%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM541+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:24:44 PM UTC 2026
% Result : Theorem 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 121 ( 9 unt; 7 def)
% Number of atoms : 459 ( 35 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 566 ( 228 ~; 241 |; 70 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 75 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f32,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccLess) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
fof(f34,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTrans) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
fof(f53,axiom,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1936) ).
fof(f54,conjecture,
( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
=> ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) )
& ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn )
=> ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f55,negated_conjecture,
~ ( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
=> ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) )
& ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn )
=> ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f92,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f100,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f101,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f103,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f107,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f109,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f108]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f129,plain,
( ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& ~ aElementOf0(xm,slbdtrb0(xn))
& xm != xn
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
| ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn ) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f130,plain,
( ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& ~ aElementOf0(xm,slbdtrb0(xn))
& xm != xn
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
| ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn ) ) ),
inference(flattening,[],[f129]) ).
fof(f137,definition,
( ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& ~ aElementOf0(xm,slbdtrb0(xn))
& xm != xn
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f138,plain,
( sP4
| ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn ) ) ),
inference(definition_folding,[],[f130,f137]) ).
fof(f160,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
& ( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f127]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f172]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f173]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ( ( ~ aElementOf0(sK13(X0,X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK13(X0,X1)),X0)
| ~ aElementOf0(sK13(X0,X1),X1) )
& ( ( aElementOf0(sK13(X0,X1),szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(sK13(X0,X1)),X0) )
| aElementOf0(sK13(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f174]) ).
fof(f176,plain,
( ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& ~ aElementOf0(xm,slbdtrb0(xn))
& xm != xn
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
| ~ sP4 ),
inference(nnf_transformation,[],[f137]) ).
fof(f226,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f233,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f234,plain,
! [X0,X1] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f235,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f236,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f237,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f238,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f239,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f261,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f268,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f53]) ).
fof(f269,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f53]) ).
fof(f271,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sP4 ),
inference(cnf_transformation,[],[f176]) ).
fof(f272,plain,
( xm != xn
| ~ sP4 ),
inference(cnf_transformation,[],[f176]) ).
fof(f274,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sP4 ),
inference(cnf_transformation,[],[f176]) ).
fof(f276,plain,
( sP4
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn ),
inference(cnf_transformation,[],[f138]) ).
fof(f277,plain,
( sP4
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
inference(cnf_transformation,[],[f138]) ).
fof(f278,plain,
( sP4
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f292,plain,
! [X3,X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f261]) ).
fof(f296,definition,
( spl14_1
<=> xm = xn ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f297,plain,
( xm != xn
| spl14_1 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( xm = xn
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f304,definition,
( spl14_3
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f309,definition,
( spl14_4
<=> sdtlseqdt0(szszuzczcdt0(xm),xn) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f310,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| spl14_4 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f311,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,plain,
( spl14_1
| spl14_4
| spl14_3 ),
inference(avatar_split_clause,[],[f276,f304,f309,f296]) ).
fof(f314,definition,
( spl14_5
<=> aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f316,plain,
( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| spl14_5 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f317,plain,
( ~ spl14_5
| spl14_3 ),
inference(avatar_split_clause,[],[f277,f304,f314]) ).
fof(f319,definition,
( spl14_6
<=> sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f320,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f321,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| spl14_6 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f322,plain,
( ~ spl14_6
| spl14_3 ),
inference(avatar_split_clause,[],[f278,f304,f319]) ).
fof(f324,plain,
( ~ spl14_3
| spl14_6 ),
inference(avatar_split_clause,[],[f271,f319,f304]) ).
fof(f325,plain,
( ~ spl14_3
| ~ spl14_1 ),
inference(avatar_split_clause,[],[f272,f296,f304]) ).
fof(f327,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f274,f309,f304]) ).
fof(f780,plain,
( sdtlseqdt0(xn,xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| spl14_4 ),
inference(resolution,[],[f310,f239]) ).
fof(f781,plain,
( sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| spl14_4 ),
inference(forward_subsumption_resolution,[],[f780,f268]) ).
fof(f782,plain,
( sdtlseqdt0(xn,xm)
| spl14_4 ),
inference(forward_subsumption_resolution,[],[f781,f269]) ).
fof(f846,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl14_6 ),
inference(resolution,[],[f234,f320]) ).
fof(f853,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f846,f269]) ).
fof(f854,plain,
( sdtlseqdt0(xm,xn)
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f853,f268]) ).
fof(f930,plain,
( ~ sdtlseqdt0(xn,xm)
| xm = xn
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ spl14_6 ),
inference(resolution,[],[f237,f854]) ).
fof(f941,plain,
( xm = xn
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| spl14_4
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f930,f782]) ).
fof(f953,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| spl14_1
| spl14_4
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f941,f297]) ).
fof(f956,definition,
( spl14_45
<=> aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl14_45])],[avatar_definition]) ).
fof(f957,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ spl14_45 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f958,plain,
( ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| spl14_45 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f991,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl14_1
| spl14_4
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f953,f268]) ).
fof(f1001,plain,
( $false
| spl14_1
| spl14_4
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f991,f269]) ).
fof(f1002,plain,
( spl14_1
| spl14_4
| ~ spl14_6 ),
inference(avatar_contradiction_clause,[],[f1001]) ).
fof(f1026,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl14_45 ),
inference(resolution,[],[f958,f226]) ).
fof(f1029,plain,
( $false
| spl14_45 ),
inference(forward_subsumption_resolution,[],[f1026,f269]) ).
fof(f1030,plain,
spl14_45,
inference(avatar_contradiction_clause,[],[f1029]) ).
fof(f1032,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| spl14_6 ),
inference(resolution,[],[f321,f233]) ).
fof(f1035,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| spl14_6 ),
inference(forward_subsumption_resolution,[],[f1032,f269]) ).
fof(f1037,plain,
( ~ sdtlseqdt0(xm,xn)
| spl14_6 ),
inference(forward_subsumption_resolution,[],[f1035,f268]) ).
fof(f1061,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xm))
| ~ spl14_45 ),
inference(resolution,[],[f957,f236]) ).
fof(f1259,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,szszuzczcdt0(xm))
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl14_4 ),
inference(resolution,[],[f238,f311]) ).
fof(f1272,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,szszuzczcdt0(xm))
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl14_4
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1259,f957]) ).
fof(f1284,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,szszuzczcdt0(xm))
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl14_4
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1272,f268]) ).
fof(f1329,plain,
( ~ aElementOf0(xm,szNzAzT0)
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ spl14_45 ),
inference(resolution,[],[f1061,f292]) ).
fof(f1335,plain,
( ~ aElementOf0(xm,szNzAzT0)
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xm)))
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1329,f226]) ).
fof(f1336,plain,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xm)))
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1335,f269]) ).
fof(f1739,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ spl14_4
| ~ spl14_45 ),
inference(resolution,[],[f1284,f235]) ).
fof(f1747,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ spl14_4
| ~ spl14_45 ),
inference(duplicate_literal_removal,[],[f1739]) ).
fof(f1751,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ spl14_4
| spl14_6
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1747,f1037]) ).
fof(f1754,plain,
( $false
| ~ spl14_4
| spl14_6
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1751,f269]) ).
fof(f1755,plain,
( ~ spl14_4
| spl14_6
| ~ spl14_45 ),
inference(avatar_contradiction_clause,[],[f1754]) ).
fof(f1757,plain,
( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xm)))
| ~ spl14_1
| spl14_5 ),
inference(superposition,[],[f316,f298]) ).
fof(f1789,plain,
( $false
| ~ spl14_1
| spl14_5
| ~ spl14_45 ),
inference(forward_subsumption_resolution,[],[f1757,f1336]) ).
fof(f1790,plain,
( ~ spl14_1
| spl14_5
| ~ spl14_45 ),
inference(avatar_contradiction_clause,[],[f1789]) ).
cnf(s2,plain,
( spl14_1
| spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f312]) ).
cnf(s3,plain,
( spl14_3
| ~ spl14_5 ),
inference(sat_conversion,[],[f317]) ).
cnf(s4,plain,
( spl14_3
| ~ spl14_6 ),
inference(sat_conversion,[],[f322]) ).
cnf(s6,plain,
( ~ spl14_3
| spl14_6 ),
inference(sat_conversion,[],[f324]) ).
cnf(s7,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(sat_conversion,[],[f325]) ).
cnf(s9,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f327]) ).
cnf(s58,plain,
( spl14_1
| spl14_4
| ~ spl14_6 ),
inference(sat_conversion,[],[f1002]) ).
cnf(s62,plain,
spl14_45,
inference(sat_conversion,[],[f1030]) ).
cnf(s109,plain,
( ~ spl14_4
| spl14_6
| ~ spl14_45 ),
inference(sat_conversion,[],[f1755]) ).
cnf(s113,plain,
( ~ spl14_1
| spl14_5
| ~ spl14_45 ),
inference(sat_conversion,[],[f1790]) ).
cnf(s158,plain,
( ~ spl14_3
| spl14_1 ),
inference(rat,[],[s58,s6,s9]) ).
cnf(s159,plain,
spl14_1,
inference(rat,[],[s109,s2,s4,s158,s62]) ).
cnf(s160,plain,
spl14_5,
inference(rat,[],[s113,s62,s159]) ).
cnf(s162,plain,
~ spl14_3,
inference(rat,[],[s7,s159]) ).
cnf(s164,plain,
$false,
inference(rat,[],[s3,s160,s162]) ).
fof(f1791,plain,
$false,
inference(avatar_sat_refutation,[],[s164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM541+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:24:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.49 % (525714)Will run a generic schedule for satisfiability detection.
% 0.15/0.49 % (525719)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2201297245_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.49 % (525720)% WARNING: option uhcvi not known.
% 0.15/0.49 % TRYING [1]
% 0.15/0.49 % TRYING [2]
% 0.15/0.49 % TRYING [3]
% 0.15/0.49 % (525720)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3935607144:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.49 % (525721)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=181880401:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.49 % (525722)dis+10_1_sil=32000:sp=arity:random_seed=2947953586:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.49 % (525723)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=306628715:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.49 % (525725)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=959571838:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.49 % (525724)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=328462864:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.49 % TRYING [4]
% 0.15/0.49 % TRYING [5]
% 0.15/0.49 % (525722) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-525714-525722"...
% 0.15/0.49 % (525724) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-525714-525724"...
% 0.15/0.49 % (525722)...printing done.
% 0.15/0.49 % TRYING [6]
% 0.15/0.49 % (525724)...printing done.
% 0.15/0.49 % (525722)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Theorem for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (525722)------------------------------
% 0.15/0.49 % (525722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (525722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (525722)CaDiCaL version: 2.1.3
% 0.15/0.49 % (525722)Termination reason: Refutation
% 0.15/0.49 % (525722)Time elapsed: 0.033 s
% 0.15/0.49 % (525722)Peak memory usage: 13 MB
% 0.15/0.49 % (525722)Instructions burned: 46 (million)
% 0.15/0.49 % (525714)Success in time 0.073 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------