%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG085+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 : n019.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 12:35:27 PM UTC 2026
% Result : Theorem 28.41s 4.67s
% Output : Refutation 28.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 134 ( 22 unt; 7 def)
% Number of atoms : 494 ( 40 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 606 ( 246 ~; 238 |; 84 &)
% ( 9 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 184 ( 0 sgn 158 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
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(f25,axiom,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f26,conjecture,
( ( aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ)) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f27,negated_conjecture,
~ ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ)) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f32,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) )
& ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) ) ) )
& aIdeal0(xJ) ),
inference(rectify,[],[f25]) ).
fof(f33,plain,
~ ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) )
=> ( ! [X3] :
( aElementOf0(X3,sdtpldt1(xI,xJ))
=> ( ! [X4] :
( aElementOf0(X4,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X3,X4),sdtpldt1(xI,xJ)) )
& ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ),
inference(rectify,[],[f27]) ).
fof(f39,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f41]) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f64,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ) )
& ! [X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5) ) )
| ~ aElementOf0(X3,xJ) )
& aIdeal0(xJ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f65,plain,
( ? [X3] :
( ( ? [X4] :
( ~ aElementOf0(sdtpldt0(X3,X4),sdtpldt1(xI,xJ))
& aElementOf0(X4,sdtpldt1(xI,xJ)) )
| ? [X5] :
( ~ aElementOf0(sdtasdt0(X5,X3),sdtpldt1(xI,xJ))
& aElement0(X5) ) )
& aElementOf0(X3,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f66,plain,
( ? [X3] :
( ( ? [X4] :
( ~ aElementOf0(sdtpldt0(X3,X4),sdtpldt1(xI,xJ))
& aElementOf0(X4,sdtpldt1(xI,xJ)) )
| ? [X5] :
( ~ aElementOf0(sdtasdt0(X5,X3),sdtpldt1(xI,xJ))
& aElement0(X5) ) )
& aElementOf0(X3,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) ),
inference(flattening,[],[f65]) ).
fof(f85,plain,
( ? [X3] :
( ( ? [X4] :
( ~ aElementOf0(sdtpldt0(X3,X4),sdtpldt1(xI,xJ))
& aElementOf0(X4,sdtpldt1(xI,xJ)) )
| ? [X5] :
( ~ aElementOf0(sdtasdt0(X5,X3),sdtpldt1(xI,xJ))
& aElement0(X5) ) )
& aElementOf0(X3,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( ( aElementOf0(X0,sdtpldt1(xI,xJ))
| ! [X1,X2] :
( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xJ)
| sdtpldt0(X1,X2) != X0 ) )
& ( ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 )
| ~ aElementOf0(X0,sdtpldt1(xI,xJ)) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f86,plain,
( ? [X0] :
( ( ? [X1] :
( ~ aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& aElementOf0(X1,sdtpldt1(xI,xJ)) )
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ))
& aElement0(X2) ) )
& aElementOf0(X0,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt1(xI,xJ))
| ! [X4,X5] :
( ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X6,X7] :
( aElementOf0(X6,xI)
& aElementOf0(X7,xJ)
& sdtpldt0(X6,X7) = X3 )
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
( ( ( ~ aElementOf0(sdtpldt0(sK13,sK14),sdtpldt1(xI,xJ))
& aElementOf0(sK14,sdtpldt1(xI,xJ)) )
| ( ~ aElementOf0(sdtasdt0(sK15,sK13),sdtpldt1(xI,xJ))
& aElement0(sK15) ) )
& aElementOf0(sK13,sdtpldt1(xI,xJ))
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt1(xI,xJ))
| ! [X4,X5] :
( ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ)
| sdtpldt0(X4,X5) != X3 ) )
& ( ( aElementOf0(sK16(X3),xI)
& aElementOf0(sK17(X3),xJ)
& sdtpldt0(sK16(X3),sK17(X3)) = X3 )
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X6,sK16(X3)),skolemize(X7,sK17(X3))],[f86]) ).
fof(f93,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f94,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f104,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,[],[f51]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f144,plain,
! [X3,X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5)
| ~ aElementOf0(X3,xJ) ),
inference(cnf_transformation,[],[f64]) ).
fof(f145,plain,
! [X3,X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ)
| ~ aElementOf0(X3,xJ) ),
inference(cnf_transformation,[],[f64]) ).
fof(f146,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f64]) ).
fof(f148,plain,
! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f64]) ).
fof(f149,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f64]) ).
fof(f150,plain,
aSet0(xI),
inference(cnf_transformation,[],[f64]) ).
fof(f151,plain,
! [X3] :
( sdtpldt0(sK16(X3),sK17(X3)) = X3
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f152,plain,
! [X3] :
( aElementOf0(sK17(X3),xJ)
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f153,plain,
! [X3] :
( aElementOf0(sK16(X3),xI)
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f154,plain,
! [X3,X4,X5] :
( aElementOf0(X3,sdtpldt1(xI,xJ))
| ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ)
| sdtpldt0(X4,X5) != X3 ),
inference(cnf_transformation,[],[f87]) ).
fof(f155,plain,
aSet0(sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f87]) ).
fof(f157,plain,
aElementOf0(sK13,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f87]) ).
fof(f158,plain,
( aElementOf0(sK14,sdtpldt1(xI,xJ))
| aElement0(sK15) ),
inference(cnf_transformation,[],[f87]) ).
fof(f159,plain,
( aElementOf0(sK14,sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(sK15,sK13),sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f160,plain,
( ~ aElementOf0(sdtpldt0(sK13,sK14),sdtpldt1(xI,xJ))
| aElement0(sK15) ),
inference(cnf_transformation,[],[f87]) ).
fof(f161,plain,
( ~ aElementOf0(sdtpldt0(sK13,sK14),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(sK15,sK13),sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f168,plain,
! [X4,X5] :
( aElementOf0(sdtpldt0(X4,X5),sdtpldt1(xI,xJ))
| ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ) ),
inference(equality_resolution,[],[f154]) ).
fof(f169,definition,
sF18 = sdtpldt0(sK13,sK14),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f170,plain,
sdtpldt0(sK13,sK14) = sF18,
inference(reorient_equations,[],[f169]) ).
fof(f171,definition,
sF19 = sdtpldt1(xI,xJ),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f172,plain,
sdtpldt1(xI,xJ) = sF19,
inference(reorient_equations,[],[f171]) ).
fof(f173,definition,
sF20 = sdtasdt0(sK15,sK13),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f174,plain,
sdtasdt0(sK15,sK13) = sF20,
inference(reorient_equations,[],[f173]) ).
fof(f175,plain,
( ~ aElementOf0(sF18,sF19)
| ~ aElementOf0(sF20,sF19) ),
inference(definition_folding,[],[f161,f172,f174,f172,f170]) ).
fof(f176,plain,
( ~ aElementOf0(sF18,sF19)
| aElement0(sK15) ),
inference(definition_folding,[],[f160,f172,f170]) ).
fof(f177,plain,
( aElementOf0(sK14,sF19)
| ~ aElementOf0(sF20,sF19) ),
inference(definition_folding,[],[f159,f172,f174,f172]) ).
fof(f178,plain,
( aElementOf0(sK14,sF19)
| aElement0(sK15) ),
inference(definition_folding,[],[f158,f172]) ).
fof(f179,plain,
aElementOf0(sK13,sF19),
inference(definition_folding,[],[f157,f172]) ).
fof(f181,plain,
aSet0(sF19),
inference(definition_folding,[],[f155,f172]) ).
fof(f182,plain,
! [X4,X5] :
( aElementOf0(sdtpldt0(X4,X5),sF19)
| ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ) ),
inference(definition_folding,[],[f168,f172]) ).
fof(f183,plain,
! [X3] :
( aElementOf0(sK16(X3),xI)
| ~ aElementOf0(X3,sF19) ),
inference(definition_folding,[],[f153,f172]) ).
fof(f184,plain,
! [X3] :
( aElementOf0(sK17(X3),xJ)
| ~ aElementOf0(X3,sF19) ),
inference(definition_folding,[],[f152,f172]) ).
fof(f185,plain,
! [X3] :
( sdtpldt0(sK16(X3),sK17(X3)) = X3
| ~ aElementOf0(X3,sF19) ),
inference(definition_folding,[],[f151,f172]) ).
fof(f187,definition,
( spl21_1
<=> aElement0(sK15) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f189,plain,
( aElement0(sK15)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl21_2
<=> aElementOf0(sK14,sF19) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f193,plain,
( aElementOf0(sK14,sF19)
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f178,f191,f187]) ).
fof(f196,definition,
( spl21_3
<=> aElementOf0(sF20,sF19) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f198,plain,
( ~ aElementOf0(sF20,sF19)
| spl21_3 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f199,plain,
( ~ spl21_3
| spl21_2 ),
inference(avatar_split_clause,[],[f177,f191,f196]) ).
fof(f201,definition,
( spl21_4
<=> aElementOf0(sF18,sF19) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f203,plain,
( ~ aElementOf0(sF18,sF19)
| spl21_4 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( spl21_1
| ~ spl21_4 ),
inference(avatar_split_clause,[],[f176,f201,f187]) ).
fof(f205,plain,
( ~ spl21_3
| ~ spl21_4 ),
inference(avatar_split_clause,[],[f175,f201,f196]) ).
fof(f231,plain,
aElementOf0(sK16(sK13),xI),
inference(unit_resulting_resolution,[],[f183,f179]) ).
fof(f233,plain,
aElementOf0(sK17(sK13),xJ),
inference(unit_resulting_resolution,[],[f184,f179]) ).
fof(f263,plain,
( aElement0(sK14)
| ~ spl21_2 ),
inference(unit_resulting_resolution,[],[f111,f181,f193]) ).
fof(f268,plain,
! [X0] :
( aElement0(sK16(X0))
| ~ aSet0(xI)
| ~ aElementOf0(X0,sF19) ),
inference(resolution,[],[f111,f183]) ).
fof(f270,plain,
( aElement0(sK16(sK13))
| ~ aSet0(xI) ),
inference(resolution,[],[f111,f231]) ).
fof(f273,plain,
! [X0] :
( aElement0(sK17(X0))
| ~ aSet0(xJ)
| ~ aElementOf0(X0,sF19) ),
inference(resolution,[],[f111,f184]) ).
fof(f275,plain,
( aElement0(sK17(sK13))
| ~ aSet0(xJ) ),
inference(resolution,[],[f111,f233]) ).
fof(f278,plain,
aElement0(sK17(sK13)),
inference(forward_subsumption_resolution,[],[f275,f146]) ).
fof(f280,plain,
! [X0] :
( aElement0(sK17(X0))
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f273,f146]) ).
fof(f283,plain,
aElement0(sK16(sK13)),
inference(forward_subsumption_resolution,[],[f270,f150]) ).
fof(f285,plain,
! [X0] :
( aElement0(sK16(X0))
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f268,f150]) ).
fof(f298,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(sK16(X0),sdtpldt0(sK17(X0),X1))
| ~ aElement0(sK16(X0))
| ~ aElement0(sK17(X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(superposition,[],[f94,f185]) ).
fof(f302,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X0,sdtpldt0(X1,X2)),sF19)
| ~ aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X2,xJ)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(superposition,[],[f182,f94]) ).
fof(f306,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(sK16(X0),sdtpldt0(sK17(X0),X1))
| ~ aElement0(sK17(X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f298,f285]) ).
fof(f309,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(sK16(X0),sdtpldt0(sK17(X0),X1))
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f306,f280]) ).
fof(f617,plain,
! [X2,X0,X1] :
( aElementOf0(sdtasdt0(X0,sdtpldt0(X1,X2)),sF19)
| ~ aElementOf0(sdtasdt0(X0,X1),xI)
| ~ aElementOf0(sdtasdt0(X0,X2),xJ)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(superposition,[],[f182,f104]) ).
fof(f660,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),sF19)
| ~ aElementOf0(sdtpldt0(X1,sK16(X0)),xI)
| ~ aElementOf0(sK17(X0),xJ)
| ~ aElement0(X1)
| ~ aElement0(sK16(X0))
| ~ aElement0(sK17(X0))
| ~ aElementOf0(X0,sF19) ),
inference(superposition,[],[f302,f185]) ).
fof(f670,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),sF19)
| ~ aElementOf0(sdtpldt0(X1,sK16(X0)),xI)
| ~ aElementOf0(sK17(X0),xJ)
| ~ aElement0(X1)
| ~ aElement0(sK17(X0))
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f660,f285]) ).
fof(f678,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),sF19)
| ~ aElementOf0(sdtpldt0(X1,sK16(X0)),xI)
| ~ aElementOf0(sK17(X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f670,f280]) ).
fof(f683,plain,
! [X0,X1] :
( ~ aElementOf0(sdtpldt0(X1,sK16(X0)),xI)
| aElementOf0(sdtpldt0(X1,X0),sF19)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f678,f184]) ).
fof(f684,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElementOf0(sK16(X1),xI)
| ~ aElementOf0(X0,xI) ),
inference(resolution,[],[f683,f149]) ).
fof(f689,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElementOf0(X0,xI) ),
inference(forward_subsumption_resolution,[],[f684,f183]) ).
fof(f2976,plain,
( sdtpldt0(sK13,sK14) = sdtpldt0(sK16(sK13),sdtpldt0(sK17(sK13),sK14))
| ~ spl21_2 ),
inference(unit_resulting_resolution,[],[f309,f263,f179]) ).
fof(f2997,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElementOf0(sK16(X0),xI)
| ~ aElementOf0(sdtpldt0(sK17(X0),X1),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(superposition,[],[f182,f309]) ).
fof(f3010,plain,
! [X0,X1] :
( ~ aElementOf0(sdtpldt0(sK17(X0),X1),xJ)
| aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f2997,f183]) ).
fof(f3023,plain,
( sF18 = sdtpldt0(sK16(sK13),sdtpldt0(sK17(sK13),sK14))
| ~ spl21_2 ),
inference(forward_demodulation,[],[f2976,f170]) ).
fof(f3048,plain,
( aElementOf0(sF18,sF19)
| ~ aElement0(sK16(sK13))
| ~ aElementOf0(sdtpldt0(sK17(sK13),sK14),sF19)
| ~ aElementOf0(sK16(sK13),xI)
| ~ spl21_2 ),
inference(superposition,[],[f689,f3023]) ).
fof(f3052,plain,
( ~ aElement0(sK16(sK13))
| ~ aElementOf0(sdtpldt0(sK17(sK13),sK14),sF19)
| ~ aElementOf0(sK16(sK13),xI)
| ~ spl21_2
| spl21_4 ),
inference(forward_subsumption_resolution,[],[f3048,f203]) ).
fof(f3068,plain,
( ~ aElementOf0(sdtpldt0(sK17(sK13),sK14),sF19)
| ~ aElementOf0(sK16(sK13),xI)
| ~ spl21_2
| spl21_4 ),
inference(forward_subsumption_resolution,[],[f3052,f283]) ).
fof(f3094,plain,
( ~ aElementOf0(sdtpldt0(sK17(sK13),sK14),sF19)
| ~ spl21_2
| spl21_4 ),
inference(forward_subsumption_resolution,[],[f3068,f231]) ).
fof(f3186,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(sK17(X0),xJ) ),
inference(resolution,[],[f3010,f145]) ).
fof(f3196,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19)
| ~ aElementOf0(X1,xJ) ),
inference(forward_subsumption_resolution,[],[f3186,f184]) ).
fof(f3207,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElementOf0(X0,xJ)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(superposition,[],[f3196,f93]) ).
fof(f3224,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElementOf0(X0,xJ)
| ~ aElement0(X1) ),
inference(duplicate_literal_removal,[],[f3207]) ).
fof(f3258,plain,
( ~ aElement0(sK17(sK13))
| ~ spl21_2
| spl21_4 ),
inference(unit_resulting_resolution,[],[f3224,f263,f193,f233,f3094]) ).
fof(f3289,plain,
( $false
| ~ spl21_2
| spl21_4 ),
inference(forward_subsumption_resolution,[],[f3258,f278]) ).
fof(f3290,plain,
( ~ spl21_2
| spl21_4 ),
inference(avatar_contradiction_clause,[],[f3289]) ).
fof(f19592,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),sF19)
| ~ aElementOf0(sdtasdt0(X1,sK16(X0)),xI)
| ~ aElementOf0(sdtasdt0(X1,sK17(X0)),xJ)
| ~ aElement0(X1)
| ~ aElement0(sK16(X0))
| ~ aElement0(sK17(X0))
| ~ aElementOf0(X0,sF19) ),
inference(superposition,[],[f617,f185]) ).
fof(f19616,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),sF19)
| ~ aElementOf0(sdtasdt0(X1,sK16(X0)),xI)
| ~ aElementOf0(sdtasdt0(X1,sK17(X0)),xJ)
| ~ aElement0(X1)
| ~ aElement0(sK17(X0))
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f19592,f285]) ).
fof(f19626,plain,
! [X0,X1] :
( ~ aElementOf0(sdtasdt0(X1,sK17(X0)),xJ)
| ~ aElementOf0(sdtasdt0(X1,sK16(X0)),xI)
| aElementOf0(sdtasdt0(X1,X0),sF19)
| ~ aElement0(X1)
| ~ aElementOf0(X0,sF19) ),
inference(forward_subsumption_resolution,[],[f19616,f280]) ).
fof(f19629,plain,
! [X0,X1] :
( ~ aElementOf0(sdtasdt0(X0,sK16(X1)),xI)
| aElementOf0(sdtasdt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElement0(X0)
| ~ aElementOf0(sK17(X1),xJ) ),
inference(resolution,[],[f19626,f144]) ).
fof(f19637,plain,
! [X0,X1] :
( ~ aElementOf0(sdtasdt0(X0,sK16(X1)),xI)
| aElementOf0(sdtasdt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElementOf0(sK17(X1),xJ) ),
inference(duplicate_literal_removal,[],[f19629]) ).
fof(f19642,plain,
! [X0,X1] :
( ~ aElementOf0(sdtasdt0(X0,sK16(X1)),xI)
| aElementOf0(sdtasdt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19) ),
inference(forward_subsumption_resolution,[],[f19637,f184]) ).
fof(f19645,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElement0(X0)
| ~ aElementOf0(sK16(X1),xI) ),
inference(resolution,[],[f19642,f148]) ).
fof(f19653,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19)
| ~ aElementOf0(sK16(X1),xI) ),
inference(duplicate_literal_removal,[],[f19645]) ).
fof(f19658,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),sF19)
| ~ aElement0(X0)
| ~ aElementOf0(X1,sF19) ),
inference(forward_subsumption_resolution,[],[f19653,f183]) ).
fof(f19897,plain,
( aElementOf0(sF20,sF19)
| ~ aElement0(sK15)
| ~ aElementOf0(sK13,sF19) ),
inference(superposition,[],[f19658,f174]) ).
fof(f19900,plain,
( ~ aElement0(sK15)
| ~ aElementOf0(sK13,sF19)
| spl21_3 ),
inference(forward_subsumption_resolution,[],[f19897,f198]) ).
fof(f19964,plain,
( ~ aElementOf0(sK13,sF19)
| ~ spl21_1
| spl21_3 ),
inference(forward_subsumption_resolution,[],[f19900,f189]) ).
fof(f19969,plain,
( $false
| ~ spl21_1
| spl21_3 ),
inference(forward_subsumption_resolution,[],[f19964,f179]) ).
fof(f19970,plain,
( ~ spl21_1
| spl21_3 ),
inference(avatar_contradiction_clause,[],[f19969]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f194]) ).
cnf(s2,plain,
( spl21_2
| ~ spl21_3 ),
inference(sat_conversion,[],[f199]) ).
cnf(s3,plain,
( spl21_1
| ~ spl21_4 ),
inference(sat_conversion,[],[f204]) ).
cnf(s4,plain,
( ~ spl21_3
| ~ spl21_4 ),
inference(sat_conversion,[],[f205]) ).
cnf(s44,plain,
( ~ spl21_2
| spl21_4 ),
inference(sat_conversion,[],[f3290]) ).
cnf(s84,plain,
( ~ spl21_1
| spl21_3 ),
inference(sat_conversion,[],[f19970]) ).
cnf(s98,plain,
spl21_1,
inference(rat,[],[s44,s1,s3]) ).
cnf(s99,plain,
spl21_3,
inference(rat,[],[s84,s98]) ).
cnf(s100,plain,
~ spl21_4,
inference(rat,[],[s4,s99]) ).
cnf(s101,plain,
spl21_2,
inference(rat,[],[s2,s99]) ).
cnf(s102,plain,
$false,
inference(rat,[],[s44,s100,s101]) ).
fof(f19971,plain,
$false,
inference(avatar_sat_refutation,[],[s102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG085+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:11:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 11.15/2.24 % (3513689)Detected formulas, will run a generic FOF schedule.
% 11.15/2.24 % (3513699)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=692291333:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.15/2.24 % (3513696)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=2118665045:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.15/2.24 % (3513700)dis-21_1_sil=8000:lcm=predicate:random_seed=262466496: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)
% 11.15/2.24 % (3513698)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3074760496:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.15/2.24 % (3513694)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=1659391810:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.15/2.24 % (3513697)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=363309781:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.15/2.24 % (3513695)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=4293236042:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.15/2.24 % (3513699)Instruction limit reached!
% 11.15/2.24 % (3513699)------------------------------
% 11.15/2.24 % (3513699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.15/2.24 % (3513699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.15/2.24 % (3513699)CaDiCaL version: 2.1.3
% 11.15/2.24 % (3513699)Termination reason: Instruction limit
% 11.15/2.24 % (3513699)Termination phase: Saturation
% 11.15/2.24 % (3513699)Time elapsed: 0.056 s
% 11.15/2.24 % (3513699)Peak memory usage: 90 MB
% 11.15/2.24 % (3513699)Instructions burned: 140 (million)
% 11.15/2.24 % (3513697)Instruction limit reached!
% 11.15/2.24 % (3513697)------------------------------
% 11.15/2.24 % (3513697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.15/2.24 % (3513697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.15/2.24 % (3513697)CaDiCaL version: 2.1.3
% 11.15/2.24 % (3513697)Termination reason: Instruction limit
% 11.15/2.24 % (3513697)Termination phase: Saturation
% 11.15/2.24 % (3513697)Time elapsed: 0.072 s
% 11.15/2.24 % (3513697)Peak memory usage: 89 MB
% 11.15/2.24 % (3513697)Instructions burned: 110 (million)
% 11.15/2.24 % (3513698)Instruction limit reached!
% 11.15/2.24 % (3513698)------------------------------
% 11.15/2.24 % (3513698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.15/2.24 % (3513698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.15/2.24 % (3513698)CaDiCaL version: 2.1.3
% 11.15/2.24 % (3513698)Termination reason: Instruction limit
% 11.15/2.24 % (3513698)Termination phase: Saturation
% 11.15/2.24 % (3513698)Time elapsed: 0.073 s
% 11.15/2.24 % (3513698)Peak memory usage: 88 MB
% 11.15/2.24 % (3513698)Instructions burned: 119 (million)
% 11.15/2.24 % (3513700)Instruction limit reached!
% 11.15/2.24 % (3513700)------------------------------
% 11.15/2.24 % (3513700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.15/2.24 % (3513700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.15/2.24 % (3513700)CaDiCaL version: 2.1.3
% 11.15/2.24 % (3513700)Termination reason: Instruction limit
% 11.15/2.24 % (3513700)Termination phase: Saturation
% 11.15/2.24 % (3513700)Time elapsed: 0.079 s
% 11.15/2.24 % (3513700)Peak memory usage: 90 MB
% 11.15/2.24 % (3513700)Instructions burned: 134 (million)
% 11.15/2.24 % (3513708)lrs+10_1_sil=8000:sp=occurrence:random_seed=3482503610:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.15/2.24 % (3513709)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1683350428:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.15/2.24 % (3513710)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2490990714:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.15/2.24 % (3513711)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=2984978042:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 11.15/2.24 % (3513708)Instruction limit reached!
% 17.26/3.05 % (3513708)------------------------------
% 17.26/3.05 % (3513708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.26/3.05 % (3513708)CaDiCaL version: 2.1.3
% 17.26/3.05 % (3513708)Termination reason: Instruction limit
% 17.26/3.05 % (3513708)Termination phase: Saturation
% 17.26/3.05 % (3513708)Time elapsed: 0.090 s
% 17.26/3.05 % (3513708)Peak memory usage: 92 MB
% 17.26/3.05 % (3513708)Instructions burned: 288 (million)
% 17.26/3.05 % (3513709)Instruction limit reached!
% 17.26/3.05 % (3513709)------------------------------
% 17.26/3.05 % (3513709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.26/3.05 % (3513709)CaDiCaL version: 2.1.3
% 17.26/3.05 % (3513709)Termination reason: Instruction limit
% 17.26/3.05 % (3513709)Termination phase: Saturation
% 17.26/3.05 % (3513709)Time elapsed: 0.083 s
% 17.26/3.05 % (3513709)Peak memory usage: 94 MB
% 17.26/3.05 % (3513709)Instructions burned: 158 (million)
% 17.26/3.05 % (3513711)Instruction limit reached!
% 17.26/3.05 % (3513711)------------------------------
% 17.26/3.05 % (3513711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.26/3.05 % (3513711)CaDiCaL version: 2.1.3
% 17.26/3.05 % (3513711)Termination reason: Instruction limit
% 17.26/3.05 % (3513711)Termination phase: Saturation
% 17.26/3.05 % (3513711)Time elapsed: 0.123 s
% 17.26/3.05 % (3513711)Peak memory usage: 94 MB
% 17.26/3.05 % (3513711)Instructions burned: 249 (million)
% 17.26/3.05 % (3513716)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3721641095:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 17.26/3.05 % (3513710)Instruction limit reached!
% 17.26/3.05 % (3513710)------------------------------
% 17.26/3.05 % (3513710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.26/3.05 % (3513710)CaDiCaL version: 2.1.3
% 17.26/3.05 % (3513710)Termination reason: Instruction limit
% 17.26/3.05 % (3513710)Termination phase: Saturation
% 17.26/3.05 % (3513710)Time elapsed: 0.212 s
% 17.26/3.05 % (3513710)Peak memory usage: 93 MB
% 17.26/3.05 % (3513710)Instructions burned: 326 (million)
% 17.26/3.05 % (3513717)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=545964516:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 17.26/3.05 % (3513716)Instruction limit reached!
% 17.26/3.05 % (3513716)------------------------------
% 17.26/3.05 % (3513716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.26/3.05 % (3513716)CaDiCaL version: 2.1.3
% 17.26/3.05 % (3513716)Termination reason: Instruction limit
% 17.26/3.05 % (3513716)Termination phase: Saturation
% 17.26/3.05 % (3513716)Time elapsed: 0.094 s
% 17.26/3.05 % (3513716)Peak memory usage: 89 MB
% 17.26/3.05 % (3513716)Instructions burned: 296 (million)
% 17.26/3.05 % (3513718)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2128002849:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 17.26/3.05 % (3513720)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=198251290:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 17.26/3.05 % (3513722)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2141846739:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 17.26/3.05 % (3513718)Instruction limit reached!
% 17.26/3.05 % (3513718)------------------------------
% 17.26/3.05 % (3513718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.26/3.05 % (3513718)CaDiCaL version: 2.1.3
% 17.26/3.05 % (3513718)Termination reason: Instruction limit
% 17.26/3.05 % (3513718)Termination phase: Saturation
% 17.26/3.05 % (3513718)Time elapsed: 0.079 s
% 17.26/3.05 % (3513718)Peak memory usage: 90 MB
% 17.26/3.05 % (3513718)Instructions burned: 113 (million)
% 17.26/3.05 % (3513722)Instruction limit reached!
% 17.26/3.05 % (3513722)------------------------------
% 17.26/3.05 % (3513722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.26/3.05 % (3513722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513722)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513722)Termination reason: Instruction limit
% 28.41/4.67 % (3513722)Termination phase: Saturation
% 28.41/4.67 % (3513722)Time elapsed: 0.035 s
% 28.41/4.67 % (3513722)Peak memory usage: 89 MB
% 28.41/4.67 % (3513722)Instructions burned: 114 (million)
% 28.41/4.67 % (3513720)Instruction limit reached!
% 28.41/4.67 % (3513720)------------------------------
% 28.41/4.67 % (3513720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513720)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513720)Termination reason: Instruction limit
% 28.41/4.67 % (3513720)Termination phase: Saturation
% 28.41/4.67 % (3513720)Time elapsed: 0.064 s
% 28.41/4.67 % (3513720)Peak memory usage: 89 MB
% 28.41/4.67 % (3513720)Instructions burned: 128 (million)
% 28.41/4.67 % (3513727)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3301086802:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 28.41/4.67 % (3513726)lrs+10_1_sil=8000:sp=occurrence:random_seed=2329576844:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 28.41/4.67 % (3513728)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3942783414:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 28.41/4.67 % (3513727)Instruction limit reached!
% 28.41/4.67 % (3513727)------------------------------
% 28.41/4.67 % (3513727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513727)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513727)Termination reason: Instruction limit
% 28.41/4.67 % (3513727)Termination phase: Saturation
% 28.41/4.67 % (3513727)Time elapsed: 0.148 s
% 28.41/4.67 % (3513727)Peak memory usage: 92 MB
% 28.41/4.67 % (3513727)Instructions burned: 440 (million)
% 28.41/4.67 % (3513732)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1514015077:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 28.41/4.67 % (3513732)Instruction limit reached!
% 28.41/4.67 % (3513732)------------------------------
% 28.41/4.67 % (3513732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513732)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513732)Termination reason: Instruction limit
% 28.41/4.67 % (3513732)Termination phase: Saturation
% 28.41/4.67 % (3513732)Time elapsed: 0.032 s
% 28.41/4.67 % (3513732)Peak memory usage: 90 MB
% 28.41/4.67 % (3513732)Instructions burned: 136 (million)
% 28.41/4.67 % (3513734)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2923238443:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 28.41/4.67 % (3513726)Instruction limit reached!
% 28.41/4.67 % (3513726)------------------------------
% 28.41/4.67 % (3513726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513726)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513726)Termination reason: Instruction limit
% 28.41/4.67 % (3513726)Termination phase: Saturation
% 28.41/4.67 % (3513726)Time elapsed: 0.507 s
% 28.41/4.67 % (3513726)Peak memory usage: 103 MB
% 28.41/4.67 % (3513726)Instructions burned: 909 (million)
% 28.41/4.67 % (3513734)Instruction limit reached!
% 28.41/4.67 % (3513734)------------------------------
% 28.41/4.67 % (3513734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513734)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513734)Termination reason: Instruction limit
% 28.41/4.67 % (3513734)Termination phase: Saturation
% 28.41/4.67 % (3513734)Time elapsed: 0.165 s
% 28.41/4.67 % (3513734)Peak memory usage: 97 MB
% 28.41/4.67 % (3513734)Instructions burned: 596 (million)
% 28.41/4.67 % (3513736)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1662523126:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 28.41/4.67 % (3513737)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=1063254187:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/125Mi)
% 28.41/4.67 % (3513737)Instruction limit reached!
% 28.41/4.67 % (3513737)------------------------------
% 28.41/4.67 % (3513737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513737)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513737)Termination reason: Instruction limit
% 28.41/4.67 % (3513737)Termination phase: Saturation
% 28.41/4.67 % (3513737)Time elapsed: 0.040 s
% 28.41/4.67 % (3513737)Peak memory usage: 91 MB
% 28.41/4.67 % (3513737)Instructions burned: 127 (million)
% 28.41/4.67 % (3513740)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3454995644:i=134:gtgl=5:slsql=off:gtg=exists_sym_2983 on theBenchmark for (2983ds/134Mi)
% 28.41/4.67 % (3513740)Instruction limit reached!
% 28.41/4.67 % (3513740)------------------------------
% 28.41/4.67 % (3513740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513740)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513740)Termination reason: Instruction limit
% 28.41/4.67 % (3513740)Termination phase: Saturation
% 28.41/4.67 % (3513740)Time elapsed: 0.040 s
% 28.41/4.67 % (3513740)Peak memory usage: 90 MB
% 28.41/4.67 % (3513740)Instructions burned: 137 (million)
% 28.41/4.67 % (3513742)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=1918041671:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/141Mi)
% 28.41/4.67 % (3513742)Instruction limit reached!
% 28.41/4.67 % (3513742)------------------------------
% 28.41/4.67 % (3513742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513742)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513742)Termination reason: Instruction limit
% 28.41/4.67 % (3513742)Termination phase: Saturation
% 28.41/4.67 % (3513742)Time elapsed: 0.046 s
% 28.41/4.67 % (3513742)Peak memory usage: 91 MB
% 28.41/4.67 % (3513742)Instructions burned: 144 (million)
% 28.41/4.67 % (3513717)Instruction limit reached!
% 28.41/4.67 % (3513717)------------------------------
% 28.41/4.67 % (3513717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513717)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513717)Termination reason: Instruction limit
% 28.41/4.67 % (3513717)Termination phase: Saturation
% 28.41/4.67 % (3513717)Time elapsed: 1.482 s
% 28.41/4.67 % (3513717)Peak memory usage: 143 MB
% 28.41/4.67 % (3513717)Instructions burned: 2350 (million)
% 28.41/4.67 % (3513744)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1339311898:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2979 on theBenchmark for (2979ds/431Mi)
% 28.41/4.67 % (3513744)Instruction limit reached!
% 28.41/4.67 % (3513744)------------------------------
% 28.41/4.67 % (3513744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513744)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513744)Termination reason: Instruction limit
% 28.41/4.67 % (3513744)Termination phase: Saturation
% 28.41/4.67 % (3513744)Time elapsed: 0.131 s
% 28.41/4.67 % (3513744)Peak memory usage: 94 MB
% 28.41/4.67 % (3513744)Instructions burned: 434 (million)
% 28.41/4.67 % (3513745)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2481645084:i=6060:aac=none:ins=25_2978 on theBenchmark for (2978ds/6060Mi)
% 28.41/4.67 % (3513747)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=3547887618:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2977 on theBenchmark for (2977ds/150Mi)
% 28.41/4.67 % (3513747)Instruction limit reached!
% 28.41/4.67 % (3513747)------------------------------
% 28.41/4.67 % (3513747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.41/4.67 % (3513747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.41/4.67 % (3513747)CaDiCaL version: 2.1.3
% 28.41/4.67 % (3513747)Termination reason: Instruction limit
% 28.41/4.67 % (3513747)Termination phase: Saturation
% 28.41/4.67 % (3513747)Time elapsed: 0.045 s
% 28.41/4.67 % (3513747)Peak memory usage: 92 MB
% 28.41/4.67 % (3513747)Instructions burned: 154 (million)
% 28.41/4.67 % (3513750)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=1805313307:i=14155:bd=all_2975 on theBenchmark for (2975ds/14155Mi)
% 28.41/4.67 % (3513750)First to succeed.
% 28.41/4.67 % (3513750)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3513689"
% 28.41/4.67 % (3513750)Refutation found. Thanks to Tanya!
% 28.41/4.67 % SZS status Theorem for theBenchmark
% 28.41/4.67 % SZS output start Proof for theBenchmark
% See solution above
% 28.94/4.76 % (3513750)------------------------------
% 28.94/4.76 % (3513750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.94/4.76 % (3513750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.94/4.76 % (3513750)CaDiCaL version: 2.1.3
% 28.94/4.76 % (3513750)Termination reason: Refutation
% 28.94/4.76 % (3513750)Time elapsed: 1.309 s
% 28.94/4.76 % (3513750)Peak memory usage: 167 MB
% 28.94/4.76 % (3513750)Instructions burned: 4373 (million)
% 28.94/4.76 % (3513750)------------------------------
% 28.94/4.76 % (3513750)------------------------------
% 28.94/4.76 % (3513689)Success in time 4.049 s
% 28.94/4.76 % Vampire exiting
%------------------------------------------------------------------------------