%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM598+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:15:55 PM UTC 2026
% Result : Theorem 7.50s 2.06s
% Output : Refutation 8.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 21 unt; 5 def)
% Number of atoms : 302 ( 49 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 361 ( 156 ~; 160 |; 29 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f67,axiom,
! [X0,X1] :
( ( aFunction0(X0)
& aElement0(X1) )
=> aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
fof(f71,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( ( aSubsetOf0(X1,szDzozmdt0(X0))
& isCountable0(X1) )
=> ( ! [X2,X3] :
( ( aElementOf0(X2,szDzozmdt0(X0))
& aElementOf0(X3,szDzozmdt0(X0))
& X2 != X3 )
=> sdtlpdtrp0(X0,X2) != sdtlpdtrp0(X0,X3) )
=> isCountable0(sdtlcdtrc0(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgCount) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(f84,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& X0 != X1 )
=> szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
fof(f95,axiom,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
fof(f96,conjecture,
isCountable0(xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f97,negated_conjecture,
~ isCountable0(xO),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f105,plain,
~ isCountable0(xO),
inference(flattening,[],[f97]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f196,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f197,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f196]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( isCountable0(sdtlcdtrc0(X0,X1))
| ? [X2,X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X0,X2)
& aElementOf0(X2,szDzozmdt0(X0))
& aElementOf0(X3,szDzozmdt0(X0))
& X2 != X3 )
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( isCountable0(sdtlcdtrc0(X0,X1))
| ? [X2,X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X0,X2)
& aElementOf0(X2,szDzozmdt0(X0))
& aElementOf0(X3,szDzozmdt0(X0))
& X2 != X3 )
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f201]) ).
fof(f212,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(ennf_transformation,[],[f84]) ).
fof(f213,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(flattening,[],[f212]) ).
fof(f225,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f226,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f227,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f226]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( isCountable0(sdtlcdtrc0(X0,X1))
| ( sdtlpdtrp0(X0,sK22(X0)) = sdtlpdtrp0(X0,sK21(X0))
& aElementOf0(sK21(X0),szDzozmdt0(X0))
& aElementOf0(sK22(X0),szDzozmdt0(X0))
& sK21(X0) != sK22(X0) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1) )
| ~ aFunction0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X2,sK21(X0)),skolemize(X3,sK22(X0))],[f202]) ).
fof(f296,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f419,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f433,plain,
! [X0,X1] :
( sK21(X0) != sK22(X0)
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f434,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| aElementOf0(sK22(X0),szDzozmdt0(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f435,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| aElementOf0(sK21(X0),szDzozmdt0(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f436,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlpdtrp0(X0,sK22(X0)) = sdtlpdtrp0(X0,sK21(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f440,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f463,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(cnf_transformation,[],[f213]) ).
fof(f478,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f479,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(cnf_transformation,[],[f225]) ).
fof(f480,plain,
aFunction0(xe),
inference(cnf_transformation,[],[f225]) ).
fof(f482,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f227]) ).
fof(f483,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f227]) ).
fof(f485,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f94]) ).
fof(f486,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f94]) ).
fof(f487,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f95]) ).
fof(f489,plain,
~ isCountable0(xO),
inference(cnf_transformation,[],[f105]) ).
fof(f566,plain,
( aElement0(szDzizrdt0(xd))
| ~ aSet0(xT) ),
inference(resolution,[],[f296,f486]) ).
fof(f567,plain,
aElement0(szDzizrdt0(xd)),
inference(forward_subsumption_resolution,[],[f566,f440]) ).
fof(f586,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aFunction0(xd)
| ~ aElement0(X0) ),
inference(superposition,[],[f419,f482]) ).
fof(f587,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f586,f483]) ).
fof(f770,definition,
( spl28_25
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl28_25])],[avatar_definition]) ).
fof(f771,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl28_25 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f772,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| spl28_25 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f774,plain,
( ~ aElement0(szDzizrdt0(xd))
| spl28_25 ),
inference(resolution,[],[f772,f587]) ).
fof(f775,plain,
( $false
| spl28_25 ),
inference(forward_subsumption_resolution,[],[f774,f567]) ).
fof(f776,plain,
spl28_25,
inference(avatar_contradiction_clause,[],[f775]) ).
fof(f848,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,sK22(xe)) = sdtlpdtrp0(xe,sK21(xe))
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f436,f479]) ).
fof(f852,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,sK22(xe)) = sdtlpdtrp0(xe,sK21(xe))
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f848,f480]) ).
fof(f865,definition,
( spl28_33
<=> sdtlpdtrp0(xe,sK22(xe)) = sdtlpdtrp0(xe,sK21(xe)) ),
introduced(definition,[new_symbols(definition,[spl28_33])],[avatar_definition]) ).
fof(f867,plain,
( sdtlpdtrp0(xe,sK22(xe)) = sdtlpdtrp0(xe,sK21(xe))
| ~ spl28_33 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f869,definition,
( spl28_34
<=> ! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| ~ isCountable0(X0)
| isCountable0(sdtlcdtrc0(xe,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl28_34])],[avatar_definition]) ).
fof(f870,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) )
| ~ spl28_34 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f871,plain,
( spl28_33
| spl28_34 ),
inference(avatar_split_clause,[],[f852,f869,f865]) ).
fof(f959,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK22(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f434,f479]) ).
fof(f963,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK22(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f959,f480]) ).
fof(f973,definition,
( spl28_44
<=> aElementOf0(sK22(xe),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl28_44])],[avatar_definition]) ).
fof(f975,plain,
( aElementOf0(sK22(xe),szNzAzT0)
| ~ spl28_44 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f976,plain,
( spl28_44
| spl28_34 ),
inference(avatar_split_clause,[],[f963,f869,f973]) ).
fof(f987,plain,
( isCountable0(xO)
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl28_34 ),
inference(superposition,[],[f870,f487]) ).
fof(f988,plain,
( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl28_34 ),
inference(forward_subsumption_resolution,[],[f987,f489]) ).
fof(f990,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl28_34 ),
inference(forward_subsumption_resolution,[],[f988,f485]) ).
fof(f991,plain,
( $false
| ~ spl28_25
| ~ spl28_34 ),
inference(forward_subsumption_resolution,[],[f990,f771]) ).
fof(f992,plain,
( ~ spl28_25
| ~ spl28_34 ),
inference(avatar_contradiction_clause,[],[f991]) ).
fof(f999,plain,
( sdtlpdtrp0(xe,sK22(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK22(xe)))
| ~ spl28_44 ),
inference(resolution,[],[f975,f478]) ).
fof(f1002,plain,
( sdtlpdtrp0(xe,sK21(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK22(xe)))
| ~ spl28_33
| ~ spl28_44 ),
inference(forward_demodulation,[],[f999,f867]) ).
fof(f1050,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK21(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f435,f479]) ).
fof(f1053,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK21(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f1050,f480]) ).
fof(f1056,definition,
( spl28_49
<=> aElementOf0(sK21(xe),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl28_49])],[avatar_definition]) ).
fof(f1058,plain,
( aElementOf0(sK21(xe),szNzAzT0)
| ~ spl28_49 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1059,plain,
( spl28_49
| spl28_34 ),
inference(avatar_split_clause,[],[f1053,f869,f1056]) ).
fof(f1062,plain,
( sdtlpdtrp0(xe,sK21(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK21(xe)))
| ~ spl28_49 ),
inference(resolution,[],[f1058,f478]) ).
fof(f1314,plain,
( ! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != sdtlpdtrp0(xe,sK21(xe))
| ~ aElementOf0(sK21(xe),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sK21(xe) = X0 )
| ~ spl28_49 ),
inference(superposition,[],[f463,f1062]) ).
fof(f1316,plain,
( ! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != sdtlpdtrp0(xe,sK21(xe))
| ~ aElementOf0(X0,szNzAzT0)
| sK21(xe) = X0 )
| ~ spl28_49 ),
inference(forward_subsumption_resolution,[],[f1314,f1058]) ).
fof(f1320,plain,
( sdtlpdtrp0(xe,sK21(xe)) != sdtlpdtrp0(xe,sK21(xe))
| ~ aElementOf0(sK22(xe),szNzAzT0)
| sK22(xe) = sK21(xe)
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(superposition,[],[f1316,f1002]) ).
fof(f1321,plain,
( ~ aElementOf0(sK22(xe),szNzAzT0)
| sK22(xe) = sK21(xe)
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(trivial_inequality_removal,[],[f1320]) ).
fof(f1322,plain,
( sK22(xe) = sK21(xe)
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(forward_subsumption_resolution,[],[f1321,f975]) ).
fof(f1328,plain,
( ! [X0] :
( sK21(xe) != sK21(xe)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0)
| ~ aFunction0(xe) )
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(superposition,[],[f433,f1322]) ).
fof(f1329,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0)
| ~ aFunction0(xe) )
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(trivial_inequality_removal,[],[f1328]) ).
fof(f1330,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0) )
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(forward_subsumption_resolution,[],[f1329,f480]) ).
fof(f1331,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) )
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(forward_demodulation,[],[f1330,f479]) ).
fof(f1332,plain,
( spl28_34
| ~ spl28_33
| ~ spl28_44
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f1331,f1056,f973,f865,f869]) ).
cnf(s18,plain,
spl28_25,
inference(sat_conversion,[],[f776]) ).
cnf(s25,plain,
( spl28_33
| spl28_34 ),
inference(sat_conversion,[],[f871]) ).
cnf(s33,plain,
( spl28_34
| spl28_44 ),
inference(sat_conversion,[],[f976]) ).
cnf(s36,plain,
( ~ spl28_25
| ~ spl28_34 ),
inference(sat_conversion,[],[f992]) ).
cnf(s39,plain,
( spl28_34
| spl28_49 ),
inference(sat_conversion,[],[f1059]) ).
cnf(s50,plain,
( ~ spl28_33
| spl28_34
| ~ spl28_44
| ~ spl28_49 ),
inference(sat_conversion,[],[f1332]) ).
cnf(s51,plain,
~ spl28_34,
inference(rat,[],[s36,s18]) ).
cnf(s53,plain,
spl28_49,
inference(rat,[],[s39,s51]) ).
cnf(s54,plain,
spl28_44,
inference(rat,[],[s33,s51]) ).
cnf(s55,plain,
spl28_33,
inference(rat,[],[s25,s51]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s50,s53,s51,s54,s55]) ).
fof(f1333,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM598+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.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 20:46:46 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.50/2.06 % (3934439)Detected formulas, will run a generic FOF schedule.
% 7.50/2.06 % (3934448)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=39460596:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.50/2.06 % (3934448)Instruction limit reached!
% 7.50/2.06 % (3934448)------------------------------
% 7.50/2.06 % (3934448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934448)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934448)Termination reason: Instruction limit
% 7.50/2.06 % (3934448)Termination phase: Saturation
% 7.50/2.06 % (3934448)Time elapsed: 0.040 s
% 7.50/2.06 % (3934448)Peak memory usage: 89 MB
% 7.50/2.06 % (3934448)Instructions burned: 119 (million)
% 7.50/2.06 % (3934444)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=3076013663:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.50/2.06 % (3934445)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=4270773593:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.50/2.06 % (3934447)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1446228721:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.50/2.06 % (3934446)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=3476453214:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.50/2.06 % (3934449)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3040308230:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.50/2.06 % (3934450)dis-21_1_sil=8000:lcm=predicate:random_seed=3849666814: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)
% 7.50/2.06 % (3934447)Instruction limit reached!
% 7.50/2.06 % (3934447)------------------------------
% 7.50/2.06 % (3934447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934447)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934447)Termination reason: Instruction limit
% 7.50/2.06 % (3934447)Termination phase: Saturation
% 7.50/2.06 % (3934447)Time elapsed: 0.064 s
% 7.50/2.06 % (3934447)Peak memory usage: 89 MB
% 7.50/2.06 % (3934447)Instructions burned: 109 (million)
% 7.50/2.06 % (3934450)Instruction limit reached!
% 7.50/2.06 % (3934450)------------------------------
% 7.50/2.06 % (3934450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934450)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934450)Termination reason: Instruction limit
% 7.50/2.06 % (3934450)Termination phase: Saturation
% 7.50/2.06 % (3934450)Time elapsed: 0.075 s
% 7.50/2.06 % (3934450)Peak memory usage: 90 MB
% 7.50/2.06 % (3934450)Instructions burned: 131 (million)
% 7.50/2.06 % (3934449)Instruction limit reached!
% 7.50/2.06 % (3934449)------------------------------
% 7.50/2.06 % (3934449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934449)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934449)Termination reason: Instruction limit
% 7.50/2.06 % (3934449)Termination phase: Saturation
% 7.50/2.06 % (3934449)Time elapsed: 0.104 s
% 7.50/2.06 % (3934449)Peak memory usage: 90 MB
% 7.50/2.06 % (3934449)Instructions burned: 139 (million)
% 7.50/2.06 % (3934452)lrs+10_1_sil=8000:sp=occurrence:random_seed=1524348523:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.50/2.06 % (3934452)Instruction limit reached!
% 7.50/2.06 % (3934452)------------------------------
% 7.50/2.06 % (3934452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934452)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934452)Termination reason: Instruction limit
% 7.50/2.06 % (3934452)Termination phase: Saturation
% 7.50/2.06 % (3934452)Time elapsed: 0.097 s
% 7.50/2.06 % (3934452)Peak memory usage: 92 MB
% 7.50/2.06 % (3934452)Instructions burned: 287 (million)
% 7.50/2.06 % (3934459)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2202972846:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.50/2.06 % (3934459)Refutation not found, incomplete strategy
% 7.50/2.06 % (3934459)------------------------------
% 7.50/2.06 % (3934459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934459)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934459)Termination reason: Refutation not found, incomplete strategy
% 7.50/2.06 % (3934459)Time elapsed: 0.002 s
% 7.50/2.06 % (3934459)Peak memory usage: 88 MB
% 7.50/2.06 % (3934459)Instructions burned: 1 (million)
% 7.50/2.06 % (3934460)lrs+1011_1_sil=32000:sp=occurrence:random_seed=387430070:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.50/2.06 % (3934462)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1166571832:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.50/2.06 % (3934464)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3661429915:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 7.50/2.06 % (3934462)Instruction limit reached!
% 7.50/2.06 % (3934462)------------------------------
% 7.50/2.06 % (3934462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934462)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934462)Termination reason: Instruction limit
% 7.50/2.06 % (3934462)Termination phase: Saturation
% 7.50/2.06 % (3934462)Time elapsed: 0.151 s
% 7.50/2.06 % (3934462)Peak memory usage: 92 MB
% 7.50/2.06 % (3934462)Instructions burned: 249 (million)
% 7.50/2.06 % (3934464)Instruction limit reached!
% 7.50/2.06 % (3934464)------------------------------
% 7.50/2.06 % (3934464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934464)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934464)Termination reason: Instruction limit
% 7.50/2.06 % (3934464)Termination phase: Saturation
% 7.50/2.06 % (3934464)Time elapsed: 0.098 s
% 7.50/2.06 % (3934464)Peak memory usage: 90 MB
% 7.50/2.06 % (3934464)Instructions burned: 296 (million)
% 7.50/2.06 % (3934459)------------------------------
% 7.50/2.06 % (3934459)------------------------------
% 7.50/2.06 % (3934460)Instruction limit reached!
% 7.50/2.06 % (3934460)------------------------------
% 7.50/2.06 % (3934460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934460)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934460)Termination reason: Instruction limit
% 7.50/2.06 % (3934460)Termination phase: Saturation
% 7.50/2.06 % (3934460)Time elapsed: 0.227 s
% 7.50/2.06 % (3934460)Peak memory usage: 92 MB
% 7.50/2.06 % (3934460)Instructions burned: 325 (million)
% 7.50/2.06 % (3934469)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=714254160:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 7.50/2.06 % (3934468)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3982063346:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.50/2.06 % (3934469)Instruction limit reached!
% 7.50/2.06 % (3934469)------------------------------
% 7.50/2.06 % (3934469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934469)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934469)Termination reason: Instruction limit
% 7.50/2.06 % (3934469)Termination phase: Saturation
% 7.50/2.06 % (3934469)Time elapsed: 0.040 s
% 7.50/2.06 % (3934469)Peak memory usage: 91 MB
% 7.50/2.06 % (3934469)Instructions burned: 114 (million)
% 7.50/2.06 % (3934470)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3725419568:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 7.50/2.06 % (3934471)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1592977158:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 7.50/2.06 % (3934470)Instruction limit reached!
% 7.50/2.06 % (3934470)------------------------------
% 7.50/2.06 % (3934470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934470)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934470)Termination reason: Instruction limit
% 7.50/2.06 % (3934470)Termination phase: Saturation
% 7.50/2.06 % (3934470)Time elapsed: 0.068 s
% 7.50/2.06 % (3934470)Peak memory usage: 89 MB
% 7.50/2.06 % (3934470)Instructions burned: 127 (million)
% 7.50/2.06 % (3934471)Instruction limit reached!
% 7.50/2.06 % (3934471)------------------------------
% 7.50/2.06 % (3934471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.06 % (3934471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.06 % (3934471)CaDiCaL version: 2.1.3
% 7.50/2.06 % (3934471)Termination reason: Instruction limit
% 7.50/2.06 % (3934471)Termination phase: Saturation
% 7.50/2.06 % (3934471)Time elapsed: 0.076 s
% 7.50/2.06 % (3934471)Peak memory usage: 89 MB
% 7.50/2.06 % (3934471)Instructions burned: 115 (million)
% 7.50/2.06 % (3934474)lrs+10_1_sil=8000:sp=occurrence:random_seed=1890455930:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 7.50/2.06 % (3934444)First to succeed.
% 7.50/2.06 % (3934444)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3934439"
% 7.50/2.06 % (3934445)Also succeeded, but the first one will report.
% 7.50/2.06 % (3934477)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3549567495:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 7.50/2.06 % (3934478)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3522828209:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 7.50/2.06 % (3934444)Refutation found. Thanks to Tanya!
% 7.50/2.06 % SZS status Theorem for theBenchmark
% 7.50/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 8.98/2.25 % (3934444)------------------------------
% 8.98/2.25 % (3934444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.98/2.25 % (3934444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.98/2.25 % (3934444)CaDiCaL version: 2.1.3
% 8.98/2.25 % (3934444)Termination reason: Refutation
% 8.98/2.25 % (3934444)Time elapsed: 0.750 s
% 8.98/2.25 % (3934444)Peak memory usage: 130 MB
% 8.98/2.25 % (3934444)Instructions burned: 1107 (million)
% 8.98/2.25 % (3934444)------------------------------
% 8.98/2.25 % (3934444)------------------------------
% 8.98/2.25 % (3934439)Success in time 1.194 s
% 8.98/2.25 % Vampire exiting
%------------------------------------------------------------------------------