%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM629+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 : n004.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 12:16:03 PM UTC 2026
% Result : Theorem 5.64s 1.91s
% Output : Refutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 24 unt; 2 def)
% Number of atoms : 334 ( 50 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 415 ( 166 ~; 161 |; 69 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 14 con; 0-3 aty)
% Number of variables : 104 ( 0 sgn 98 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(f88,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4331) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5217) ).
fof(f111,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(f113,axiom,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5334) ).
fof(f114,axiom,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).
fof(f115,conjecture,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f116,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f124,plain,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(flattening,[],[f116]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f154,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f199,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f200,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f199]) ).
fof(f226,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f227,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f226]) ).
fof(f228,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f238]) ).
fof(f258,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,[],[f131]) ).
fof(f259,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,[],[f258]) ).
fof(f260,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,[],[f259]) ).
fof(f261,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))],[f260]) ).
fof(f295,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f296,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f295]) ).
fof(f297,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f296]) ).
fof(f298,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f297]) ).
fof(f325,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f363,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f366,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f419,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f475,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f476,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f477,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f481,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f482,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f492,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk))
| aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ isCountable0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f523,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f528,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f531,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f534,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f113]) ).
fof(f535,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[],[f114]) ).
fof(f536,plain,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(cnf_transformation,[],[f124]) ).
fof(f555,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f419]) ).
fof(f556,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f555]) ).
fof(f574,definition,
sF29 = slbdtsldtrb0(xD,xk),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f575,plain,
slbdtsldtrb0(xD,xk) = sF29,
inference(reorient_equations,[],[f574]) ).
fof(f576,plain,
~ aElementOf0(xP,sF29),
inference(definition_folding,[],[f536,f575]) ).
fof(f578,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f476,f481]) ).
fof(f579,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f477,f482]) ).
fof(f595,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f578,f482]) ).
fof(f596,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f579,f481]) ).
fof(f597,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f556,f528]) ).
fof(f598,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f597,f475]) ).
fof(f630,definition,
( spl30_8
<=> aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
introduced(definition,[new_symbols(definition,[spl30_8])],[avatar_definition]) ).
fof(f631,plain,
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ spl30_8 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f632,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| spl30_8 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f677,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f482,f325]) ).
fof(f680,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f677,f363]) ).
fof(f1029,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl30_8 ),
inference(resolution,[],[f680,f632]) ).
fof(f2959,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f596,f492]) ).
fof(f2971,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(duplicate_literal_removal,[],[f2959]) ).
fof(f2980,plain,
! [X0,X1] :
( aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2971,f595]) ).
fof(f3309,plain,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xD,xk))
| ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f2980,f535]) ).
fof(f3311,plain,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xD,xk))
| ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk)) ),
inference(forward_subsumption_resolution,[],[f3309,f531]) ).
fof(f3318,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ aSet0(X0)
| aElementOf0(X0,sF29) ),
inference(forward_demodulation,[],[f3311,f575]) ).
fof(f3323,plain,
( ~ aSet0(xP)
| aElementOf0(xP,sF29)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[],[f3318,f598]) ).
fof(f3351,plain,
( aElementOf0(xP,sF29)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(forward_subsumption_resolution,[],[f3323,f523]) ).
fof(f3352,plain,
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(forward_subsumption_resolution,[],[f3351,f576]) ).
fof(f3353,plain,
~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(forward_subsumption_resolution,[],[f3352,f534]) ).
fof(f3354,plain,
( $false
| ~ spl30_8 ),
inference(forward_subsumption_resolution,[],[f3353,f631]) ).
fof(f3355,plain,
~ spl30_8,
inference(avatar_contradiction_clause,[],[f3354]) ).
fof(f5295,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl30_8 ),
inference(resolution,[],[f366,f1029]) ).
fof(f5307,plain,
( $false
| spl30_8 ),
inference(forward_subsumption_resolution,[],[f5295,f531]) ).
fof(f5308,plain,
spl30_8,
inference(avatar_contradiction_clause,[],[f5307]) ).
cnf(s170,plain,
~ spl30_8,
inference(sat_conversion,[],[f3355]) ).
cnf(s272,plain,
spl30_8,
inference(sat_conversion,[],[f5308]) ).
cnf(s273,plain,
$false,
inference(rat,[],[s170,s272]) ).
fof(f5309,plain,
$false,
inference(avatar_sat_refutation,[],[s273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM629+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n004.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 20:50:08 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 5.64/1.91 % (3865696)Detected formulas, will run a generic FOF schedule.
% 5.64/1.91 % (3865720)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=1408181645:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.64/1.91 % (3865726)dis-21_1_sil=8000:lcm=predicate:random_seed=962284713: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)
% 5.64/1.91 % (3865721)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=170694007:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.64/1.91 % (3865723)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3988512314:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.64/1.91 % (3865724)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=116022679:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.64/1.91 % (3865725)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1937853979:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.64/1.91 % (3865722)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=476625501:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.64/1.91 % (3865726)Instruction limit reached!
% 5.64/1.91 % (3865726)------------------------------
% 5.64/1.91 % (3865726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865726)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865726)Termination reason: Instruction limit
% 5.64/1.91 % (3865726)Termination phase: Saturation
% 5.64/1.91 % (3865726)Time elapsed: 0.086 s
% 5.64/1.91 % (3865726)Peak memory usage: 91 MB
% 5.64/1.91 % (3865726)Instructions burned: 129 (million)
% 5.64/1.91 % (3865723)Instruction limit reached!
% 5.64/1.91 % (3865723)------------------------------
% 5.64/1.91 % (3865723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865723)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865723)Termination reason: Instruction limit
% 5.64/1.91 % (3865723)Termination phase: Saturation
% 5.64/1.91 % (3865723)Time elapsed: 0.068 s
% 5.64/1.91 % (3865723)Peak memory usage: 90 MB
% 5.64/1.91 % (3865723)Instructions burned: 111 (million)
% 5.64/1.91 % (3865724)Instruction limit reached!
% 5.64/1.91 % (3865724)------------------------------
% 5.64/1.91 % (3865724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865724)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865724)Termination reason: Instruction limit
% 5.64/1.91 % (3865724)Termination phase: Saturation
% 5.64/1.91 % (3865724)Time elapsed: 0.070 s
% 5.64/1.91 % (3865724)Peak memory usage: 89 MB
% 5.64/1.91 % (3865724)Instructions burned: 120 (million)
% 5.64/1.91 % (3865725)Instruction limit reached!
% 5.64/1.91 % (3865725)------------------------------
% 5.64/1.91 % (3865725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865725)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865725)Termination reason: Instruction limit
% 5.64/1.91 % (3865725)Termination phase: Saturation
% 5.64/1.91 % (3865725)Time elapsed: 0.101 s
% 5.64/1.91 % (3865725)Peak memory usage: 90 MB
% 5.64/1.91 % (3865725)Instructions burned: 140 (million)
% 5.64/1.91 % (3865736)lrs+10_1_sil=8000:sp=occurrence:random_seed=3211562852:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.64/1.91 % (3865738)lrs+1011_1_sil=32000:sp=occurrence:random_seed=394036379:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.64/1.91 % (3865737)lrs+10_1_sil=32000:urr=on:br=off:random_seed=337284954:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.64/1.91 % (3865737)Refutation not found, incomplete strategy
% 5.64/1.91 % (3865737)------------------------------
% 5.64/1.91 % (3865737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865737)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865737)Termination reason: Refutation not found, incomplete strategy
% 5.64/1.91 % (3865737)Time elapsed: 0.002 s
% 5.64/1.91 % (3865737)Peak memory usage: 89 MB
% 5.64/1.91 % (3865737)Instructions burned: 2 (million)
% 5.64/1.91 % (3865739)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=3800677687:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.64/1.91 % (3865736)Instruction limit reached!
% 5.64/1.91 % (3865736)------------------------------
% 5.64/1.91 % (3865736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865736)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865736)Termination reason: Instruction limit
% 5.64/1.91 % (3865736)Termination phase: Saturation
% 5.64/1.91 % (3865736)Time elapsed: 0.181 s
% 5.64/1.91 % (3865736)Peak memory usage: 92 MB
% 5.64/1.91 % (3865736)Instructions burned: 286 (million)
% 5.64/1.91 % (3865739)Instruction limit reached!
% 5.64/1.91 % (3865739)------------------------------
% 5.64/1.91 % (3865739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865739)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865739)Termination reason: Instruction limit
% 5.64/1.91 % (3865739)Termination phase: Saturation
% 5.64/1.91 % (3865739)Time elapsed: 0.144 s
% 5.64/1.91 % (3865739)Peak memory usage: 92 MB
% 5.64/1.91 % (3865739)Instructions burned: 248 (million)
% 5.64/1.91 % (3865738)Instruction limit reached!
% 5.64/1.91 % (3865738)------------------------------
% 5.64/1.91 % (3865738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865738)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865738)Termination reason: Instruction limit
% 5.64/1.91 % (3865738)Termination phase: Saturation
% 5.64/1.91 % (3865738)Time elapsed: 0.225 s
% 5.64/1.91 % (3865738)Peak memory usage: 92 MB
% 5.64/1.91 % (3865738)Instructions burned: 325 (million)
% 5.64/1.91 % (3865737)------------------------------
% 5.64/1.91 % (3865737)------------------------------
% 5.64/1.91 % (3865745)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=599915428:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.64/1.91 % (3865746)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3496046520:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.64/1.91 % (3865752)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=671720411:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.64/1.91 % (3865758)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2466199992:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.64/1.91 % (3865752)Instruction limit reached!
% 5.64/1.91 % (3865752)------------------------------
% 5.64/1.91 % (3865752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865752)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865752)Termination reason: Instruction limit
% 5.64/1.91 % (3865752)Termination phase: Saturation
% 5.64/1.91 % (3865752)Time elapsed: 0.073 s
% 5.64/1.91 % (3865752)Peak memory usage: 91 MB
% 5.64/1.91 % (3865752)Instructions burned: 113 (million)
% 5.64/1.91 % (3865720)First to succeed.
% 5.64/1.91 % (3865720)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3865696"
% 5.64/1.91 % (3865758)Instruction limit reached!
% 5.64/1.91 % (3865758)------------------------------
% 5.64/1.91 % (3865758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865758)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865758)Termination reason: Instruction limit
% 5.64/1.91 % (3865758)Termination phase: Saturation
% 5.64/1.91 % (3865758)Time elapsed: 0.068 s
% 5.64/1.91 % (3865758)Peak memory usage: 89 MB
% 5.64/1.91 % (3865758)Instructions burned: 127 (million)
% 5.64/1.91 % (3865745)Instruction limit reached!
% 5.64/1.91 % (3865745)------------------------------
% 5.64/1.91 % (3865745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.91 % (3865745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.91 % (3865745)CaDiCaL version: 2.1.3
% 5.64/1.91 % (3865745)Termination reason: Instruction limit
% 5.64/1.91 % (3865745)Termination phase: Saturation
% 5.64/1.91 % (3865745)Time elapsed: 0.189 s
% 5.64/1.91 % (3865745)Peak memory usage: 90 MB
% 5.64/1.91 % (3865745)Instructions burned: 295 (million)
% 5.64/1.91 % (3865792)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1960762014:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 5.64/1.91 % (3865793)lrs+10_1_sil=8000:sp=occurrence:random_seed=2066023848:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 5.64/1.91 % (3865720)Refutation found. Thanks to Tanya!
% 5.64/1.91 % SZS status Theorem for theBenchmark
% 5.64/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 7.60/2.10 % (3865720)------------------------------
% 7.60/2.10 % (3865720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.60/2.10 % (3865720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.60/2.10 % (3865720)CaDiCaL version: 2.1.3
% 7.60/2.10 % (3865720)Termination reason: Refutation
% 7.60/2.10 % (3865720)Time elapsed: 0.689 s
% 7.60/2.10 % (3865720)Peak memory usage: 136 MB
% 7.60/2.10 % (3865720)Instructions burned: 1568 (million)
% 7.60/2.10 % (3865720)------------------------------
% 7.60/2.10 % (3865720)------------------------------
% 7.60/2.10 % (3865696)Success in time 0.993 s
% 7.60/2.10 % Vampire exiting
%------------------------------------------------------------------------------