%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG100+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 : n011.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 12:35:31 PM UTC 2026
% Result : Theorem 5.74s 2.70s
% Output : Refutation 13.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 13 unt; 4 def)
% Number of atoms : 446 ( 66 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 556 ( 221 ~; 217 |; 85 &)
% ( 13 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 144 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f39,conjecture,
( ( 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,
~ ( ( 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,
~ ( ( aSet0(slsdtgt0(xc))
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = X0 ) ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xc))
=> ( ! [X3] :
( aElementOf0(X3,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc)) )
& ! [X4] :
( aElement0(X4)
=> aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc)) ) ) )
| aIdeal0(slsdtgt0(xc)) ) ),
inference(rectify,[],[f40]) ).
fof(f51,plain,
( ? [X2] :
( ( ? [X3] :
( ~ aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc))
& aElementOf0(X3,slsdtgt0(xc)) )
| ? [X4] :
( ~ aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc))
& aElement0(X4) ) )
& aElementOf0(X2,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = X0 ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f52,plain,
( ? [X2] :
( ( ? [X3] :
( ~ aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc))
& aElementOf0(X3,slsdtgt0(xc)) )
| ? [X4] :
( ~ aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc))
& aElement0(X4) ) )
& aElementOf0(X2,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = X0 ) ) ),
inference(flattening,[],[f51]) ).
fof(f53,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(f61,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f68]) ).
fof(f76,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f77,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f76]) ).
fof(f89,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f90,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f92,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f94,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f93]) ).
fof(f104,plain,
( ? [X2] :
( ( ? [X3] :
( ~ aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc))
& aElementOf0(X3,slsdtgt0(xc)) )
| ? [X4] :
( ~ aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc))
& aElement0(X4) ) )
& aElementOf0(X2,slsdtgt0(xc)) )
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X0] :
( ( aElementOf0(X0,slsdtgt0(xc))
| ! [X1] :
( ~ aElement0(X1)
| sdtasdt0(xc,X1) != X0 ) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = X0 )
| ~ aElementOf0(X0,slsdtgt0(xc)) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f105,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)) ) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
( ( ( ~ aElementOf0(sdtpldt0(sK2,sK3),slsdtgt0(xc))
& aElementOf0(sK3,slsdtgt0(xc)) )
| ( ~ aElementOf0(sdtasdt0(sK4,sK2),slsdtgt0(xc))
& aElement0(sK4) ) )
& aElementOf0(sK2,slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& aSet0(slsdtgt0(xc))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xc))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xc,X4) != X3 ) )
& ( ( aElement0(sK5(X3))
& sdtasdt0(xc,sK5(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xc)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X5,sK5(X3))],[f105]) ).
fof(f107,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,[],[f53]) ).
fof(f108,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,[],[f107]) ).
fof(f109,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,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK6(X0,X1) )
| ~ aElementOf0(sK6(X0,X1),X1) )
& ( ( aElement0(sK7(X0,X1))
& sK6(X0,X1) = sdtasdt0(X0,sK7(X0,X1)) )
| aElementOf0(sK6(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK8(X0,X5))
& sdtasdt0(X0,sK8(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X2,sK6(X0,X1)),skolemize(X4,sK7(X0,X1)),skolemize(X7,sK8(X0,X5))],[f109]) ).
fof(f140,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f141,plain,
! [X3] :
( sdtasdt0(xc,sK5(X3)) = X3
| ~ aElementOf0(X3,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f142,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xc))
| aElement0(sK5(X3)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f143,plain,
! [X3,X4] :
( aElementOf0(X3,slsdtgt0(xc))
| ~ aElement0(X4)
| sdtasdt0(xc,X4) != X3 ),
inference(cnf_transformation,[],[f106]) ).
fof(f144,plain,
aSet0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f106]) ).
fof(f146,plain,
aElementOf0(sK2,slsdtgt0(xc)),
inference(cnf_transformation,[],[f106]) ).
fof(f147,plain,
( aElementOf0(sK3,slsdtgt0(xc))
| aElement0(sK4) ),
inference(cnf_transformation,[],[f106]) ).
fof(f148,plain,
( aElementOf0(sK3,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK4,sK2),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f149,plain,
( ~ aElementOf0(sdtpldt0(sK2,sK3),slsdtgt0(xc))
| aElement0(sK4) ),
inference(cnf_transformation,[],[f106]) ).
fof(f150,plain,
( ~ aElementOf0(sdtpldt0(sK2,sK3),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK4,sK2),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f151,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK8(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f152,plain,
! [X0,X1,X5] :
( aElement0(sK8(X0,X5))
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f202,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f209,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f222,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f223,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f224,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f240,plain,
! [X4] :
( aElementOf0(sdtasdt0(xc,X4),slsdtgt0(xc))
| ~ aElement0(X4) ),
inference(equality_resolution,[],[f143]) ).
fof(f244,plain,
! [X0,X5] :
( ~ aElementOf0(X5,slsdtgt0(X0))
| aElement0(sK8(X0,X5))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f152]) ).
fof(f245,plain,
! [X0,X5] :
( sdtasdt0(X0,sK8(X0,X5)) = X5
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f151]) ).
fof(f255,definition,
( spl26_1
<=> aElement0(sK4) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f257,plain,
( aElement0(sK4)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl26_2
<=> aElementOf0(sK3,slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f261,plain,
( aElementOf0(sK3,slsdtgt0(xc))
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f147,f259,f255]) ).
fof(f264,definition,
( spl26_3
<=> aElementOf0(sdtasdt0(sK4,sK2),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f266,plain,
( ~ aElementOf0(sdtasdt0(sK4,sK2),slsdtgt0(xc))
| spl26_3 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
( ~ spl26_3
| spl26_2 ),
inference(avatar_split_clause,[],[f148,f259,f264]) ).
fof(f269,definition,
( spl26_4
<=> aElementOf0(sdtpldt0(sK2,sK3),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl26_4])],[avatar_definition]) ).
fof(f271,plain,
( ~ aElementOf0(sdtpldt0(sK2,sK3),slsdtgt0(xc))
| spl26_4 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,plain,
( spl26_1
| ~ spl26_4 ),
inference(avatar_split_clause,[],[f149,f269,f255]) ).
fof(f273,plain,
( ~ spl26_3
| ~ spl26_4 ),
inference(avatar_split_clause,[],[f150,f269,f264]) ).
fof(f275,plain,
aElement0(sK5(sK2)),
inference(resolution,[],[f142,f146]) ).
fof(f289,plain,
( aElement0(sK8(xc,sK2))
| ~ aElement0(xc) ),
inference(resolution,[],[f244,f146]) ).
fof(f297,plain,
aElement0(sK8(xc,sK2)),
inference(forward_subsumption_resolution,[],[f289,f140]) ).
fof(f301,plain,
( aElement0(sK2)
| ~ aSet0(slsdtgt0(xc)) ),
inference(resolution,[],[f189,f146]) ).
fof(f309,plain,
aElement0(sK2),
inference(forward_subsumption_resolution,[],[f301,f144]) ).
fof(f417,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,sdtpldt0(sK8(X1,X0),X2)) = sdtpldt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(sK8(X1,X0))
| ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(superposition,[],[f202,f245]) ).
fof(f435,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,sdtpldt0(sK8(X1,X0),X2)) = sdtpldt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(sK8(X1,X0))
| ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(X1)) ),
inference(duplicate_literal_removal,[],[f417]) ).
fof(f443,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,sdtpldt0(sK8(X1,X0),X2)) = sdtpldt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(X1)) ),
inference(forward_subsumption_resolution,[],[f435,f244]) ).
fof(f559,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0),X1))
| ~ aElement0(xc)
| ~ aElement0(sK5(X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(superposition,[],[f222,f141]) ).
fof(f618,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0),X1))
| ~ aElement0(xc)
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f559,f142]) ).
fof(f621,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0),X1))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f618,f140]) ).
fof(f660,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElement0(sdtasdt0(sK5(X0),X1))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(superposition,[],[f240,f621]) ).
fof(f770,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,sdtasdt0(xc,X1)),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(sK8(xc,X0),X1))
| ~ aElement0(xc)
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(superposition,[],[f240,f443]) ).
fof(f786,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,sdtasdt0(xc,X1)),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(sK8(xc,X0),X1))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f770,f140]) ).
fof(f802,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(sK8(xc,X1),sK5(X0)))
| ~ aElement0(sK5(X0))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(superposition,[],[f786,f141]) ).
fof(f829,plain,
! [X0,X1] :
( ~ aElement0(sdtpldt0(sK8(xc,X1),sK5(X0)))
| aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[],[f802,f142]) ).
fof(f835,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(sK8(xc,X0))
| ~ aElement0(sK5(X1)) ),
inference(resolution,[],[f829,f209]) ).
fof(f840,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(sK8(xc,X0)) ),
inference(forward_subsumption_resolution,[],[f835,f142]) ).
fof(f841,plain,
( ~ aElementOf0(sK2,slsdtgt0(xc))
| ~ aElementOf0(sK3,slsdtgt0(xc))
| ~ aElement0(sK8(xc,sK2))
| spl26_4 ),
inference(resolution,[],[f840,f271]) ).
fof(f858,plain,
( ~ aElementOf0(sK3,slsdtgt0(xc))
| ~ aElement0(sK8(xc,sK2))
| spl26_4 ),
inference(forward_subsumption_resolution,[],[f841,f146]) ).
fof(f863,plain,
( ~ aElement0(sK8(xc,sK2))
| ~ spl26_2
| spl26_4 ),
inference(forward_subsumption_resolution,[],[f858,f261]) ).
fof(f865,plain,
( $false
| ~ spl26_2
| spl26_4 ),
inference(forward_subsumption_resolution,[],[f863,f297]) ).
fof(f866,plain,
( ~ spl26_2
| spl26_4 ),
inference(avatar_contradiction_clause,[],[f865]) ).
fof(f881,plain,
( ~ aElementOf0(sdtasdt0(sK2,sK4),slsdtgt0(xc))
| ~ aElement0(sK4)
| ~ aElement0(sK2)
| spl26_3 ),
inference(superposition,[],[f266,f223]) ).
fof(f882,plain,
( ~ aElementOf0(sdtasdt0(sK2,sK4),slsdtgt0(xc))
| ~ aElement0(sK2)
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f881,f257]) ).
fof(f885,plain,
( ~ aElementOf0(sdtasdt0(sK2,sK4),slsdtgt0(xc))
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f882,f309]) ).
fof(f896,plain,
( ~ aElement0(sdtasdt0(sK5(sK2),sK4))
| ~ aElement0(sK4)
| ~ aElementOf0(sK2,slsdtgt0(xc))
| ~ spl26_1
| spl26_3 ),
inference(resolution,[],[f885,f660]) ).
fof(f897,plain,
( ~ aElement0(sdtasdt0(sK5(sK2),sK4))
| ~ aElementOf0(sK2,slsdtgt0(xc))
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f896,f257]) ).
fof(f898,plain,
( ~ aElement0(sdtasdt0(sK5(sK2),sK4))
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f897,f146]) ).
fof(f900,plain,
( ~ aElement0(sdtasdt0(sK4,sK5(sK2)))
| ~ aElement0(sK4)
| ~ aElement0(sK5(sK2))
| ~ spl26_1
| spl26_3 ),
inference(superposition,[],[f898,f223]) ).
fof(f903,plain,
( ~ aElement0(sK4)
| ~ aElement0(sK5(sK2))
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f900,f224]) ).
fof(f906,plain,
( ~ aElement0(sK5(sK2))
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f903,f257]) ).
fof(f911,plain,
( $false
| ~ spl26_1
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f906,f275]) ).
fof(f912,plain,
( ~ spl26_1
| spl26_3 ),
inference(avatar_contradiction_clause,[],[f911]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f262]) ).
cnf(s2,plain,
( spl26_2
| ~ spl26_3 ),
inference(sat_conversion,[],[f267]) ).
cnf(s3,plain,
( spl26_1
| ~ spl26_4 ),
inference(sat_conversion,[],[f272]) ).
cnf(s4,plain,
( ~ spl26_3
| ~ spl26_4 ),
inference(sat_conversion,[],[f273]) ).
cnf(s8,plain,
( ~ spl26_2
| spl26_4 ),
inference(sat_conversion,[],[f866]) ).
cnf(s13,plain,
( ~ spl26_1
| spl26_3 ),
inference(sat_conversion,[],[f912]) ).
cnf(s14,plain,
spl26_1,
inference(rat,[],[s8,s1,s3]) ).
cnf(s15,plain,
spl26_3,
inference(rat,[],[s13,s14]) ).
cnf(s16,plain,
~ spl26_4,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
spl26_2,
inference(rat,[],[s2,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s8,s16,s17]) ).
fof(f913,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG100+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:15:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 11.99/2.51 % (2871705)Detected formulas, will run a generic FOF schedule.
% 11.99/2.51 % (2871713)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2154666648:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.99/2.51 % (2871713)Instruction limit reached!
% 11.99/2.51 % (2871713)------------------------------
% 11.99/2.51 % (2871713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.51 % (2871713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.51 % (2871713)CaDiCaL version: 2.1.3
% 11.99/2.51 % (2871713)Termination reason: Instruction limit
% 11.99/2.51 % (2871713)Termination phase: Saturation
% 11.99/2.51 % (2871713)Time elapsed: 0.038 s
% 11.99/2.51 % (2871713)Peak memory usage: 89 MB
% 11.99/2.51 % (2871713)Instructions burned: 113 (million)
% 11.99/2.51 % (2871716)dis-21_1_sil=8000:lcm=predicate:random_seed=3131210139: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)
% 11.99/2.51 % (2871715)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3249874363:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.99/2.51 % (2871714)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1234422139:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.99/2.51 % (2871710)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=711554769:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.99/2.51 % (2871711)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=394190196:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.99/2.51 % (2871712)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=3414562168:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.99/2.51 % (2871716)Instruction limit reached!
% 11.99/2.51 % (2871716)------------------------------
% 11.99/2.51 % (2871716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.51 % (2871716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.51 % (2871716)CaDiCaL version: 2.1.3
% 11.99/2.51 % (2871716)Termination reason: Instruction limit
% 11.99/2.51 % (2871716)Termination phase: Saturation
% 11.99/2.51 % (2871716)Time elapsed: 0.071 s
% 11.99/2.51 % (2871716)Peak memory usage: 89 MB
% 11.99/2.51 % (2871716)Instructions burned: 130 (million)
% 11.99/2.51 % (2871714)Instruction limit reached!
% 11.99/2.51 % (2871714)------------------------------
% 11.99/2.51 % (2871714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.51 % (2871714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.51 % (2871714)CaDiCaL version: 2.1.3
% 11.99/2.51 % (2871714)Termination reason: Instruction limit
% 11.99/2.51 % (2871714)Termination phase: Saturation
% 11.99/2.51 % (2871714)Time elapsed: 0.070 s
% 11.99/2.51 % (2871714)Peak memory usage: 89 MB
% 11.99/2.51 % (2871714)Instructions burned: 120 (million)
% 11.99/2.51 % (2871719)lrs+10_1_sil=8000:sp=occurrence:random_seed=1442513499:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.99/2.51 % (2871715)Instruction limit reached!
% 11.99/2.51 % (2871715)------------------------------
% 11.99/2.51 % (2871715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.51 % (2871715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.51 % (2871715)CaDiCaL version: 2.1.3
% 11.99/2.51 % (2871715)Termination reason: Instruction limit
% 11.99/2.51 % (2871715)Termination phase: Saturation
% 11.99/2.51 % (2871715)Time elapsed: 0.093 s
% 11.99/2.51 % (2871715)Peak memory usage: 90 MB
% 11.99/2.51 % (2871715)Instructions burned: 140 (million)
% 11.99/2.51 % (2871719)Instruction limit reached!
% 11.99/2.51 % (2871719)------------------------------
% 11.99/2.51 % (2871719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.51 % (2871719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.51 % (2871719)CaDiCaL version: 2.1.3
% 11.99/2.51 % (2871719)Termination reason: Instruction limit
% 11.99/2.51 % (2871719)Termination phase: Saturation
% 11.99/2.51 % (2871719)Time elapsed: 0.092 s
% 11.99/2.51 % (2871719)Peak memory usage: 93 MB
% 11.99/2.51 % (2871719)Instructions burned: 286 (million)
% 5.74/2.70 % (2871725)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3087091104:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.74/2.70 % (2871726)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3008924249:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.74/2.70 % (2871728)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=3435915517:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.74/2.70 % (2871729)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3737836522:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 5.74/2.70 % (2871725)Instruction limit reached!
% 5.74/2.70 % (2871725)------------------------------
% 5.74/2.70 % (2871725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871725)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871725)Termination reason: Instruction limit
% 5.74/2.70 % (2871725)Termination phase: Saturation
% 5.74/2.70 % (2871725)Time elapsed: 0.079 s
% 5.74/2.70 % (2871725)Peak memory usage: 91 MB
% 5.74/2.70 % (2871725)Instructions burned: 159 (million)
% 5.74/2.70 % (2871728)Instruction limit reached!
% 5.74/2.70 % (2871728)------------------------------
% 5.74/2.70 % (2871728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871728)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871728)Termination reason: Instruction limit
% 5.74/2.70 % (2871728)Termination phase: Saturation
% 5.74/2.70 % (2871728)Time elapsed: 0.122 s
% 5.74/2.70 % (2871728)Peak memory usage: 94 MB
% 5.74/2.70 % (2871728)Instructions burned: 250 (million)
% 5.74/2.70 % (2871729)Instruction limit reached!
% 5.74/2.70 % (2871729)------------------------------
% 5.74/2.70 % (2871729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871729)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871729)Termination reason: Instruction limit
% 5.74/2.70 % (2871729)Termination phase: Saturation
% 5.74/2.70 % (2871729)Time elapsed: 0.094 s
% 5.74/2.70 % (2871729)Peak memory usage: 90 MB
% 5.74/2.70 % (2871729)Instructions burned: 297 (million)
% 5.74/2.70 % (2871726)Instruction limit reached!
% 5.74/2.70 % (2871726)------------------------------
% 5.74/2.70 % (2871726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871726)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871726)Termination reason: Instruction limit
% 5.74/2.70 % (2871726)Termination phase: Saturation
% 5.74/2.70 % (2871726)Time elapsed: 0.197 s
% 5.74/2.70 % (2871726)Peak memory usage: 93 MB
% 5.74/2.70 % (2871726)Instructions burned: 325 (million)
% 5.74/2.70 % (2871734)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=797860931:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.74/2.70 % (2871736)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3296103710:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.74/2.70 % (2871735)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3973824629:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 5.74/2.70 % (2871736)Instruction limit reached!
% 5.74/2.70 % (2871736)------------------------------
% 5.74/2.70 % (2871736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871736)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871736)Termination reason: Instruction limit
% 5.74/2.70 % (2871736)Termination phase: Saturation
% 5.74/2.70 % (2871736)Time elapsed: 0.035 s
% 5.74/2.70 % (2871736)Peak memory usage: 89 MB
% 5.74/2.70 % (2871736)Instructions burned: 130 (million)
% 5.74/2.70 % (2871737)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2866051097:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 5.74/2.70 % (2871735)Instruction limit reached!
% 5.74/2.70 % (2871735)------------------------------
% 5.74/2.70 % (2871735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871735)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871735)Termination reason: Instruction limit
% 5.74/2.70 % (2871735)Termination phase: Saturation
% 5.74/2.70 % (2871735)Time elapsed: 0.075 s
% 5.74/2.70 % (2871735)Peak memory usage: 90 MB
% 5.74/2.70 % (2871735)Instructions burned: 114 (million)
% 5.74/2.70 % (2871741)lrs+10_1_sil=8000:sp=occurrence:random_seed=3255458424:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 5.74/2.70 % (2871737)Instruction limit reached!
% 5.74/2.70 % (2871737)------------------------------
% 5.74/2.70 % (2871737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871737)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871737)Termination reason: Instruction limit
% 5.74/2.70 % (2871737)Termination phase: Saturation
% 5.74/2.70 % (2871737)Time elapsed: 0.067 s
% 5.74/2.70 % (2871737)Peak memory usage: 89 MB
% 5.74/2.70 % (2871737)Instructions burned: 114 (million)
% 5.74/2.70 % (2871743)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2232419101:i=437:sd=1:aac=none:ss=included_2993 on theBenchmark for (2993ds/437Mi)
% 5.74/2.70 % (2871745)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3144945021:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 5.74/2.70 % (2871741)Instruction limit reached!
% 5.74/2.70 % (2871741)------------------------------
% 5.74/2.70 % (2871741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871741)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871741)Termination reason: Instruction limit
% 5.74/2.70 % (2871741)Termination phase: Saturation
% 5.74/2.70 % (2871741)Time elapsed: 0.273 s
% 5.74/2.70 % (2871741)Peak memory usage: 103 MB
% 5.74/2.70 % (2871741)Instructions burned: 907 (million)
% 5.74/2.70 % (2871743)Instruction limit reached!
% 5.74/2.70 % (2871743)------------------------------
% 5.74/2.70 % (2871743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871743)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871743)Termination reason: Instruction limit
% 5.74/2.70 % (2871743)Termination phase: Saturation
% 5.74/2.70 % (2871743)Time elapsed: 0.269 s
% 5.74/2.70 % (2871743)Peak memory usage: 92 MB
% 5.74/2.70 % (2871743)Instructions burned: 438 (million)
% 5.74/2.70 % (2871748)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2574937715:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 5.74/2.70 % (2871748)Instruction limit reached!
% 5.74/2.70 % (2871748)------------------------------
% 5.74/2.70 % (2871748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871748)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871748)Termination reason: Instruction limit
% 5.74/2.70 % (2871748)Termination phase: Saturation
% 5.74/2.70 % (2871748)Time elapsed: 0.035 s
% 5.74/2.70 % (2871748)Peak memory usage: 91 MB
% 5.74/2.70 % (2871748)Instructions burned: 138 (million)
% 5.74/2.70 % (2871751)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4069696293:st=3:i=13193:sd=3:ss=axioms_2988 on theBenchmark for (2988ds/13193Mi)
% 5.74/2.70 % (2871749)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1200085968:st=8:i=592:sd=3:ep=RST:ss=axioms_2989 on theBenchmark for (2989ds/592Mi)
% 5.74/2.70 % (2871749)Instruction limit reached!
% 5.74/2.70 % (2871749)------------------------------
% 5.74/2.70 % (2871749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871749)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871749)Termination reason: Instruction limit
% 5.74/2.70 % (2871749)Termination phase: Saturation
% 5.74/2.70 % (2871749)Time elapsed: 0.311 s
% 5.74/2.70 % (2871749)Peak memory usage: 98 MB
% 5.74/2.70 % (2871749)Instructions burned: 594 (million)
% 5.74/2.70 % (2871745)First to succeed.
% 5.74/2.70 % (2871745)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2871705"
% 5.74/2.70 % (2871754)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=3556936197:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/125Mi)
% 5.74/2.70 % (2871754)Instruction limit reached!
% 5.74/2.70 % (2871754)------------------------------
% 5.74/2.70 % (2871754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/2.70 % (2871754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/2.70 % (2871754)CaDiCaL version: 2.1.3
% 5.74/2.70 % (2871754)Termination reason: Instruction limit
% 5.74/2.70 % (2871754)Termination phase: Saturation
% 5.74/2.70 % (2871754)Time elapsed: 0.069 s
% 5.74/2.70 % (2871754)Peak memory usage: 91 MB
% 5.74/2.70 % (2871754)Instructions burned: 126 (million)
% 5.74/2.70 % (2871745)Refutation found. Thanks to Tanya!
% 5.74/2.70 % SZS status Theorem for theBenchmark
% 5.74/2.70 % SZS output start Proof for theBenchmark
% See solution above
% 13.78/2.90 % (2871745)------------------------------
% 13.78/2.90 % (2871745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.78/2.90 % (2871745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.78/2.90 % (2871745)CaDiCaL version: 2.1.3
% 13.78/2.90 % (2871745)Termination reason: Refutation
% 13.78/2.90 % (2871745)Time elapsed: 0.703 s
% 13.78/2.90 % (2871745)Peak memory usage: 130 MB
% 13.78/2.90 % (2871745)Instructions burned: 1073 (million)
% 13.78/2.90 % (2871745)------------------------------
% 13.78/2.90 % (2871745)------------------------------
% 13.78/2.90 % (2871705)Success in time 1.855 s
% 13.78/2.90 % Vampire exiting
%------------------------------------------------------------------------------