%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG095+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 : n020.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 12:35:29 PM UTC 2026
% Result : Theorem 2.64s 1.24s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 15 unt; 7 def)
% Number of atoms : 384 ( 35 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 497 ( 197 ~; 194 |; 82 &)
% ( 16 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 192 ( 0 sgn 156 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f28,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(f29,axiom,
! [X0] :
( aElement0(X0)
=> aElementOf0(X0,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).
fof(f31,conjecture,
? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f32,negated_conjecture,
~ ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sz10 ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f35,plain,
! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sz10 != sdtpldt0(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f37,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f49,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(f50,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(f51,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(definition_folding,[],[f41,f50,f49]) ).
fof(f52,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f53,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
& aElementOf0(sK3(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
& aElement0(sK4(X0)) ) )
& aElementOf0(sK2(X0),X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0)),skolemize(X3,sK4(X0))],[f54]) ).
fof(f56,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,[],[f50]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f49]) ).
fof(f59,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,[],[f58]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != sK5(X0,X1,X2) )
| ~ aElementOf0(sK5(X0,X1,X2),X0) )
& ( ( aElementOf0(sK6(X0,X1,X2),X1)
& aElementOf0(sK7(X0,X1,X2),X2)
& sK5(X0,X1,X2) = sdtpldt0(sK6(X0,X1,X2),sK7(X0,X1,X2)) )
| aElementOf0(sK5(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ( aElementOf0(sK8(X1,X2,X8),X1)
& aElementOf0(sK9(X1,X2,X8),X2)
& sdtpldt0(sK8(X1,X2,X8),sK9(X1,X2,X8)) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X3,sK5(X0,X1,X2)),skolemize(X6,sK6(X0,X1,X2)),skolemize(X7,sK7(X0,X1,X2)),skolemize(X11,sK8(X1,X2,X8)),skolemize(X12,sK9(X1,X2,X8))],[f60]) ).
fof(f62,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f63,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f28]) ).
fof(f64,plain,
! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sz10 != sdtpldt0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f70,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f77,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f78,plain,
! [X2,X0,X1] :
( sdtpldt1(X1,X0) = X2
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f79,plain,
! [X2,X0,X1,X8] :
( sdtpldt0(sK8(X1,X2,X8),sK9(X1,X2,X8)) = X8
| ~ aElementOf0(X8,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f80,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK9(X1,X2,X8),X2)
| ~ aElementOf0(X8,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f81,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK8(X1,X2,X8),X1)
| ~ aElementOf0(X8,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f96,definition,
~ sP10(sz10),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f97,plain,
! [X0,X1] :
( sP10(sdtpldt0(X0,X1))
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(inequality_splitting,[],[f67,f96]) ).
fof(f100,plain,
! [X0,X1] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f77]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(sK9(X1,X2,X0),xJ)
| sP10(X0)
| ~ aElementOf0(sK8(X1,X2,X0),xI)
| ~ aElementOf0(X0,X3)
| ~ sP0(X3,X1,X2) ),
inference(superposition,[],[f97,f79]) ).
fof(f118,plain,
aSet0(xJ),
inference(resolution,[],[f62,f70]) ).
fof(f119,plain,
aSet0(xI),
inference(resolution,[],[f63,f70]) ).
fof(f123,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ sP0(X0,xI,xJ)
| ~ sP1(xJ,xI) ),
inference(superposition,[],[f64,f78]) ).
fof(f125,definition,
( spl13_1
<=> sP1(xJ,xI) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f126,plain,
( sP1(xJ,xI)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( ~ sP1(xJ,xI)
| spl13_1 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f129,definition,
( spl13_2
<=> ! [X0,X1] :
( aElementOf0(X1,X0)
| ~ sP0(X0,xI,xJ)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f130,plain,
( ! [X0,X1] :
( ~ sP0(X0,xI,xJ)
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f123,f129,f125]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(sK8(X1,xJ,X0),xI)
| sP10(X0)
| ~ aElementOf0(X0,X2)
| ~ sP0(X2,X1,xJ)
| ~ aElementOf0(X0,X3)
| ~ sP0(X3,X1,xJ) ),
inference(resolution,[],[f108,f80]) ).
fof(f220,plain,
( ~ aSet0(xI)
| ~ aSet0(xJ)
| spl13_1 ),
inference(resolution,[],[f127,f88]) ).
fof(f221,plain,
( ~ aSet0(xJ)
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f220,f119]) ).
fof(f222,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f221,f118]) ).
fof(f223,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f291,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X3,xI,xJ)
| ~ aElementOf0(X0,X1)
| ~ sP0(X1,xI,xJ)
| ~ aElementOf0(X0,X2)
| ~ sP0(X2,xI,xJ)
| ~ aElementOf0(X0,X3)
| sP10(X0) ),
inference(resolution,[],[f181,f81]) ).
fof(f599,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| ~ sP0(X1,xI,xJ)
| ~ aElementOf0(X0,X2)
| ~ sP0(X2,xI,xJ)
| ~ aElementOf0(X0,sdtpldt1(xI,xJ))
| sP10(X0)
| ~ sP1(xJ,xI) ),
inference(resolution,[],[f291,f100]) ).
fof(f600,plain,
( ! [X2,X0,X1] :
( ~ aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ sP0(X1,xI,xJ)
| ~ aElementOf0(X0,X2)
| ~ sP0(X2,xI,xJ)
| ~ aElementOf0(X0,X1)
| sP10(X0) )
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f599,f126]) ).
fof(f679,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,xI,xJ)
| ~ aElementOf0(X1,X2)
| ~ sP0(X2,xI,xJ)
| ~ aElementOf0(X1,X0)
| sP10(X1)
| ~ aElement0(X1) )
| ~ spl13_1 ),
inference(resolution,[],[f600,f64]) ).
fof(f703,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,xI,xJ)
| ~ aElementOf0(X1,X2)
| ~ sP0(X2,xI,xJ)
| sP10(X1)
| ~ aElement0(X1) )
| ~ spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f679,f130]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,xI,xJ)
| ~ sP0(X2,xI,xJ)
| sP10(X1)
| ~ aElement0(X1) )
| ~ spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f703,f130]) ).
fof(f734,definition,
( spl13_21
<=> ! [X1] :
( sP10(X1)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
fof(f735,plain,
( ! [X1] :
( ~ aElement0(X1)
| sP10(X1) )
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f737,definition,
( spl13_22
<=> ! [X2] : ~ sP0(X2,xI,xJ) ),
introduced(definition,[new_symbols(definition,[spl13_22])],[avatar_definition]) ).
fof(f738,plain,
( ! [X2] : ~ sP0(X2,xI,xJ)
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f739,plain,
( spl13_21
| spl13_22
| spl13_22
| ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f732,f129,f125,f737,f737,f734]) ).
fof(f743,plain,
( sP10(sz10)
| ~ spl13_21 ),
inference(resolution,[],[f735,f92]) ).
fof(f747,plain,
( $false
| ~ spl13_21 ),
inference(forward_subsumption_resolution,[],[f743,f96]) ).
fof(f748,plain,
~ spl13_21,
inference(avatar_contradiction_clause,[],[f747]) ).
fof(f750,plain,
( ~ sP1(xJ,xI)
| ~ spl13_22 ),
inference(resolution,[],[f738,f100]) ).
fof(f751,plain,
( $false
| ~ spl13_1
| ~ spl13_22 ),
inference(forward_subsumption_resolution,[],[f750,f126]) ).
fof(f752,plain,
( ~ spl13_1
| ~ spl13_22 ),
inference(avatar_contradiction_clause,[],[f751]) ).
cnf(s1,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f131]) ).
cnf(s5,plain,
spl13_1,
inference(sat_conversion,[],[f223]) ).
cnf(s16,plain,
( spl13_22
| ~ spl13_2
| spl13_21
| ~ spl13_1
| spl13_22 ),
inference(sat_conversion,[],[f739]) ).
cnf(s17,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_21
| spl13_22 ),
inference(rat,[],[s16]) ).
cnf(s18,plain,
~ spl13_21,
inference(sat_conversion,[],[f748]) ).
cnf(s19,plain,
( ~ spl13_1
| ~ spl13_22 ),
inference(sat_conversion,[],[f752]) ).
cnf(s20,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_22 ),
inference(rat,[],[s17,s18]) ).
cnf(s21,plain,
~ spl13_22,
inference(rat,[],[s19,s5]) ).
cnf(s22,plain,
~ spl13_2,
inference(rat,[],[s20,s21,s5]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s1,s22,s5]) ).
fof(f753,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG095+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 23:15:05 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 2.64/1.24 % (3876290)Detected formulas, will run a generic FOF schedule.
% 2.64/1.24 % (3876296)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=4081760519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.24 % (3876300)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3585469716:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.24 % (3876301)dis-21_1_sil=8000:lcm=predicate:random_seed=1286413059:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.64/1.24 % (3876299)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1735863405:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.24 % (3876297)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=91807638:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.24 % (3876298)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=948682036:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.24 % (3876295)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=3736341495:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.24 % (3876298)First to succeed.
% 2.64/1.24 % (3876298)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3876290"
% 2.64/1.24 % (3876299)Instruction limit reached!
% 2.64/1.24 % (3876299)------------------------------
% 2.64/1.24 % (3876299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (3876299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (3876299)CaDiCaL version: 2.1.3
% 2.64/1.24 % (3876299)Termination reason: Instruction limit
% 2.64/1.24 % (3876299)Termination phase: Saturation
% 2.64/1.24 % (3876299)Time elapsed: 0.070 s
% 2.64/1.24 % (3876299)Peak memory usage: 89 MB
% 2.64/1.24 % (3876299)Instructions burned: 119 (million)
% 2.64/1.24 % (3876301)Instruction limit reached!
% 2.64/1.24 % (3876301)------------------------------
% 2.64/1.24 % (3876301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (3876301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (3876301)CaDiCaL version: 2.1.3
% 2.64/1.24 % (3876301)Termination reason: Instruction limit
% 2.64/1.24 % (3876301)Termination phase: Saturation
% 2.64/1.24 % (3876301)Time elapsed: 0.076 s
% 2.64/1.24 % (3876301)Peak memory usage: 89 MB
% 2.64/1.24 % (3876301)Instructions burned: 130 (million)
% 2.64/1.24 % (3876300)Instruction limit reached!
% 2.64/1.24 % (3876300)------------------------------
% 2.64/1.24 % (3876300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (3876300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (3876300)CaDiCaL version: 2.1.3
% 2.64/1.24 % (3876300)Termination reason: Instruction limit
% 2.64/1.24 % (3876300)Termination phase: Saturation
% 2.64/1.24 % (3876300)Time elapsed: 0.103 s
% 2.64/1.24 % (3876300)Peak memory usage: 90 MB
% 2.64/1.24 % (3876300)Instructions burned: 172 (million)
% 2.64/1.24 % (3876309)lrs+10_1_sil=8000:sp=occurrence:random_seed=4140213251:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.64/1.24 % (3876310)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2436030862:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.64/1.24 % (3876311)lrs+1011_1_sil=32000:sp=occurrence:random_seed=684481086:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.64/1.24 % (3876298)Refutation found. Thanks to Tanya!
% 2.64/1.24 % SZS status Theorem for theBenchmark
% 2.64/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.43 % (3876298)------------------------------
% 3.53/1.43 % (3876298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.43 % (3876298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.43 % (3876298)CaDiCaL version: 2.1.3
% 3.53/1.43 % (3876298)Termination reason: Refutation
% 3.53/1.43 % (3876298)Time elapsed: 0.023 s
% 3.53/1.43 % (3876298)Peak memory usage: 90 MB
% 3.53/1.43 % (3876298)Instructions burned: 33 (million)
% 3.53/1.43 % (3876298)------------------------------
% 3.53/1.43 % (3876298)------------------------------
% 3.53/1.43 % (3876290)Success in time 0.42 s
% 3.53/1.43 % Vampire exiting
%------------------------------------------------------------------------------