7)
| ~ aElement0(X8) ),
inference(cnf_transformation,[],[f88]) ).
fof(f112,plain,
! [X10,X8,X6,X7] :
( sP3(X6,X8,X7)
| ~ aElementOf0(X6,slsdtgt0(xc))
| ~ aElement0(X10)
| sdtasdt0(xc,X10) != X7
| ~ aElement0(X8) ),
inference(cnf_transformation,[],[f88]) ).
fof(f115,plain,
! [X3] :
( sdtasdt0(xc,sK11(X3)) = X3
| ~ aElementOf0(X3,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f116,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xc))
| aElement0(sK11(X3)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f118,plain,
aSet0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f88]) ).
fof(f119,plain,
~ aIdeal0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f88]) ).
fof(f120,plain,
aElementOf0(sK8,slsdtgt0(xc)),
inference(cnf_transformation,[],[f88]) ).
fof(f121,plain,
( aElementOf0(sK9,slsdtgt0(xc))
| aElement0(sK10) ),
inference(cnf_transformation,[],[f88]) ).
fof(f122,plain,
( aElementOf0(sK9,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK10,sK8),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f123,plain,
( ~ aElementOf0(sdtpldt0(sK8,sK9),slsdtgt0(xc))
| aElement0(sK10) ),
inference(cnf_transformation,[],[f88]) ).
fof(f124,plain,
( ~ aElementOf0(sdtpldt0(sK8,sK9),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK10,sK8),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f129,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f133,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f135,plain,
! [X0] :
( aElementOf0(sK14(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f142,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f154,plain,
! [X10,X8,X6] :
( sP3(X6,X8,sdtasdt0(xc,X10))
| ~ aElementOf0(X6,slsdtgt0(xc))
| ~ aElement0(X10)
| ~ aElement0(X8) ),
inference(equality_resolution,[],[f112]) ).
fof(f161,definition,
( spl20_1
<=> aElement0(sK10) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f163,plain,
( aElement0(sK10)
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl20_2
<=> aElementOf0(sK9,slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f167,plain,
( aElementOf0(sK9,slsdtgt0(xc))
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f121,f165,f161]) ).
fof(f170,definition,
( spl20_3
<=> aElementOf0(sdtasdt0(sK10,sK8),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f172,plain,
( ~ aElementOf0(sdtasdt0(sK10,sK8),slsdtgt0(xc))
| spl20_3 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( ~ spl20_3
| spl20_2 ),
inference(avatar_split_clause,[],[f122,f165,f170]) ).
fof(f175,definition,
( spl20_4
<=> aElementOf0(sdtpldt0(sK8,sK9),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f177,plain,
( ~ aElementOf0(sdtpldt0(sK8,sK9),slsdtgt0(xc))
| spl20_4 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl20_1
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f123,f175,f161]) ).
fof(f179,plain,
( ~ spl20_3
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f124,f175,f170]) ).
fof(f181,plain,
( aElement0(sK8)
| ~ aSet0(slsdtgt0(xc)) ),
inference(resolution,[],[f120,f129]) ).
fof(f182,plain,
aElement0(sK8),
inference(forward_subsumption_resolution,[],[f181,f118]) ).
fof(f185,plain,
( aElement0(sK9)
| ~ aSet0(slsdtgt0(xc))
| ~ spl20_2 ),
inference(resolution,[],[f167,f129]) ).
fof(f186,plain,
( aElement0(sK9)
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f185,f118]) ).
fof(f190,plain,
( ~ aElementOf0(sdtpldt0(sK9,sK8),slsdtgt0(xc))
| ~ aElement0(sK8)
| ~ aElement0(sK9)
| spl20_4 ),
inference(superposition,[],[f177,f133]) ).
fof(f202,plain,
( ~ aElementOf0(sdtpldt0(sK9,sK8),slsdtgt0(xc))
| ~ aElement0(sK9)
| spl20_4 ),
inference(forward_subsumption_resolution,[],[f190,f182]) ).
fof(f204,plain,
( ~ aElementOf0(sdtpldt0(sK9,sK8),slsdtgt0(xc))
| ~ spl20_2
| spl20_4 ),
inference(forward_subsumption_resolution,[],[f202,f186]) ).
fof(f271,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xc)
| ~ aElement0(sK11(X0))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(superposition,[],[f142,f115]) ).
fof(f275,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xc)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f271,f116]) ).
fof(f286,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f275,f95]) ).
fof(f299,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| sP3(X0,X1,sK8)
| ~ aElement0(X1) ),
inference(resolution,[],[f111,f120]) ).
fof(f399,plain,
( ! [X0,X1] : ~ sP2(sK8,X0,sK9,X1)
| ~ spl20_2
| spl20_4 ),
inference(resolution,[],[f204,f101]) ).
fof(f440,plain,
( aElement0(sK14(slsdtgt0(xc)))
| ~ aSet0(slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc)) ),
inference(resolution,[],[f286,f135]) ).
fof(f441,plain,
( aElement0(sK14(slsdtgt0(xc)))
| aIdeal0(slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f440,f118]) ).
fof(f444,plain,
aElement0(sK14(slsdtgt0(xc))),
inference(forward_subsumption_resolution,[],[f441,f119]) ).
fof(f467,plain,
( ! [X0] : ~ sP3(sK9,X0,sK8)
| ~ spl20_2
| spl20_4 ),
inference(resolution,[],[f399,f96]) ).
fof(f667,plain,
( ! [X0] :
( sP3(sK9,X0,sK8)
| ~ aElement0(X0) )
| ~ spl20_2 ),
inference(resolution,[],[f299,f167]) ).
fof(f677,plain,
( ! [X0] : ~ aElement0(X0)
| ~ spl20_2
| spl20_4 ),
inference(forward_subsumption_resolution,[],[f667,f467]) ).
fof(f697,plain,
( $false
| ~ spl20_2
| spl20_4 ),
inference(resolution,[],[f677,f444]) ).
fof(f705,plain,
( ~ spl20_2
| spl20_4 ),
inference(avatar_contradiction_clause,[],[f697]) ).
fof(f713,plain,
( ! [X0,X1] : ~ sP2(X0,X1,sK8,sK10)
| spl20_3 ),
inference(resolution,[],[f172,f99]) ).
fof(f732,plain,
( ! [X0] : ~ sP3(sK8,sK10,X0)
| spl20_3 ),
inference(resolution,[],[f713,f96]) ).
fof(f745,plain,
( ! [X0] :
( ~ aElementOf0(sK8,slsdtgt0(xc))
| ~ aElement0(X0)
| ~ aElement0(sK10) )
| spl20_3 ),
inference(resolution,[],[f732,f154]) ).
fof(f746,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ aElement0(sK10) )
| spl20_3 ),
inference(forward_subsumption_resolution,[],[f745,f120]) ).
fof(f747,plain,
( ! [X0] : ~ aElement0(X0)
| ~ spl20_1
| spl20_3 ),
inference(forward_subsumption_resolution,[],[f746,f163]) ).
fof(f760,plain,
( $false
| ~ spl20_1
| spl20_3 ),
inference(resolution,[],[f747,f95]) ).
fof(f792,plain,
( ~ spl20_1
| spl20_3 ),
inference(avatar_contradiction_clause,[],[f760]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f168]) ).
cnf(s2,plain,
( spl20_2
| ~ spl20_3 ),
inference(sat_conversion,[],[f173]) ).
cnf(s3,plain,
( spl20_1
| ~ spl20_4 ),
inference(sat_conversion,[],[f178]) ).
cnf(s4,plain,
( ~ spl20_3
| ~ spl20_4 ),
inference(sat_conversion,[],[f179]) ).
cnf(s13,plain,
( ~ spl20_2
| spl20_4 ),
inference(sat_conversion,[],[f705]) ).
cnf(s32,plain,
( ~ spl20_1
| spl20_3 ),
inference(sat_conversion,[],[f792]) ).
cnf(s34,plain,
spl20_1,
inference(rat,[],[s13,s1,s3]) ).
cnf(s35,plain,
spl20_3,
inference(rat,[],[s32,s34]) ).
cnf(s36,plain,
~ spl20_4,
inference(rat,[],[s4,s35]) ).
cnf(s37,plain,
spl20_2,
inference(rat,[],[s2,s35]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s13,s36,s37]) ).
fof(f794,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG106+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 23:22:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.80/1.30 % (2124687)Detected formulas, will run a generic FOF schedule.
% 2.80/1.30 % (2124693)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=545881146:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.30 % (2124692)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=3877724602:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.30 % (2124694)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=1731053892:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.30 % (2124695)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2255741191:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.30 % (2124696)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=845586387:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.30 % (2124698)dis-21_1_sil=8000:lcm=predicate:random_seed=602288575: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)
% 2.80/1.30 % (2124697)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3256557316:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.30 % (2124695)First to succeed.
% 2.80/1.30 % (2124695)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2124687"
% 2.80/1.30 % (2124698)Also succeeded, but the first one will report.
% 2.80/1.30 % (2124696)Also succeeded, but the first one will report.
% 2.80/1.30 % (2124697)Instruction limit reached!
% 2.80/1.30 % (2124697)------------------------------
% 2.80/1.30 % (2124697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.30 % (2124697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.30 % (2124697)CaDiCaL version: 2.1.3
% 2.80/1.30 % (2124697)Termination reason: Instruction limit
% 2.80/1.30 % (2124697)Termination phase: Saturation
% 2.80/1.30 % (2124697)Time elapsed: 0.092 s
% 2.80/1.30 % (2124697)Peak memory usage: 90 MB
% 2.80/1.30 % (2124697)Instructions burned: 139 (million)
% 2.80/1.30 % (2124695)Refutation found. Thanks to Tanya!
% 2.80/1.30 % SZS status Theorem for theBenchmark
% 2.80/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.49 % (2124695)------------------------------
% 3.67/1.49 % (2124695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (2124695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (2124695)CaDiCaL version: 2.1.3
% 3.67/1.49 % (2124695)Termination reason: Refutation
% 3.67/1.49 % (2124695)Time elapsed: 0.019 s
% 3.67/1.49 % (2124695)Peak memory usage: 90 MB
% 3.67/1.49 % (2124695)Instructions burned: 25 (million)
% 3.67/1.49 % (2124695)------------------------------
% 3.67/1.49 % (2124695)------------------------------
% 3.67/1.49 % (2124687)Success in time 0.447 s
% 3.67/1.49 % Vampire exiting
%------------------------------------------------------------------------------