%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM603+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 : 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 12:15:57 PM UTC 2026
% Result : Theorem 3.53s 1.69s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 14 unt; 0 def)
% Number of atoms : 175 ( 8 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 214 ( 90 ~; 78 |; 34 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X0)
& aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
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/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f99,axiom,
( aElementOf0(xi,szNzAzT0)
& sdtlpdtrp0(xe,xi) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5034) ).
fof(f100,conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f101,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f102,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(flattening,[],[f101]) ).
fof(f112,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(f113,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,[],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f116,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f115]) ).
fof(f138,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f139,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(flattening,[],[f138]) ).
fof(f142,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f157,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f231,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,[],[f143]) ).
fof(f232,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,[],[f231]) ).
fof(f233,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,[],[f232]) ).
fof(f234,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK10(X0,X1),X0)
& aElementOf0(sK10(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f233]) ).
fof(f278,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f292,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f113]) ).
fof(f297,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f331,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f99]) ).
fof(f332,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(cnf_transformation,[],[f102]) ).
fof(f335,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f337,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f139]) ).
fof(f339,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f341,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f364,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f369,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f493,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f341,f278]) ).
fof(f500,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[],[f493,f335]) ).
fof(f957,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(forward_subsumption_resolution,[],[f337,f341]) ).
fof(f958,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(forward_subsumption_resolution,[],[f957,f341]) ).
fof(f968,plain,
! [X0] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f958,f332]) ).
fof(f973,plain,
! [X0] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f968,f500]) ).
fof(f1090,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),xS) ),
inference(resolution,[],[f297,f973]) ).
fof(f1100,plain,
! [X0] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,xi) ),
inference(forward_subsumption_resolution,[],[f1090,f331]) ).
fof(f1106,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,xi) ),
inference(superposition,[],[f1100,f292]) ).
fof(f1107,plain,
( ~ sdtlseqdt0(sz00,xi)
| ~ aSubsetOf0(xS,xS) ),
inference(forward_subsumption_resolution,[],[f1106,f369]) ).
fof(f1124,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[],[f1107,f364]) ).
fof(f1125,plain,
~ aSubsetOf0(xS,xS),
inference(forward_subsumption_resolution,[],[f1124,f331]) ).
fof(f1126,plain,
~ aSet0(xS),
inference(resolution,[],[f1125,f339]) ).
fof(f1129,plain,
$false,
inference(forward_subsumption_resolution,[],[f1126,f500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM603+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.59 % Computer : n004.cluster.edu
% 0.13/0.59 % Model : x86_64 x86_64
% 0.13/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.59 % Memory : 8046.5625MB
% 0.13/0.59 % OS : Linux 6.8.0-71-generic
% 0.13/0.59 % CPULimit : 300
% 0.13/0.59 % WCLimit : 300
% 0.13/0.59 % DateTime : Sun Sep 27 20:42:38 UTC 2026
% 0.13/0.60 % CPUTime :
% 0.13/0.60 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.63 Running first-order theorem proving
% 0.16/0.63 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
% 3.53/1.69 % (3860650)Detected formulas, will run a generic FOF schedule.
% 3.53/1.69 % (3860657)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=1487463876:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.69 % (3860660)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3797323354:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.69 % (3860659)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1477504493:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.69 % (3860658)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2101352622:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.69 % (3860655)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=2388535620:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.69 % (3860656)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=1924349864:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.69 % (3860661)dis-21_1_sil=8000:lcm=predicate:random_seed=4052886675: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)
% 3.53/1.69 % (3860659)First to succeed.
% 3.53/1.69 % (3860659)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3860650"
% 3.53/1.69 % (3860658)Also succeeded, but the first one will report.
% 3.53/1.69 % (3860661)Instruction limit reached!
% 3.53/1.69 % (3860661)------------------------------
% 3.53/1.69 % (3860661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.69 % (3860661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.69 % (3860661)CaDiCaL version: 2.1.3
% 3.53/1.69 % (3860661)Termination reason: Instruction limit
% 3.53/1.69 % (3860661)Termination phase: Saturation
% 3.53/1.69 % (3860661)Time elapsed: 0.074 s
% 3.53/1.69 % (3860661)Peak memory usage: 91 MB
% 3.53/1.69 % (3860661)Instructions burned: 131 (million)
% 3.53/1.69 % (3860660)Also succeeded, but the first one will report.
% 3.53/1.69 % (3860669)lrs+10_1_sil=8000:sp=occurrence:random_seed=2369057841:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.69 % (3860659)Refutation found. Thanks to Tanya!
% 3.53/1.69 % SZS status Theorem for theBenchmark
% 3.53/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.69 % (3860659)------------------------------
% 3.53/1.69 % (3860659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.69 % (3860659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.69 % (3860659)CaDiCaL version: 2.1.3
% 3.53/1.69 % (3860659)Termination reason: Refutation
% 3.53/1.69 % (3860659)Time elapsed: 0.023 s
% 3.53/1.69 % (3860659)Peak memory usage: 89 MB
% 3.53/1.69 % (3860659)Instructions burned: 33 (million)
% 3.53/1.69 % (3860659)------------------------------
% 3.53/1.69 % (3860659)------------------------------
% 3.53/1.69 % (3860650)Success in time 0.422 s
% 3.53/1.69 % Vampire exiting
%------------------------------------------------------------------------------