%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM625+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 : n011.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 12:16:02 PM UTC 2026
% Result : ContradictoryAxioms 2.45s 1.30s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 18 unt; 2 def)
% Number of atoms : 229 ( 38 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 281 ( 104 ~; 98 |; 63 &)
% ( 11 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 89 ( 83 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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(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(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f113,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f120,axiom,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5496) ).
fof(f164,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f189,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(f190,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,[],[f189]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f242,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f243,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f244,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f190,f243,f242]) ).
fof(f252,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,[],[f164]) ).
fof(f253,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,[],[f252]) ).
fof(f254,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,[],[f253]) ).
fof(f255,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))],[f254]) ).
fof(f263,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f243]) ).
fof(f264,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f263]) ).
fof(f265,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f242]) ).
fof(f266,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f265]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| X2 = X3
| ~ aElementOf0(X3,X0) )
& ( ( aElement0(X3)
& aElementOf0(X3,X1)
& X2 != X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f266]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK18(X0,X1,X2))
| ~ aElementOf0(sK18(X0,X1,X2),X1)
| sK18(X0,X1,X2) = X2
| ~ aElementOf0(sK18(X0,X1,X2),X0) )
& ( ( aElement0(sK18(X0,X1,X2))
& aElementOf0(sK18(X0,X1,X2),X1)
& sK18(X0,X1,X2) != X2 )
| aElementOf0(sK18(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X3,sK18(X0,X1,X2))],[f267]) ).
fof(f354,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f356,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f357,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f358,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f369,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f379,plain,
xp = xx,
inference(cnf_transformation,[],[f120]) ).
fof(f382,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f388,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f421,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f264]) ).
fof(f423,plain,
! [X2,X0,X1,X4] :
( X2 != X4
| ~ aElementOf0(X4,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
fof(f432,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f496,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f497,plain,
szmzizndt0(xQ) = xx,
inference(definition_unfolding,[],[f356,f379]) ).
fof(f507,plain,
! [X0,X1] :
( sP0(sdtmndt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f421]) ).
fof(f508,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f423]) ).
fof(f535,plain,
xP = sdtmndt0(xQ,xx),
inference(forward_demodulation,[],[f357,f497]) ).
fof(f555,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f388,f354]) ).
fof(f559,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f555,f382]) ).
fof(f592,plain,
( aElement0(xx)
| ~ aSet0(xP) ),
inference(resolution,[],[f496,f369]) ).
fof(f593,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f592,f358]) ).
fof(f643,plain,
( sP0(xP,xQ,xx)
| ~ sP1(xx,xQ) ),
inference(superposition,[],[f507,f535]) ).
fof(f650,plain,
( ~ sP1(xx,xQ)
| ~ aElementOf0(xx,xP) ),
inference(resolution,[],[f643,f508]) ).
fof(f652,plain,
~ sP1(xx,xQ),
inference(forward_subsumption_resolution,[],[f650,f369]) ).
fof(f653,plain,
( ~ aSet0(xQ)
| ~ aElement0(xx) ),
inference(resolution,[],[f652,f432]) ).
fof(f654,plain,
~ aElement0(xx),
inference(forward_subsumption_resolution,[],[f653,f559]) ).
fof(f655,plain,
$false,
inference(forward_subsumption_resolution,[],[f654,f593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM625+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:50:01 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.45/1.30 % (2743913)Detected formulas, will run a generic FOF schedule.
% 2.45/1.30 % (2743924)dis-21_1_sil=8000:lcm=predicate:random_seed=2086366142:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.45/1.30 % (2743921)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3626432736:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/1.30 % (2743918)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=1601539466:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/1.30 % (2743919)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=953132506:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/1.30 % (2743920)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=3811759716:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/1.30 % (2743922)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1939473161:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/1.30 % (2743923)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2720314939:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/1.30 % (2743924)Instruction limit reached!
% 2.45/1.30 % (2743924)------------------------------
% 2.45/1.30 % (2743924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.30 % (2743924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.30 % (2743924)CaDiCaL version: 2.1.3
% 2.45/1.30 % (2743924)Termination reason: Instruction limit
% 2.45/1.30 % (2743924)Termination phase: Saturation
% 2.45/1.30 % (2743924)Time elapsed: 0.042 s
% 2.45/1.30 % (2743924)Peak memory usage: 91 MB
% 2.45/1.30 % (2743924)Instructions burned: 132 (million)
% 2.45/1.30 % (2743922)First to succeed.
% 2.45/1.30 % (2743922)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2743913"
% 2.45/1.30 % (2743921)Instruction limit reached!
% 2.45/1.30 % (2743921)------------------------------
% 2.45/1.30 % (2743921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.30 % (2743921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.30 % (2743921)CaDiCaL version: 2.1.3
% 2.45/1.30 % (2743921)Termination reason: Instruction limit
% 2.45/1.30 % (2743921)Termination phase: Saturation
% 2.45/1.30 % (2743921)Time elapsed: 0.071 s
% 2.45/1.30 % (2743921)Peak memory usage: 89 MB
% 2.45/1.30 % (2743921)Instructions burned: 110 (million)
% 2.45/1.30 % (2743923)Also succeeded, but the first one will report.
% 2.45/1.30 % (2743932)lrs+10_1_sil=8000:sp=occurrence:random_seed=1562342816:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.45/1.30 % (2743932)Also succeeded, but the first one will report.
% 2.45/1.30 % (2743933)lrs+10_1_sil=32000:urr=on:br=off:random_seed=134741803:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.45/1.30 % (2743933)Refutation not found, incomplete strategy
% 2.45/1.30 % (2743933)------------------------------
% 2.45/1.30 % (2743933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.30 % (2743933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.30 % (2743933)CaDiCaL version: 2.1.3
% 2.45/1.30 % (2743933)Termination reason: Refutation not found, incomplete strategy
% 2.45/1.30 % (2743933)Time elapsed: 0.001 s
% 2.45/1.30 % (2743933)Peak memory usage: 87 MB
% 2.45/1.30 % (2743933)Instructions burned: 1 (million)
% 2.45/1.30 % (2743922)Refutation found. Thanks to Tanya!
% 2.45/1.30 % SZS status ContradictoryAxioms for theBenchmark
% 2.45/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.39 % (2743922)------------------------------
% 3.44/1.39 % (2743922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.39 % (2743922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.39 % (2743922)CaDiCaL version: 2.1.3
% 3.44/1.39 % (2743922)Termination reason: Refutation
% 3.44/1.39 % (2743922)Time elapsed: 0.011 s
% 3.44/1.39 % (2743922)Peak memory usage: 89 MB
% 3.44/1.39 % (2743922)Instructions burned: 15 (million)
% 3.44/1.39 % (2743922)------------------------------
% 3.44/1.39 % (2743922)------------------------------
% 3.44/1.39 % (2743913)Success in time 0.423 s
% 3.44/1.39 % Vampire exiting
%------------------------------------------------------------------------------