%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM541+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 5.53s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 146 ( 15 unt; 9 def)
% Number of atoms : 530 ( 31 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 679 ( 295 ~; 312 |; 43 &)
% ( 18 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 83 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
fof(f34,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f53,axiom,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1936) ).
fof(f54,conjecture,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
<=> ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f55,negated_conjecture,
~ ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
<=> ( aElementOf0(xm,slbdtrb0(xn))
| xm = 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,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
<~> ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f157,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(f169,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(f170,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,[],[f169]) ).
fof(f171,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,[],[f170]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ( ( ~ aElementOf0(sK12(X0,X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
| ~ aElementOf0(sK12(X0,X1),X1) )
& ( ( aElementOf0(sK12(X0,X1),szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0) )
| aElementOf0(sK12(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,[sK12]),skolemize(X2,sK12(X0,X1))],[f171]) ).
fof(f173,plain,
( ( ( ~ aElementOf0(xm,slbdtrb0(xn))
& xm != xn )
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ),
inference(nnf_transformation,[],[f129]) ).
fof(f174,plain,
( ( ( ~ aElementOf0(xm,slbdtrb0(xn))
& xm != xn )
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ),
inference(flattening,[],[f173]) ).
fof(f224,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f231,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f232,plain,
! [X0,X1] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f233,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f234,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f235,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f236,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(f237,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f257,plain,
! [X3,X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f259,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f266,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f53]) ).
fof(f267,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f53]) ).
fof(f268,plain,
( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
inference(cnf_transformation,[],[f174]) ).
fof(f269,plain,
( xm != xn
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
inference(cnf_transformation,[],[f174]) ).
fof(f270,plain,
( ~ aElementOf0(xm,slbdtrb0(xn))
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
inference(cnf_transformation,[],[f174]) ).
fof(f284,plain,
! [X3,X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f259]) ).
fof(f286,plain,
! [X3,X0] :
( ~ aElementOf0(X3,slbdtrb0(X0))
| sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f257]) ).
fof(f288,definition,
( spl13_1
<=> aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f290,plain,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f292,definition,
( spl13_2
<=> xm = xn ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f293,plain,
( xm != xn
| spl13_2 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( xm = xn
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,definition,
( spl13_3
<=> aElementOf0(xm,slbdtrb0(xn)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f297,plain,
( ~ aElementOf0(xm,slbdtrb0(xn))
| spl13_3 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( aElementOf0(xm,slbdtrb0(xn))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f299,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f268,f296,f292,f288]) ).
fof(f300,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f269,f292,f288]) ).
fof(f301,plain,
( ~ spl13_1
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f270,f296,f288]) ).
fof(f1012,definition,
( spl13_47
<=> aElementOf0(xn,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_47])],[avatar_definition]) ).
fof(f1013,plain,
( aElementOf0(xn,szNzAzT0)
| ~ spl13_47 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1042,plain,
spl13_47,
inference(avatar_split_clause,[],[f266,f1012]) ).
fof(f1044,definition,
( spl13_53
<=> aElementOf0(xm,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_53])],[avatar_definition]) ).
fof(f1045,plain,
( aElementOf0(xm,szNzAzT0)
| ~ spl13_53 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f1055,definition,
( spl13_54
<=> sdtlseqdt0(szszuzczcdt0(xm),xn) ),
introduced(definition,[new_symbols(definition,[spl13_54])],[avatar_definition]) ).
fof(f1056,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| spl13_54 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1057,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ spl13_54 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1100,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ spl13_1 ),
inference(resolution,[],[f290,f286]) ).
fof(f1117,definition,
( spl13_62
<=> aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_62])],[avatar_definition]) ).
fof(f1118,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ spl13_62 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f1119,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl13_62 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f1122,definition,
( spl13_63
<=> sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
introduced(definition,[new_symbols(definition,[spl13_63])],[avatar_definition]) ).
fof(f1123,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| spl13_63 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1124,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ spl13_63 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1125,plain,
( ~ spl13_62
| spl13_63
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f1100,f288,f1122,f1117]) ).
fof(f1126,plain,
spl13_53,
inference(avatar_split_clause,[],[f267,f1044]) ).
fof(f1181,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,szszuzczcdt0(X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(resolution,[],[f236,f233]) ).
fof(f1193,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,szszuzczcdt0(X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(duplicate_literal_removal,[],[f1181]) ).
fof(f1202,plain,
! [X0,X1] :
( sdtlseqdt0(X0,szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1193,f224]) ).
fof(f1320,plain,
( sdtlseqdt0(xm,xm)
| ~ spl13_53 ),
inference(resolution,[],[f1045,f234]) ).
fof(f1458,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl13_62 ),
inference(resolution,[],[f1119,f224]) ).
fof(f1462,plain,
( $false
| ~ spl13_47
| spl13_62 ),
inference(forward_subsumption_resolution,[],[f1458,f1013]) ).
fof(f1463,plain,
( ~ spl13_47
| spl13_62 ),
inference(avatar_contradiction_clause,[],[f1462]) ).
fof(f1551,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_63 ),
inference(resolution,[],[f1124,f232]) ).
fof(f1552,plain,
( ~ aElementOf0(xm,szNzAzT0)
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ spl13_63 ),
inference(resolution,[],[f1124,f284]) ).
fof(f1557,plain,
( sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_53
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1551,f1045]) ).
fof(f1559,definition,
( spl13_72
<=> aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_72])],[avatar_definition]) ).
fof(f1560,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ spl13_72 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1561,plain,
( ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| spl13_72 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1575,plain,
( sdtlseqdt0(xm,xn)
| ~ spl13_47
| ~ spl13_53
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1557,f1013]) ).
fof(f1577,plain,
( ~ sdtlseqdt0(xn,xm)
| xm = xn
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ spl13_47
| ~ spl13_53
| ~ spl13_63 ),
inference(resolution,[],[f1575,f235]) ).
fof(f1578,plain,
( ~ sdtlseqdt0(xn,xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| spl13_2
| ~ spl13_47
| ~ spl13_53
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1577,f293]) ).
fof(f1580,plain,
( ~ sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| spl13_2
| ~ spl13_47
| ~ spl13_53
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1578,f1013]) ).
fof(f1582,plain,
( ~ sdtlseqdt0(xn,xm)
| spl13_2
| ~ spl13_47
| ~ spl13_53
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1580,f1045]) ).
fof(f1924,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl13_72 ),
inference(resolution,[],[f1561,f224]) ).
fof(f1928,plain,
( $false
| ~ spl13_53
| spl13_72 ),
inference(forward_subsumption_resolution,[],[f1924,f1045]) ).
fof(f1929,plain,
( ~ spl13_53
| spl13_72 ),
inference(avatar_contradiction_clause,[],[f1928]) ).
fof(f2996,plain,
( ~ aElementOf0(xm,szNzAzT0)
| aElementOf0(xm,slbdtrb0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_54 ),
inference(resolution,[],[f1057,f284]) ).
fof(f3001,plain,
( aElementOf0(xm,slbdtrb0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_53
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f2996,f1045]) ).
fof(f3004,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl13_3
| ~ spl13_53
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f3001,f297]) ).
fof(f3014,plain,
( $false
| spl13_3
| ~ spl13_47
| ~ spl13_53
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f3004,f1013]) ).
fof(f3015,plain,
( spl13_3
| ~ spl13_47
| ~ spl13_53
| ~ spl13_54 ),
inference(avatar_contradiction_clause,[],[f3014]) ).
fof(f3018,plain,
( sdtlseqdt0(xn,xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| spl13_54 ),
inference(resolution,[],[f1056,f237]) ).
fof(f3019,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_54
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f3018,f1582]) ).
fof(f3020,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_54
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f3019,f1013]) ).
fof(f3021,plain,
( $false
| spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_54
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f3020,f1045]) ).
fof(f3022,plain,
( spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_54
| ~ spl13_63 ),
inference(avatar_contradiction_clause,[],[f3021]) ).
fof(f3024,plain,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ spl13_53
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1552,f1045]) ).
fof(f3026,plain,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ spl13_53
| ~ spl13_62
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f3024,f1118]) ).
fof(f3028,plain,
( spl13_1
| ~ spl13_53
| ~ spl13_62
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f3026,f1122,f1117,f1044,f288]) ).
fof(f3029,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_3 ),
inference(resolution,[],[f298,f286]) ).
fof(f3036,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ spl13_3
| ~ spl13_47 ),
inference(forward_subsumption_resolution,[],[f3029,f1013]) ).
fof(f3038,plain,
( spl13_54
| ~ spl13_3
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f3036,f1012,f296,f1055]) ).
fof(f3054,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_63 ),
inference(resolution,[],[f1123,f231]) ).
fof(f3057,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_53
| spl13_63 ),
inference(forward_subsumption_resolution,[],[f3054,f1045]) ).
fof(f3059,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ spl13_47
| ~ spl13_53
| spl13_63 ),
inference(forward_subsumption_resolution,[],[f3057,f1013]) ).
fof(f3424,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_63 ),
inference(resolution,[],[f1202,f1123]) ).
fof(f3468,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_63
| ~ spl13_72 ),
inference(forward_subsumption_resolution,[],[f3424,f1560]) ).
fof(f3470,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ spl13_47
| spl13_63
| ~ spl13_72 ),
inference(forward_subsumption_resolution,[],[f3468,f1013]) ).
fof(f3471,plain,
( ~ spl13_54
| ~ spl13_47
| spl13_63
| ~ spl13_72 ),
inference(avatar_split_clause,[],[f3470,f1559,f1122,f1012,f1055]) ).
fof(f3511,plain,
( ~ sdtlseqdt0(xm,xm)
| ~ spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_63 ),
inference(superposition,[],[f3059,f294]) ).
fof(f3516,plain,
( $false
| ~ spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_63 ),
inference(forward_subsumption_resolution,[],[f3511,f1320]) ).
fof(f3517,plain,
( ~ spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_63 ),
inference(avatar_contradiction_clause,[],[f3516]) ).
cnf(s1,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f299]) ).
cnf(s2,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f300]) ).
cnf(s3,plain,
( ~ spl13_1
| ~ spl13_3 ),
inference(sat_conversion,[],[f301]) ).
cnf(s50,plain,
spl13_47,
inference(sat_conversion,[],[f1042]) ).
cnf(s64,plain,
( ~ spl13_1
| ~ spl13_62
| spl13_63 ),
inference(sat_conversion,[],[f1125]) ).
cnf(s65,plain,
spl13_53,
inference(sat_conversion,[],[f1126]) ).
cnf(s75,plain,
( ~ spl13_47
| spl13_62 ),
inference(sat_conversion,[],[f1463]) ).
cnf(s134,plain,
( ~ spl13_53
| spl13_72 ),
inference(sat_conversion,[],[f1929]) ).
cnf(s193,plain,
( spl13_3
| ~ spl13_47
| ~ spl13_53
| ~ spl13_54 ),
inference(sat_conversion,[],[f3015]) ).
cnf(s200,plain,
( spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_54
| ~ spl13_63 ),
inference(sat_conversion,[],[f3022]) ).
cnf(s204,plain,
( spl13_1
| ~ spl13_53
| ~ spl13_62
| ~ spl13_63 ),
inference(sat_conversion,[],[f3028]) ).
cnf(s205,plain,
( ~ spl13_3
| ~ spl13_47
| spl13_54 ),
inference(sat_conversion,[],[f3038]) ).
cnf(s252,plain,
( ~ spl13_47
| ~ spl13_54
| spl13_63
| ~ spl13_72 ),
inference(sat_conversion,[],[f3471]) ).
cnf(s254,plain,
( ~ spl13_2
| ~ spl13_47
| ~ spl13_53
| spl13_63 ),
inference(sat_conversion,[],[f3517]) ).
cnf(s258,plain,
spl13_72,
inference(rat,[],[s134,s65]) ).
cnf(s266,plain,
spl13_62,
inference(rat,[],[s75,s50]) ).
cnf(s299,plain,
spl13_1,
inference(rat,[],[s205,s1,s252,s254,s204,s50,s258,s65,s266]) ).
cnf(s300,plain,
spl13_63,
inference(rat,[],[s64,s266,s299]) ).
cnf(s303,plain,
~ spl13_3,
inference(rat,[],[s3,s299]) ).
cnf(s304,plain,
~ spl13_2,
inference(rat,[],[s2,s299]) ).
cnf(s306,plain,
spl13_54,
inference(rat,[],[s200,s304,s50,s65,s300]) ).
cnf(s308,plain,
$false,
inference(rat,[],[s193,s50,s65,s306,s303]) ).
fof(f3520,plain,
$false,
inference(avatar_sat_refutation,[],[s308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM541+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/5.39 % Computer : n009.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sun Sep 27 20:24:06 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/5.42 Running first-order model finding
% 0.15/5.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.53 % (2370712)Will run a generic schedule for satisfiability detection.
% 0.15/5.53 % (2370717)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=383169473_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/5.53 % (2370718)% WARNING: option uhcvi not known.
% 0.15/5.53 % TRYING [1]
% 0.15/5.53 % TRYING [2]
% 0.15/5.53 % TRYING [3]
% 0.15/5.53 % (2370718)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2666080842:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/5.53 % (2370719)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=70558382:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/5.53 % (2370720)dis+10_1_sil=32000:sp=arity:random_seed=3343176983:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/5.53 % (2370721)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1425045655:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/5.53 % (2370723)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2044952295:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/5.53 % (2370722)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3014372261:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/5.53 % TRYING [4]
% 0.15/5.53 % TRYING [5]
% 0.15/5.53 % TRYING [6]
% 0.15/5.53 % (2370720) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2370712-2370720"...
% 0.15/5.53 % (2370720)...printing done.
% 0.15/5.53 % (2370720)Refutation found. Thanks to Tanya!
% 0.15/5.53 % SZS status Theorem for theBenchmark
% 0.15/5.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/5.54 % (2370720)------------------------------
% 0.15/5.54 % (2370720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/5.54 % (2370720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/5.54 % (2370720)CaDiCaL version: 2.1.3
% 0.15/5.54 % (2370720)Termination reason: Refutation
% 0.15/5.54 % (2370720)Time elapsed: 0.067 s
% 0.15/5.54 % (2370720)Peak memory usage: 14 MB
% 0.15/5.54 % (2370720)Instructions burned: 96 (million)
% 0.15/5.54 % (2370712)Success in time 0.103 s
% 0.15/5.54 % Vampire exiting
%------------------------------------------------------------------------------