%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:25:04 PM UTC 2026
% Result : Theorem 7.40s 1.69s
% Output : Refutation 7.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 90 ( 27 unt; 1 def)
% Number of atoms : 270 ( 38 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 300 ( 120 ~; 107 |; 46 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?)
% 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(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X0)
& aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
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(f65,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElement0(sdtlpdtrp0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).
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(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(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(f117,plain,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(flattening,[],[f116]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f136,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f137,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(flattening,[],[f136]) ).
fof(f140,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f141,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f140]) ).
fof(f202,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(f203,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,[],[f202]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( aElement0(sdtlpdtrp0(X0,X1))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f230,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(f231,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,[],[f230]) ).
fof(f232,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f248,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f262,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f266,plain,
! [X2,X0,X1] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(cnf_transformation,[],[f137]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aSet0(X2)
| sdtmndt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f141]) ).
fof(f292,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f348,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| slbdtsldtrb0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f203]) ).
fof(f361,plain,
! [X0,X1] :
( aElement0(sdtlpdtrp0(X0,X1))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f404,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f406,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f231]) ).
fof(f410,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f411,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f428,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f429,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(cnf_transformation,[],[f248]) ).
fof(f430,plain,
aFunction0(xe),
inference(cnf_transformation,[],[f248]) ).
fof(f452,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f457,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f459,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f460,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f463,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f113]) ).
fof(f464,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[],[f114]) ).
fof(f465,plain,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(cnf_transformation,[],[f117]) ).
fof(f475,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f284]) ).
fof(f492,plain,
! [X2,X3,X0] :
( ~ aElementOf0(sbrdtbr0(X3),szNzAzT0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| slbdtsldtrb0(X0,sbrdtbr0(X3)) != X2 ),
inference(equality_resolution,[],[f348]) ).
fof(f493,plain,
! [X3,X0] :
( aElementOf0(X3,slbdtsldtrb0(X0,sbrdtbr0(X3)))
| ~ aSet0(X0)
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(sbrdtbr0(X3),szNzAzT0) ),
inference(equality_resolution,[],[f492]) ).
fof(f632,plain,
( aSet0(xD)
| ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(superposition,[],[f475,f464]) ).
fof(f654,plain,
( aElement0(xp)
| ~ aElementOf0(xn,szDzozmdt0(xe))
| ~ aFunction0(xe) ),
inference(superposition,[],[f361,f459]) ).
fof(f659,plain,
( aElement0(xp)
| ~ aElementOf0(xn,szDzozmdt0(xe)) ),
inference(forward_subsumption_resolution,[],[f654,f430]) ).
fof(f663,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aElement0(xp) ),
inference(forward_demodulation,[],[f659,f429]) ).
fof(f666,plain,
aElement0(xp),
inference(forward_subsumption_resolution,[],[f663,f460]) ).
fof(f701,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[],[f428,f460]) ).
fof(f708,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[],[f701,f459]) ).
fof(f1260,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X2)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2) ),
inference(forward_subsumption_resolution,[],[f266,f262]) ).
fof(f1475,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0)
| ~ aSubsetOf0(xP,X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f493,f457]) ).
fof(f1478,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0)
| ~ aSubsetOf0(xP,X0) ),
inference(forward_subsumption_resolution,[],[f1475,f404]) ).
fof(f2374,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(forward_subsumption_resolution,[],[f406,f410]) ).
fof(f2375,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2374,f411]) ).
fof(f2390,plain,
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f2375,f464]) ).
fof(f2391,plain,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
inference(forward_subsumption_resolution,[],[f2390,f460]) ).
fof(f3625,definition,
( spl25_50
<=> aSet0(xD) ),
introduced(definition,[new_symbols(definition,[spl25_50])],[avatar_definition]) ).
fof(f3626,plain,
( aSet0(xD)
| ~ spl25_50 ),
inference(avatar_component_clause,[],[f3625]) ).
fof(f3627,plain,
( ~ aSet0(xD)
| spl25_50 ),
inference(avatar_component_clause,[],[f3625]) ).
fof(f4335,plain,
( ~ aSet0(xD)
| ~ aSubsetOf0(xP,xD) ),
inference(resolution,[],[f1478,f465]) ).
fof(f4832,plain,
( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xn)))
| spl25_50 ),
inference(forward_subsumption_resolution,[],[f632,f3627]) ).
fof(f4833,plain,
( ~ aElement0(xp)
| ~ aSet0(sdtlpdtrp0(xN,xn))
| spl25_50 ),
inference(forward_demodulation,[],[f4832,f708]) ).
fof(f4834,plain,
( ~ aSet0(sdtlpdtrp0(xN,xn))
| spl25_50 ),
inference(forward_subsumption_resolution,[],[f4833,f666]) ).
fof(f4835,plain,
( ! [X0] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),X0)
| ~ aSet0(X0) )
| spl25_50 ),
inference(resolution,[],[f4834,f262]) ).
fof(f4853,plain,
( ~ aSet0(szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0)
| spl25_50 ),
inference(resolution,[],[f4835,f411]) ).
fof(f4864,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl25_50 ),
inference(forward_subsumption_resolution,[],[f4853,f292]) ).
fof(f4867,plain,
( $false
| spl25_50 ),
inference(forward_subsumption_resolution,[],[f4864,f460]) ).
fof(f4868,plain,
spl25_50,
inference(avatar_contradiction_clause,[],[f4867]) ).
fof(f4881,plain,
( ~ aSubsetOf0(xP,xD)
| ~ spl25_50 ),
inference(forward_subsumption_resolution,[],[f4335,f3626]) ).
fof(f4889,plain,
( ! [X0] :
( ~ aSet0(xP)
| ~ aSubsetOf0(X0,xD)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(xD) )
| ~ spl25_50 ),
inference(resolution,[],[f4881,f1260]) ).
fof(f4890,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,xD)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(xD) )
| ~ spl25_50 ),
inference(forward_subsumption_resolution,[],[f4889,f452]) ).
fof(f4891,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,xD)
| ~ aSubsetOf0(xP,X0) )
| ~ spl25_50 ),
inference(forward_subsumption_resolution,[],[f4890,f3626]) ).
fof(f4900,plain,
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ spl25_50 ),
inference(resolution,[],[f4891,f2391]) ).
fof(f4911,plain,
( $false
| ~ spl25_50 ),
inference(forward_subsumption_resolution,[],[f4900,f463]) ).
fof(f4912,plain,
~ spl25_50,
inference(avatar_contradiction_clause,[],[f4911]) ).
cnf(s64,plain,
spl25_50,
inference(sat_conversion,[],[f4868]) ).
cnf(s66,plain,
~ spl25_50,
inference(sat_conversion,[],[f4912]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s64,s66]) ).
fof(f4914,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM629+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n001.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:56:02 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.40/1.69 % (3939582)Will run a generic schedule for satisfiability detection.
% 7.40/1.69 % (3939590)dis+10_1_sil=32000:sp=arity:random_seed=1067399122:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.40/1.69 % (3939588)% WARNING: option uhcvi not known.
% 7.40/1.69 % (3939587)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3885698650_2999 on theBenchmark for (2999ds/0Mi)
% 7.40/1.69 % (3939588)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3517079332:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.40/1.69 % (3939592)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1533608862:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.40/1.69 % (3939589)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4003469386:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.40/1.69 % (3939591)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3372643893:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.40/1.69 % (3939593)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=434048703:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.40/1.69 % TRYING [1]
% 7.40/1.69 % TRYING [2]
% 7.40/1.69 % (3939590)Instruction limit reached!
% 7.40/1.69 % (3939590)------------------------------
% 7.40/1.69 % (3939590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939590)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939590)Termination reason: Instruction limit
% 7.40/1.69 % (3939590)Termination phase: Saturation
% 7.40/1.69 % (3939590)Time elapsed: 0.037 s
% 7.40/1.69 % (3939590)Peak memory usage: 13 MB
% 7.40/1.69 % (3939590)Instructions burned: 103 (million)
% 7.40/1.69 % TRYING [3]
% 7.40/1.69 % (3939601)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=69477667:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.40/1.69 % TRYING [4]
% 7.40/1.69 % TRYING [1]
% 7.40/1.69 % TRYING [2]
% 7.40/1.69 % TRYING [3]
% 7.40/1.69 % (3939591)Instruction limit reached!
% 7.40/1.69 % (3939591)------------------------------
% 7.40/1.69 % (3939591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939591)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939591)Termination reason: Instruction limit
% 7.40/1.69 % (3939591)Termination phase: Saturation
% 7.40/1.69 % (3939591)Time elapsed: 0.074 s
% 7.40/1.69 % (3939591)Peak memory usage: 13 MB
% 7.40/1.69 % (3939591)Instructions burned: 116 (million)
% 7.40/1.69 % (3939592)Instruction limit reached!
% 7.40/1.69 % (3939592)------------------------------
% 7.40/1.69 % (3939592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939592)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939592)Termination reason: Instruction limit
% 7.40/1.69 % (3939592)Termination phase: Saturation
% 7.40/1.69 % (3939592)Time elapsed: 0.078 s
% 7.40/1.69 % (3939592)Peak memory usage: 13 MB
% 7.40/1.69 % (3939592)Instructions burned: 133 (million)
% 7.40/1.69 % TRYING [4]
% 7.40/1.69 % (3939603)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=616736823:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 7.40/1.69 % (3939604)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3767991928:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.40/1.69 % (3939593)Instruction limit reached!
% 7.40/1.69 % (3939593)------------------------------
% 7.40/1.69 % (3939593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939593)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939593)Termination reason: Instruction limit
% 7.40/1.69 % (3939593)Termination phase: Saturation
% 7.40/1.69 % (3939593)Time elapsed: 0.099 s
% 7.40/1.69 % (3939593)Peak memory usage: 14 MB
% 7.40/1.69 % (3939593)Instructions burned: 159 (million)
% 7.40/1.69 % (3939607)ott-21_1_sil=16000:fs=off:random_seed=4127968006:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.40/1.69 % TRYING [5]
% 7.40/1.69 % TRYING [5]
% 7.40/1.69 % (3939603)Instruction limit reached!
% 7.40/1.69 % (3939603)------------------------------
% 7.40/1.69 % (3939603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939603)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939603)Termination reason: Instruction limit
% 7.40/1.69 % (3939603)Termination phase: Saturation
% 7.40/1.69 % (3939603)Time elapsed: 0.088 s
% 7.40/1.69 % (3939603)Peak memory usage: 14 MB
% 7.40/1.69 % (3939603)Instructions burned: 132 (million)
% 7.40/1.69 % (3939609)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1275484841:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 7.40/1.69 % (3939601)Instruction limit reached!
% 7.40/1.69 % (3939601)------------------------------
% 7.40/1.69 % (3939601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939601)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939601)Termination reason: Instruction limit
% 7.40/1.69 % (3939601)Termination phase: Finite model building constraint generation
% 7.40/1.69 % (3939601)Time elapsed: 0.167 s
% 7.40/1.69 % (3939601)Peak memory usage: 35 MB
% 7.40/1.69 % (3939601)Instructions burned: 718 (million)
% 7.40/1.69 % (3939607)Instruction limit reached!
% 7.40/1.69 % (3939607)------------------------------
% 7.40/1.69 % (3939607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939607)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939607)Termination reason: Instruction limit
% 7.40/1.69 % (3939607)Termination phase: Saturation
% 7.40/1.69 % (3939607)Time elapsed: 0.103 s
% 7.40/1.69 % (3939607)Peak memory usage: 13 MB
% 7.40/1.69 % (3939607)Instructions burned: 180 (million)
% 7.40/1.69 % (3939611)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1179792218:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 7.40/1.69 % TRYING [1]
% 7.40/1.69 % TRYING [2]
% 7.40/1.69 % (3939612)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4060175945:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 7.40/1.69 % TRYING [3]
% 7.40/1.69 % TRYING [6]
% 7.40/1.69 % TRYING [4]
% 7.40/1.69 % (3939611)Instruction limit reached!
% 7.40/1.69 % (3939611)------------------------------
% 7.40/1.69 % (3939611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939611)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939611)Termination reason: Instruction limit
% 7.40/1.69 % (3939611)Termination phase: Finite model building SAT solving
% 7.40/1.69 % (3939611)Time elapsed: 0.190 s
% 7.40/1.69 % (3939611)Peak memory usage: 23 MB
% 7.40/1.69 % (3939611)Instructions burned: 866 (million)
% 7.40/1.69 % (3939615)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3356743617:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 7.40/1.69 % (3939604)Instruction limit reached!
% 7.40/1.69 % (3939604)------------------------------
% 7.40/1.69 % (3939604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939604)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939604)Termination reason: Instruction limit
% 7.40/1.69 % (3939604)Termination phase: Saturation
% 7.40/1.69 % (3939604)Time elapsed: 0.392 s
% 7.40/1.69 % (3939604)Peak memory usage: 18 MB
% 7.40/1.69 % (3939604)Instructions burned: 686 (million)
% 7.40/1.69 % (3939617)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2962897978:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 7.40/1.69 % (3939609)Instruction limit reached!
% 7.40/1.69 % (3939609)------------------------------
% 7.40/1.69 % (3939609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939609)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939609)Termination reason: Instruction limit
% 7.40/1.69 % (3939609)Termination phase: Saturation
% 7.40/1.69 % (3939609)Time elapsed: 0.333 s
% 7.40/1.69 % (3939609)Peak memory usage: 15 MB
% 7.40/1.69 % (3939609)Instructions burned: 485 (million)
% 7.40/1.69 % (3939619)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=994170901:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 7.40/1.69 % TRYING [7]
% 7.40/1.69 % (3939617)Instruction limit reached!
% 7.40/1.69 % (3939617)------------------------------
% 7.40/1.69 % (3939617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939617)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939617)Termination reason: Instruction limit
% 7.40/1.69 % (3939617)Termination phase: Saturation
% 7.40/1.69 % (3939617)Time elapsed: 0.266 s
% 7.40/1.69 % (3939617)Peak memory usage: 20 MB
% 7.40/1.69 % (3939617)Instructions burned: 693 (million)
% 7.40/1.69 % (3939621)fmb+10_1_sil=64000:random_seed=97115470:i=22061:nm=2:gsp=on_2991 on theBenchmark for (2991ds/22061Mi)
% 7.40/1.69 % TRYING [1]
% 7.40/1.69 % TRYING [2]
% 7.40/1.69 % TRYING [3]
% 7.40/1.69 % TRYING [14]
% 7.40/1.69 % TRYING [4]
% 7.40/1.69 % (3939615)Instruction limit reached!
% 7.40/1.69 % (3939615)------------------------------
% 7.40/1.69 % (3939615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939615)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939615)Termination reason: Instruction limit
% 7.40/1.69 % (3939615)Termination phase: Finite model building constraint generation
% 7.40/1.69 % (3939615)Time elapsed: 0.421 s
% 7.40/1.69 % (3939615)Peak memory usage: 98 MB
% 7.40/1.69 % (3939615)Instructions burned: 890 (million)
% 7.40/1.69 % (3939623)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2794030326:i=9515:nm=5_2990 on theBenchmark for (2990ds/9515Mi)
% 7.40/1.69 % TRYING [20]
% 7.40/1.69 % TRYING [5]
% 7.40/1.69 % (3939612)Instruction limit reached!
% 7.40/1.69 % (3939612)------------------------------
% 7.40/1.69 % (3939612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939612)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939612)Termination reason: Instruction limit
% 7.40/1.69 % (3939612)Termination phase: Saturation
% 7.40/1.69 % (3939612)Time elapsed: 0.734 s
% 7.40/1.69 % (3939612)Peak memory usage: 24 MB
% 7.40/1.69 % (3939612)Instructions burned: 1180 (million)
% 7.40/1.69 % (3939625)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4186821708:fmbsr=1.7:i=920_2989 on theBenchmark for (2989ds/920Mi)
% 7.40/1.69 % TRYING [8]
% 7.40/1.69 % (3939619)Instruction limit reached!
% 7.40/1.69 % (3939619)------------------------------
% 7.40/1.69 % (3939619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939619)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939619)Termination reason: Instruction limit
% 7.40/1.69 % (3939619)Termination phase: Saturation
% 7.40/1.69 % (3939619)Time elapsed: 0.481 s
% 7.40/1.69 % (3939619)Peak memory usage: 21 MB
% 7.40/1.69 % (3939619)Instructions burned: 880 (million)
% 7.40/1.69 % (3939627)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=827541711:i=5131_2989 on theBenchmark for (2989ds/5131Mi)
% 7.40/1.69 % (3939627) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3939582-3939627"...
% 7.40/1.69 % (3939627)...printing done.
% 7.40/1.69 % (3939627)Refutation found. Thanks to Tanya!
% 7.40/1.69 % SZS status Theorem for theBenchmark
% 7.40/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 7.40/1.69 % (3939627)------------------------------
% 7.40/1.69 % (3939627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.40/1.69 % (3939627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.40/1.69 % (3939627)CaDiCaL version: 2.1.3
% 7.40/1.69 % (3939627)Termination reason: Refutation
% 7.40/1.69 % (3939627)Time elapsed: 0.130 s
% 7.40/1.69 % (3939627)Peak memory usage: 14 MB
% 7.40/1.69 % (3939627)Instructions burned: 202 (million)
% 7.40/1.69 % (3939582)Success in time 1.253 s
% 7.40/1.69 % Vampire exiting
%------------------------------------------------------------------------------