%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM541+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 12:15:39 PM UTC 2026
% Result : Theorem 2.35s 1.22s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 143 ( 15 unt; 9 def)
% Number of atoms : 516 ( 35 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 653 ( 280 ~; 301 |; 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 : 85 ( 0 sgn 82 !; 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,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
<=> ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) ),
file('/export/starexec/sandbox/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(f232,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(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] :
( sdtlseqdt0(X0,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f235,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f236,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f237,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ 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] :
( aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),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(f289,plain,
( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| spl13_1 ),
inference(avatar_component_clause,[],[f288]) ).
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(f317,plain,
( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xm)))
| spl13_1
| ~ spl13_2 ),
inference(forward_demodulation,[],[f289,f294]) ).
fof(f318,plain,
( aElementOf0(xm,szNzAzT0)
| ~ spl13_2 ),
inference(forward_demodulation,[],[f266,f294]) ).
fof(f449,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xm))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| spl13_1
| ~ spl13_2 ),
inference(resolution,[],[f284,f317]) ).
fof(f454,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f449,f234]) ).
fof(f455,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f454,f224]) ).
fof(f456,plain,
( $false
| spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f455,f318]) ).
fof(f457,plain,
( spl13_1
| ~ spl13_2 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f458,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_3 ),
inference(resolution,[],[f298,f286]) ).
fof(f460,definition,
( spl13_12
<=> aElementOf0(xn,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f461,plain,
( aElementOf0(xn,szNzAzT0)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f464,definition,
( spl13_13
<=> sdtlseqdt0(szszuzczcdt0(xm),xn) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f465,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| spl13_13 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f466,plain,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f467,plain,
( ~ spl13_12
| spl13_13
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f458,f296,f464,f460]) ).
fof(f469,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl13_1 ),
inference(resolution,[],[f289,f284]) ).
fof(f471,definition,
( spl13_14
<=> aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f472,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f473,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl13_14 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f475,definition,
( spl13_15
<=> sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
fof(f476,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f477,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| spl13_15 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f479,definition,
( spl13_16
<=> aElementOf0(xm,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f480,plain,
( aElementOf0(xm,szNzAzT0)
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f482,plain,
( ~ spl13_14
| ~ spl13_15
| ~ spl13_16
| spl13_1 ),
inference(avatar_split_clause,[],[f469,f288,f479,f475,f471]) ).
fof(f483,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl13_14 ),
inference(resolution,[],[f473,f224]) ).
fof(f487,plain,
( ~ spl13_12
| spl13_14 ),
inference(avatar_split_clause,[],[f483,f471,f460]) ).
fof(f488,plain,
spl13_12,
inference(avatar_split_clause,[],[f266,f460]) ).
fof(f489,plain,
spl13_16,
inference(avatar_split_clause,[],[f267,f479]) ).
fof(f496,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(resolution,[],[f235,f237]) ).
fof(f500,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f496]) ).
fof(f517,definition,
( spl13_18
<=> aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f518,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f519,plain,
( ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| spl13_18 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f535,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl13_18 ),
inference(resolution,[],[f519,f224]) ).
fof(f537,plain,
( $false
| ~ spl13_16
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f535,f480]) ).
fof(f538,plain,
( ~ spl13_16
| spl13_18 ),
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f579,plain,
( ! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ sdtlseqdt0(X0,szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) )
| spl13_15 ),
inference(resolution,[],[f236,f477]) ).
fof(f585,plain,
( ! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ sdtlseqdt0(X0,szszuzczcdt0(xn))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) )
| spl13_15
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f579,f518]) ).
fof(f593,plain,
( ! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ sdtlseqdt0(X0,szszuzczcdt0(xn))
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl13_14
| spl13_15
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f585,f472]) ).
fof(f1583,plain,
( ~ sdtlseqdt0(xn,szszuzczcdt0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_13
| ~ spl13_14
| spl13_15
| ~ spl13_18 ),
inference(resolution,[],[f593,f466]) ).
fof(f1590,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ spl13_13
| ~ spl13_14
| spl13_15
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f1583,f233]) ).
fof(f1598,plain,
( $false
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| spl13_15
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f1590,f461]) ).
fof(f1599,plain,
( ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| spl13_15
| ~ spl13_18 ),
inference(avatar_contradiction_clause,[],[f1598]) ).
fof(f1604,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_3 ),
inference(resolution,[],[f297,f284]) ).
fof(f1605,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_3
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1604,f480]) ).
fof(f1609,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| spl13_3
| ~ spl13_12
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1605,f461]) ).
fof(f1610,plain,
( ~ spl13_13
| spl13_3
| ~ spl13_12
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f1609,f479,f460,f296,f464]) ).
fof(f1612,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ spl13_1 ),
inference(resolution,[],[f290,f286]) ).
fof(f1613,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ spl13_1
| ~ spl13_14 ),
inference(forward_subsumption_resolution,[],[f1612,f472]) ).
fof(f1615,plain,
( spl13_15
| ~ spl13_1
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f1613,f471,f288,f475]) ).
fof(f1617,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| xm = xn
| spl13_13 ),
inference(resolution,[],[f465,f500]) ).
fof(f1624,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| xm = xn
| ~ spl13_12
| spl13_13 ),
inference(forward_subsumption_resolution,[],[f1617,f461]) ).
fof(f1629,plain,
( ~ sdtlseqdt0(xm,xn)
| xm = xn
| ~ spl13_12
| spl13_13
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1624,f480]) ).
fof(f1631,plain,
( ~ sdtlseqdt0(xm,xn)
| spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1629,f293]) ).
fof(f1667,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_16 ),
inference(resolution,[],[f1631,f232]) ).
fof(f1670,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_15
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1667,f476]) ).
fof(f1673,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_15
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1670,f480]) ).
fof(f1675,plain,
( $false
| spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_15
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1673,f461]) ).
fof(f1676,plain,
( spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_15
| ~ spl13_16 ),
inference(avatar_contradiction_clause,[],[f1675]) ).
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(s12,plain,
( spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f457]) ).
cnf(s13,plain,
( ~ spl13_3
| ~ spl13_12
| spl13_13 ),
inference(sat_conversion,[],[f467]) ).
cnf(s14,plain,
( spl13_1
| ~ spl13_14
| ~ spl13_15
| ~ spl13_16 ),
inference(sat_conversion,[],[f482]) ).
cnf(s16,plain,
( ~ spl13_12
| spl13_14 ),
inference(sat_conversion,[],[f487]) ).
cnf(s17,plain,
spl13_12,
inference(sat_conversion,[],[f488]) ).
cnf(s18,plain,
spl13_16,
inference(sat_conversion,[],[f489]) ).
cnf(s21,plain,
( ~ spl13_16
| spl13_18 ),
inference(sat_conversion,[],[f538]) ).
cnf(s86,plain,
( ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| spl13_15
| ~ spl13_18 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s88,plain,
( spl13_3
| ~ spl13_12
| ~ spl13_13
| ~ spl13_16 ),
inference(sat_conversion,[],[f1610]) ).
cnf(s89,plain,
( ~ spl13_1
| ~ spl13_14
| spl13_15 ),
inference(sat_conversion,[],[f1615]) ).
cnf(s94,plain,
( spl13_2
| ~ spl13_12
| spl13_13
| ~ spl13_15
| ~ spl13_16 ),
inference(sat_conversion,[],[f1676]) ).
cnf(s95,plain,
spl13_18,
inference(rat,[],[s21,s18]) ).
cnf(s99,plain,
spl13_14,
inference(rat,[],[s16,s17]) ).
cnf(s104,plain,
( spl13_1
| ~ spl13_15 ),
inference(rat,[],[s14,s18,s99]) ).
cnf(s105,plain,
( ~ spl13_3
| spl13_13 ),
inference(rat,[],[s13,s17]) ).
cnf(s109,plain,
spl13_1,
inference(rat,[],[s105,s1,s86,s12,s104,s17,s99,s95]) ).
cnf(s110,plain,
spl13_15,
inference(rat,[],[s89,s99,s109]) ).
cnf(s111,plain,
~ spl13_3,
inference(rat,[],[s3,s109]) ).
cnf(s112,plain,
~ spl13_2,
inference(rat,[],[s2,s109]) ).
cnf(s113,plain,
~ spl13_13,
inference(rat,[],[s88,s18,s17,s111]) ).
cnf(s114,plain,
$false,
inference(rat,[],[s94,s18,s110,s17,s113,s112]) ).
fof(f1677,plain,
$false,
inference(avatar_sat_refutation,[],[s114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM541+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:24:53 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.35/1.22 % (3719135)Detected formulas, will run a generic FOF schedule.
% 2.35/1.22 % (3719145)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3741612904:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.35/1.22 % (3719145)First to succeed.
% 2.35/1.22 % (3719145)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3719135"
% 2.35/1.22 % (3719141)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=2831554304:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.35/1.22 % (3719144)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4244286832:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.35/1.22 % (3719140)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=115180168:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.35/1.22 % (3719146)dis-21_1_sil=8000:lcm=predicate:random_seed=2437321774: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)
% 2.35/1.22 % (3719142)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=2711675461:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.35/1.22 % (3719143)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2684755621:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.35/1.22 % (3719143)Refutation not found, incomplete strategy
% 2.35/1.22 % (3719143)------------------------------
% 2.35/1.22 % (3719143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/1.22 % (3719143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/1.22 % (3719143)CaDiCaL version: 2.1.3
% 2.35/1.22 % (3719143)Termination reason: Refutation not found, incomplete strategy
% 2.35/1.22 % (3719143)Time elapsed: 0.002 s
% 2.35/1.22 % (3719143)Peak memory usage: 88 MB
% 2.35/1.22 % (3719143)Instructions burned: 1 (million)
% 2.35/1.22 % (3719144)Also succeeded, but the first one will report.
% 2.35/1.22 % (3719146)Instruction limit reached!
% 2.35/1.22 % (3719146)------------------------------
% 2.35/1.22 % (3719146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/1.22 % (3719146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/1.22 % (3719146)CaDiCaL version: 2.1.3
% 2.35/1.22 % (3719146)Termination reason: Instruction limit
% 2.35/1.22 % (3719146)Termination phase: Saturation
% 2.35/1.22 % (3719146)Time elapsed: 0.055 s
% 2.35/1.22 % (3719146)Peak memory usage: 88 MB
% 2.35/1.22 % (3719146)Instructions burned: 131 (million)
% 2.35/1.22 % (3719145)Refutation found. Thanks to Tanya!
% 2.35/1.22 % SZS status Theorem for theBenchmark
% 2.35/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.41 % (3719145)------------------------------
% 0.17/1.41 % (3719145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.41 % (3719145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.41 % (3719145)CaDiCaL version: 2.1.3
% 0.17/1.41 % (3719145)Termination reason: Refutation
% 0.17/1.41 % (3719145)Time elapsed: 0.022 s
% 0.17/1.41 % (3719145)Peak memory usage: 90 MB
% 0.17/1.41 % (3719145)Instructions burned: 53 (million)
% 0.17/1.41 % (3719145)------------------------------
% 0.17/1.41 % (3719145)------------------------------
% 0.17/1.41 % (3719135)Success in time 0.343 s
% 0.17/1.41 % Vampire exiting
%------------------------------------------------------------------------------