%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG115+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:35:34 PM UTC 2026
% Result : Theorem 6.00s 1.65s
% Output : Refutation 7.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 89 ( 17 unt; 8 def)
% Number of atoms : 364 ( 79 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 444 ( 169 ~; 167 |; 88 &)
% ( 17 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 157 ( 0 sgn 119 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aSet0(X1) )
=> ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f47,conjecture,
? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& xu = sdtpldt0(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& xu = sdtpldt0(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f83,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f82]) ).
fof(f104,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(f106,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f107,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(flattening,[],[f106]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xu ),
inference(ennf_transformation,[],[f48]) ).
fof(f110,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f111,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f112,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(definition_folding,[],[f83,f111,f110]) ).
fof(f114,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtpldt1(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtpldt1(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f115,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X0) )
& ( ? [X6,X7] :
( aElementOf0(X6,X1)
& aElementOf0(X7,X2)
& sdtpldt0(X6,X7) = X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( aElementOf0(X11,X1)
& aElementOf0(X12,X2)
& sdtpldt0(X11,X12) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != sK4(X0,X1,X2) )
| ~ aElementOf0(sK4(X0,X1,X2),X0) )
& ( ( aElementOf0(sK5(X0,X1,X2),X1)
& aElementOf0(sK6(X0,X1,X2),X2)
& sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)) )
| aElementOf0(sK4(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ( aElementOf0(sK7(X1,X2,X8),X1)
& aElementOf0(sK8(X1,X2,X8),X2)
& sdtpldt0(sK7(X1,X2,X8),sK8(X1,X2,X8)) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X7,sK6(X0,X1,X2)),skolemize(X11,sK7(X1,X2,X8)),skolemize(X12,sK8(X1,X2,X8))],[f118]) ).
fof(f142,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,[],[f104]) ).
fof(f143,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,[],[f142]) ).
fof(f144,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,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK19(X0,X1) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ( aElement0(sK20(X0,X1))
& sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1)) )
| aElementOf0(sK19(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK21(X0,X5))
& sdtasdt0(X0,sK21(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f144]) ).
fof(f175,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f177,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| sdtpldt0(sK7(X1,X2,X8),sK8(X1,X2,X8)) = X8 ),
inference(cnf_transformation,[],[f119]) ).
fof(f178,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| aElementOf0(sK8(X1,X2,X8),X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f179,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| aElementOf0(sK7(X1,X2,X8),X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f186,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f233,plain,
! [X0,X1] :
( aSet0(X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f238,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f239,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f242,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f252,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f107]) ).
fof(f254,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xu ),
inference(cnf_transformation,[],[f109]) ).
fof(f255,plain,
! [X0,X1] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f175]) ).
fof(f262,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f233]) ).
fof(f267,definition,
sF23 = slsdtgt0(xa),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f268,plain,
slsdtgt0(xa) = sF23,
inference(reorient_equations,[],[f267]) ).
fof(f269,definition,
sF24 = slsdtgt0(xb),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f270,plain,
slsdtgt0(xb) = sF24,
inference(reorient_equations,[],[f269]) ).
fof(f271,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != xu
| ~ aElementOf0(X1,sF24)
| ~ aElementOf0(X0,sF23) ),
inference(definition_folding,[],[f254,f270,f268]) ).
fof(f317,plain,
( aSet0(sF23)
| ~ aElement0(xa) ),
inference(superposition,[],[f262,f268]) ).
fof(f318,plain,
( aSet0(sF24)
| ~ aElement0(xb) ),
inference(superposition,[],[f262,f270]) ).
fof(f319,plain,
aSet0(sF24),
inference(forward_subsumption_resolution,[],[f318,f238]) ).
fof(f320,plain,
aSet0(sF23),
inference(forward_subsumption_resolution,[],[f317,f239]) ).
fof(f357,plain,
( sP0(xI,slsdtgt0(xa),slsdtgt0(xb))
| ~ sP1(slsdtgt0(xb),slsdtgt0(xa)) ),
inference(superposition,[],[f255,f242]) ).
fof(f360,definition,
( spl25_9
<=> sP1(sF24,sF23) ),
introduced(definition,[new_symbols(definition,[spl25_9])],[avatar_definition]) ).
fof(f362,plain,
( ~ sP1(sF24,sF23)
| spl25_9 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f364,definition,
( spl25_10
<=> sP0(xI,sF23,sF24) ),
introduced(definition,[new_symbols(definition,[spl25_10])],[avatar_definition]) ).
fof(f366,plain,
( sP0(xI,sF23,sF24)
| ~ spl25_10 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f368,plain,
( sP0(xI,slsdtgt0(xa),sF24)
| ~ sP1(slsdtgt0(xb),slsdtgt0(xa)) ),
inference(forward_demodulation,[],[f357,f270]) ).
fof(f369,plain,
( sP0(xI,sF23,sF24)
| ~ sP1(slsdtgt0(xb),slsdtgt0(xa)) ),
inference(forward_demodulation,[],[f368,f268]) ).
fof(f370,plain,
( ~ sP1(slsdtgt0(xb),sF23)
| sP0(xI,sF23,sF24) ),
inference(forward_demodulation,[],[f369,f268]) ).
fof(f371,plain,
( ~ sP1(sF24,sF23)
| sP0(xI,sF23,sF24) ),
inference(forward_demodulation,[],[f370,f270]) ).
fof(f372,plain,
( spl25_10
| ~ spl25_9 ),
inference(avatar_split_clause,[],[f371,f360,f364]) ).
fof(f373,plain,
( ~ aSet0(sF23)
| ~ aSet0(sF24)
| spl25_9 ),
inference(resolution,[],[f362,f186]) ).
fof(f374,plain,
( ~ aSet0(sF24)
| spl25_9 ),
inference(forward_subsumption_resolution,[],[f373,f320]) ).
fof(f375,plain,
( $false
| spl25_9 ),
inference(forward_subsumption_resolution,[],[f374,f319]) ).
fof(f376,plain,
spl25_9,
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f377,plain,
( ! [X0] :
( aElementOf0(sK8(sF23,sF24,X0),sF24)
| ~ aElementOf0(X0,xI) )
| ~ spl25_10 ),
inference(resolution,[],[f366,f178]) ).
fof(f378,plain,
( ! [X0] :
( aElementOf0(sK7(sF23,sF24,X0),sF23)
| ~ aElementOf0(X0,xI) )
| ~ spl25_10 ),
inference(resolution,[],[f366,f179]) ).
fof(f380,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sdtpldt0(sK7(sF23,sF24,X0),sK8(sF23,sF24,X0)) = X0 )
| ~ spl25_10 ),
inference(resolution,[],[f366,f177]) ).
fof(f407,plain,
( xu = sdtpldt0(sK7(sF23,sF24,xu),sK8(sF23,sF24,xu))
| ~ spl25_10 ),
inference(resolution,[],[f380,f252]) ).
fof(f436,plain,
( xu != xu
| ~ aElementOf0(sK8(sF23,sF24,xu),sF24)
| ~ aElementOf0(sK7(sF23,sF24,xu),sF23)
| ~ spl25_10 ),
inference(superposition,[],[f271,f407]) ).
fof(f437,plain,
( ~ aElementOf0(sK8(sF23,sF24,xu),sF24)
| ~ aElementOf0(sK7(sF23,sF24,xu),sF23)
| ~ spl25_10 ),
inference(trivial_inequality_removal,[],[f436]) ).
fof(f439,definition,
( spl25_16
<=> aElementOf0(sK7(sF23,sF24,xu),sF23) ),
introduced(definition,[new_symbols(definition,[spl25_16])],[avatar_definition]) ).
fof(f441,plain,
( ~ aElementOf0(sK7(sF23,sF24,xu),sF23)
| spl25_16 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f443,definition,
( spl25_17
<=> aElementOf0(sK8(sF23,sF24,xu),sF24) ),
introduced(definition,[new_symbols(definition,[spl25_17])],[avatar_definition]) ).
fof(f445,plain,
( ~ aElementOf0(sK8(sF23,sF24,xu),sF24)
| spl25_17 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f446,plain,
( ~ spl25_16
| ~ spl25_17
| ~ spl25_10 ),
inference(avatar_split_clause,[],[f437,f364,f443,f439]) ).
fof(f447,plain,
( ~ aElementOf0(xu,xI)
| ~ spl25_10
| spl25_16 ),
inference(resolution,[],[f441,f378]) ).
fof(f448,plain,
( $false
| ~ spl25_10
| spl25_16 ),
inference(forward_subsumption_resolution,[],[f447,f252]) ).
fof(f449,plain,
( ~ spl25_10
| spl25_16 ),
inference(avatar_contradiction_clause,[],[f448]) ).
fof(f452,plain,
( ~ aElementOf0(xu,xI)
| ~ spl25_10
| spl25_17 ),
inference(resolution,[],[f445,f377]) ).
fof(f453,plain,
( $false
| ~ spl25_10
| spl25_17 ),
inference(forward_subsumption_resolution,[],[f452,f252]) ).
fof(f454,plain,
( ~ spl25_10
| spl25_17 ),
inference(avatar_contradiction_clause,[],[f453]) ).
cnf(s8,plain,
( ~ spl25_9
| spl25_10 ),
inference(sat_conversion,[],[f372]) ).
cnf(s9,plain,
spl25_9,
inference(sat_conversion,[],[f376]) ).
cnf(s14,plain,
( ~ spl25_10
| ~ spl25_16
| ~ spl25_17 ),
inference(sat_conversion,[],[f446]) ).
cnf(s15,plain,
( ~ spl25_10
| spl25_16 ),
inference(sat_conversion,[],[f449]) ).
cnf(s16,plain,
( ~ spl25_10
| spl25_17 ),
inference(sat_conversion,[],[f454]) ).
cnf(s17,plain,
spl25_10,
inference(rat,[],[s8,s9]) ).
cnf(s18,plain,
spl25_17,
inference(rat,[],[s16,s17]) ).
cnf(s19,plain,
spl25_16,
inference(rat,[],[s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s14,s18,s19,s17]) ).
fof(f455,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG115+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n008.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 23:20:55 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.00/1.65 % (1719474)Detected formulas, will run a generic FOF schedule.
% 6.00/1.65 % (1719484)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1314896558:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.00/1.65 % (1719485)dis-21_1_sil=8000:lcm=predicate:random_seed=2732344303: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)
% 6.00/1.65 % (1719480)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=3978499012:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.00/1.65 % (1719479)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=933821737:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.00/1.65 % (1719481)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=4157862745:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.00/1.65 % (1719482)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1943321904:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.00/1.65 % (1719483)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1522304809:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.00/1.65 % (1719483)Instruction limit reached!
% 6.00/1.65 % (1719483)------------------------------
% 6.00/1.65 % (1719483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719483)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719483)Termination reason: Instruction limit
% 6.00/1.65 % (1719483)Termination phase: Saturation
% 6.00/1.65 % (1719483)Time elapsed: 0.070 s
% 6.00/1.65 % (1719483)Peak memory usage: 89 MB
% 6.00/1.65 % (1719483)Instructions burned: 121 (million)
% 6.00/1.65 % (1719482)Instruction limit reached!
% 6.00/1.65 % (1719482)------------------------------
% 6.00/1.65 % (1719482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719482)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719482)Termination reason: Instruction limit
% 6.00/1.65 % (1719482)Termination phase: Saturation
% 6.00/1.65 % (1719482)Time elapsed: 0.070 s
% 6.00/1.65 % (1719482)Peak memory usage: 90 MB
% 6.00/1.65 % (1719482)Instructions burned: 109 (million)
% 6.00/1.65 % (1719485)Instruction limit reached!
% 6.00/1.65 % (1719485)------------------------------
% 6.00/1.65 % (1719485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719485)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719485)Termination reason: Instruction limit
% 6.00/1.65 % (1719485)Termination phase: Saturation
% 6.00/1.65 % (1719485)Time elapsed: 0.071 s
% 6.00/1.65 % (1719485)Peak memory usage: 89 MB
% 6.00/1.65 % (1719485)Instructions burned: 130 (million)
% 6.00/1.65 % (1719484)Instruction limit reached!
% 6.00/1.65 % (1719484)------------------------------
% 6.00/1.65 % (1719484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719484)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719484)Termination reason: Instruction limit
% 6.00/1.65 % (1719484)Termination phase: Saturation
% 6.00/1.65 % (1719484)Time elapsed: 0.091 s
% 6.00/1.65 % (1719484)Peak memory usage: 90 MB
% 6.00/1.65 % (1719484)Instructions burned: 140 (million)
% 6.00/1.65 % (1719495)lrs+1011_1_sil=32000:sp=occurrence:random_seed=837654275:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.00/1.65 % (1719493)lrs+10_1_sil=8000:sp=occurrence:random_seed=3628441274:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.00/1.65 % (1719494)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4011252411:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.00/1.65 % (1719496)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=1939232969:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.00/1.65 % (1719494)Instruction limit reached!
% 6.00/1.65 % (1719494)------------------------------
% 6.00/1.65 % (1719494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719494)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719494)Termination reason: Instruction limit
% 6.00/1.65 % (1719494)Termination phase: Saturation
% 6.00/1.65 % (1719494)Time elapsed: 0.070 s
% 6.00/1.65 % (1719494)Peak memory usage: 90 MB
% 6.00/1.65 % (1719494)Instructions burned: 158 (million)
% 6.00/1.65 % (1719496)Instruction limit reached!
% 6.00/1.65 % (1719496)------------------------------
% 6.00/1.65 % (1719496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719496)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719496)Termination reason: Instruction limit
% 6.00/1.65 % (1719496)Termination phase: Saturation
% 6.00/1.65 % (1719496)Time elapsed: 0.088 s
% 6.00/1.65 % (1719496)Peak memory usage: 94 MB
% 6.00/1.65 % (1719496)Instructions burned: 249 (million)
% 6.00/1.65 % (1719493)Instruction limit reached!
% 6.00/1.65 % (1719493)------------------------------
% 6.00/1.65 % (1719493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719493)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719493)Termination reason: Instruction limit
% 6.00/1.65 % (1719493)Termination phase: Saturation
% 6.00/1.65 % (1719493)Time elapsed: 0.163 s
% 6.00/1.65 % (1719493)Peak memory usage: 93 MB
% 6.00/1.65 % (1719493)Instructions burned: 286 (million)
% 6.00/1.65 % (1719501)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3495171870:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.00/1.65 % (1719495)Instruction limit reached!
% 6.00/1.65 % (1719495)------------------------------
% 6.00/1.65 % (1719495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719495)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719495)Termination reason: Instruction limit
% 6.00/1.65 % (1719495)Termination phase: Saturation
% 6.00/1.65 % (1719495)Time elapsed: 0.195 s
% 6.00/1.65 % (1719495)Peak memory usage: 93 MB
% 6.00/1.65 % (1719495)Instructions burned: 326 (million)
% 6.00/1.65 % (1719502)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4244404636:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.00/1.65 % (1719503)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3019433842:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 6.00/1.65 % (1719505)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2362500131:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.00/1.65 % (1719501)Instruction limit reached!
% 6.00/1.65 % (1719501)------------------------------
% 6.00/1.65 % (1719501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719501)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719501)Termination reason: Instruction limit
% 6.00/1.65 % (1719501)Termination phase: Saturation
% 6.00/1.65 % (1719501)Time elapsed: 0.158 s
% 6.00/1.65 % (1719501)Peak memory usage: 90 MB
% 6.00/1.65 % (1719501)Instructions burned: 295 (million)
% 6.00/1.65 % (1719503)Instruction limit reached!
% 6.00/1.65 % (1719503)------------------------------
% 6.00/1.65 % (1719503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719503)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719503)Termination reason: Instruction limit
% 6.00/1.65 % (1719503)Termination phase: Saturation
% 6.00/1.65 % (1719503)Time elapsed: 0.077 s
% 6.00/1.65 % (1719503)Peak memory usage: 90 MB
% 6.00/1.65 % (1719503)Instructions burned: 114 (million)
% 6.00/1.65 % (1719505)Instruction limit reached!
% 6.00/1.65 % (1719505)------------------------------
% 6.00/1.65 % (1719505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719505)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719505)Termination reason: Instruction limit
% 6.00/1.65 % (1719505)Termination phase: Saturation
% 6.00/1.65 % (1719505)Time elapsed: 0.065 s
% 6.00/1.65 % (1719505)Peak memory usage: 89 MB
% 6.00/1.65 % (1719505)Instructions burned: 127 (million)
% 6.00/1.65 % (1719479)First to succeed.
% 6.00/1.65 % (1719479)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1719474"
% 6.00/1.65 % (1719509)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3427925714:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.00/1.65 % (1719510)lrs+10_1_sil=8000:sp=occurrence:random_seed=752899144:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.00/1.65 % (1719511)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=775154415:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.00/1.65 % (1719509)Instruction limit reached!
% 6.00/1.65 % (1719509)------------------------------
% 6.00/1.65 % (1719509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.65 % (1719509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.65 % (1719509)CaDiCaL version: 2.1.3
% 6.00/1.65 % (1719509)Termination reason: Instruction limit
% 6.00/1.65 % (1719509)Termination phase: Saturation
% 6.00/1.65 % (1719509)Time elapsed: 0.067 s
% 6.00/1.65 % (1719509)Peak memory usage: 89 MB
% 6.00/1.65 % (1719509)Instructions burned: 115 (million)
% 6.00/1.65 % (1719481)Also succeeded, but the first one will report.
% 6.00/1.65 % (1719502)Also succeeded, but the first one will report.
% 6.00/1.65 % (1719511)Also succeeded, but the first one will report.
% 6.00/1.65 % (1719515)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1596053205:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.00/1.65 % (1719479)Refutation found. Thanks to Tanya!
% 6.00/1.65 % SZS status Theorem for theBenchmark
% 6.00/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 7.74/1.84 % (1719479)------------------------------
% 7.74/1.84 % (1719479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.84 % (1719479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.84 % (1719479)CaDiCaL version: 2.1.3
% 7.74/1.84 % (1719479)Termination reason: Refutation
% 7.74/1.84 % (1719479)Time elapsed: 0.643 s
% 7.74/1.84 % (1719479)Peak memory usage: 130 MB
% 7.74/1.84 % (1719479)Instructions burned: 972 (million)
% 7.74/1.84 % (1719479)------------------------------
% 7.74/1.84 % (1719479)------------------------------
% 7.74/1.84 % (1719474)Success in time 1.046 s
% 7.74/1.84 % Vampire exiting
%------------------------------------------------------------------------------