%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM620+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 : n002.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 12:16:01 PM UTC 2026
% Result : Theorem 2.84s 1.37s
% Output : Refutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 97 ( 20 unt; 7 def)
% Number of atoms : 296 ( 45 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 333 ( 134 ~; 126 |; 50 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 74 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f47,axiom,
! [X0] :
( ( aSubsetOf0(X0,szNzAzT0)
& X0 != slcrc0 )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f111,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f115,axiom,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(f116,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f117,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f118,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f127,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f130,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f131,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f155,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(ennf_transformation,[],[f47]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f185]) ).
fof(f229,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f249,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f118]) ).
fof(f256,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f127]) ).
fof(f257,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f256]) ).
fof(f258,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f257]) ).
fof(f259,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f258]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f261,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f260]) ).
fof(f262,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f261]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f262]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(nnf_transformation,[],[f186]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f281]) ).
fof(f283,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(rectify,[],[f282]) ).
fof(f284,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(X1,sK10(X0,X1))
& aElementOf0(sK10(X0,X1),X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f283]) ).
fof(f321,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f259]) ).
fof(f325,plain,
! [X0] :
( slcrc0 != X0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f326,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f327,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f365,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f368,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f394,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f284]) ).
fof(f483,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f484,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f533,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f540,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f541,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f116]) ).
fof(f542,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f249]) ).
fof(f543,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f249]) ).
fof(f544,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f321]) ).
fof(f546,plain,
( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(equality_resolution,[],[f325]) ).
fof(f552,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f394]) ).
fof(f583,definition,
( spl29_1
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f592,definition,
( spl29_3
<=> isCountable0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl29_3])],[avatar_definition]) ).
fof(f594,plain,
( ~ isCountable0(slcrc0)
| spl29_3 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f595,plain,
( ~ spl29_3
| ~ spl29_1 ),
inference(avatar_split_clause,[],[f546,f583,f592]) ).
fof(f596,plain,
spl29_1,
inference(avatar_split_clause,[],[f544,f583]) ).
fof(f691,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| slcrc0 = sdtlpdtrp0(xN,xm) ),
inference(superposition,[],[f552,f541]) ).
fof(f693,definition,
( spl29_8
<=> slcrc0 = sdtlpdtrp0(xN,xm) ),
introduced(definition,[new_symbols(definition,[spl29_8])],[avatar_definition]) ).
fof(f695,plain,
( slcrc0 = sdtlpdtrp0(xN,xm)
| ~ spl29_8 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f697,definition,
( spl29_9
<=> aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f699,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| spl29_9 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f701,definition,
( spl29_10
<=> aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
introduced(definition,[new_symbols(definition,[spl29_10])],[avatar_definition]) ).
fof(f704,plain,
( spl29_8
| ~ spl29_9
| spl29_10 ),
inference(avatar_split_clause,[],[f691,f701,f697,f693]) ).
fof(f711,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[],[f326,f543]) ).
fof(f715,definition,
( spl29_11
<=> aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
introduced(definition,[new_symbols(definition,[spl29_11])],[avatar_definition]) ).
fof(f717,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| spl29_11 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f719,definition,
( spl29_12
<=> ! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
introduced(definition,[new_symbols(definition,[spl29_12])],[avatar_definition]) ).
fof(f720,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(xx,X0) )
| ~ spl29_12 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f721,plain,
( ~ spl29_11
| spl29_12 ),
inference(avatar_split_clause,[],[f711,f719,f715]) ).
fof(f724,plain,
( ! [X0] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0)
| ~ aSet0(X0) )
| spl29_11 ),
inference(resolution,[],[f717,f327]) ).
fof(f743,plain,
( ~ aSet0(szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl29_11 ),
inference(resolution,[],[f724,f484]) ).
fof(f762,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f743,f365]) ).
fof(f765,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl29_11 ),
inference(resolution,[],[f762,f368]) ).
fof(f769,plain,
( $false
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f765,f533]) ).
fof(f770,plain,
spl29_11,
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f795,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ~ spl29_12 ),
inference(resolution,[],[f720,f542]) ).
fof(f796,plain,
( ~ spl29_10
| ~ spl29_12 ),
inference(avatar_split_clause,[],[f795,f719,f701]) ).
fof(f1935,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl29_9 ),
inference(resolution,[],[f699,f484]) ).
fof(f1946,plain,
( $false
| spl29_9 ),
inference(forward_subsumption_resolution,[],[f1935,f540]) ).
fof(f1947,plain,
spl29_9,
inference(avatar_contradiction_clause,[],[f1946]) ).
fof(f1969,plain,
( isCountable0(slcrc0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ spl29_8 ),
inference(superposition,[],[f483,f695]) ).
fof(f1998,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl29_3
| ~ spl29_8 ),
inference(forward_subsumption_resolution,[],[f1969,f594]) ).
fof(f2002,plain,
( $false
| spl29_3
| ~ spl29_8 ),
inference(forward_subsumption_resolution,[],[f1998,f540]) ).
fof(f2003,plain,
( spl29_3
| ~ spl29_8 ),
inference(avatar_contradiction_clause,[],[f2002]) ).
cnf(s2,plain,
( ~ spl29_1
| ~ spl29_3 ),
inference(sat_conversion,[],[f595]) ).
cnf(s3,plain,
spl29_1,
inference(sat_conversion,[],[f596]) ).
cnf(s7,plain,
( spl29_8
| ~ spl29_9
| spl29_10 ),
inference(sat_conversion,[],[f704]) ).
cnf(s8,plain,
( ~ spl29_11
| spl29_12 ),
inference(sat_conversion,[],[f721]) ).
cnf(s10,plain,
spl29_11,
inference(sat_conversion,[],[f770]) ).
cnf(s12,plain,
( ~ spl29_10
| ~ spl29_12 ),
inference(sat_conversion,[],[f796]) ).
cnf(s57,plain,
spl29_9,
inference(sat_conversion,[],[f1947]) ).
cnf(s61,plain,
( spl29_3
| ~ spl29_8 ),
inference(sat_conversion,[],[f2003]) ).
cnf(s74,plain,
spl29_12,
inference(rat,[],[s8,s10]) ).
cnf(s76,plain,
~ spl29_10,
inference(rat,[],[s12,s74]) ).
cnf(s77,plain,
spl29_8,
inference(rat,[],[s7,s76,s57]) ).
cnf(s78,plain,
spl29_3,
inference(rat,[],[s61,s77]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s2,s78,s3]) ).
fof(f2005,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM620+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n002.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 20:50:21 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.84/1.37 % (3861167)Detected formulas, will run a generic FOF schedule.
% 2.84/1.37 % (3861176)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3865435557:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.84/1.37 % (3861174)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=3543844320:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.84/1.37 % (3861173)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=354520847:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.84/1.37 % (3861172)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=327857985:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.84/1.37 % (3861175)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2111363432:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.84/1.37 % (3861176)Instruction limit reached!
% 2.84/1.37 % (3861176)------------------------------
% 2.84/1.37 % (3861176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (3861176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (3861176)CaDiCaL version: 2.1.3
% 2.84/1.37 % (3861176)Termination reason: Instruction limit
% 2.84/1.37 % (3861176)Termination phase: Saturation
% 2.84/1.37 % (3861176)Time elapsed: 0.041 s
% 2.84/1.37 % (3861176)Peak memory usage: 89 MB
% 2.84/1.37 % (3861176)Instructions burned: 119 (million)
% 2.84/1.37 % (3861178)dis-21_1_sil=8000:lcm=predicate:random_seed=1526991655: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)
% 2.84/1.37 % (3861177)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=719024197:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.84/1.37 % (3861177)First to succeed.
% 2.84/1.37 % (3861177)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3861167"
% 2.84/1.37 % (3861175)Instruction limit reached!
% 2.84/1.37 % (3861175)------------------------------
% 2.84/1.37 % (3861175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (3861175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (3861175)CaDiCaL version: 2.1.3
% 2.84/1.37 % (3861175)Termination reason: Instruction limit
% 2.84/1.37 % (3861175)Termination phase: Saturation
% 2.84/1.37 % (3861175)Time elapsed: 0.070 s
% 2.84/1.37 % (3861175)Peak memory usage: 89 MB
% 2.84/1.37 % (3861175)Instructions burned: 110 (million)
% 2.84/1.37 % (3861178)Instruction limit reached!
% 2.84/1.37 % (3861178)------------------------------
% 2.84/1.37 % (3861178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (3861178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (3861178)CaDiCaL version: 2.1.3
% 2.84/1.37 % (3861178)Termination reason: Instruction limit
% 2.84/1.37 % (3861178)Termination phase: Saturation
% 2.84/1.37 % (3861178)Time elapsed: 0.076 s
% 2.84/1.37 % (3861178)Peak memory usage: 91 MB
% 2.84/1.37 % (3861178)Instructions burned: 130 (million)
% 2.84/1.37 % (3861186)lrs+10_1_sil=8000:sp=occurrence:random_seed=1727960758:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.84/1.37 % (3861186)Also succeeded, but the first one will report.
% 2.84/1.37 % (3861187)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4042767516:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.84/1.37 % (3861187)Refutation not found, incomplete strategy
% 2.84/1.37 % (3861187)------------------------------
% 2.84/1.37 % (3861187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (3861187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (3861187)CaDiCaL version: 2.1.3
% 2.84/1.37 % (3861187)Termination reason: Refutation not found, incomplete strategy
% 2.84/1.37 % (3861187)Time elapsed: 0.004 s
% 2.84/1.37 % (3861187)Peak memory usage: 89 MB
% 2.84/1.37 % (3861187)Instructions burned: 3 (million)
% 2.84/1.37 % (3861188)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3434331899:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.84/1.37 % (3861177)Refutation found. Thanks to Tanya!
% 2.84/1.37 % SZS status Theorem for theBenchmark
% 2.84/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.08/1.56 % (3861177)------------------------------
% 4.08/1.56 % (3861177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.56 % (3861177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.56 % (3861177)CaDiCaL version: 2.1.3
% 4.08/1.56 % (3861177)Termination reason: Refutation
% 4.08/1.56 % (3861177)Time elapsed: 0.052 s
% 4.08/1.56 % (3861177)Peak memory usage: 90 MB
% 4.08/1.56 % (3861177)Instructions burned: 70 (million)
% 4.08/1.56 % (3861177)------------------------------
% 4.08/1.56 % (3861177)------------------------------
% 4.08/1.56 % (3861167)Success in time 0.501 s
% 4.08/1.56 % Vampire exiting
%------------------------------------------------------------------------------