%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM621+3 : 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 12:16:01 PM UTC 2026
% Result : Theorem 2.95s 1.34s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 137 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 136 ( 48 ~; 38 |; 38 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 34 ( 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,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)
=> ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(f103,axiom,
( aElementOf0(xp,xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f111,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& 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,
( aElement0(xx)
& aElementOf0(xx,xQ)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f114,axiom,
( aElementOf0(xx,szNzAzT0)
& ? [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X0) = xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
fof(f115,axiom,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
fof(f116,axiom,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).
fof(f118,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f119,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
fof(f149,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f165,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f176,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f180,plain,
! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f116]) ).
fof(f182,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f119]) ).
fof(f183,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(flattening,[],[f182]) ).
fof(f239,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f240,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f239]) ).
fof(f396,plain,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(sK54,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& xx = sdtlpdtrp0(xe,sK54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X0,sK54)],[f114]) ).
fof(f518,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f649,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f705,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f176]) ).
fof(f706,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f176]) ).
fof(f724,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f725,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f731,plain,
szmzizndt0(xQ) != xx,
inference(cnf_transformation,[],[f113]) ).
fof(f732,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f736,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f396]) ).
fof(f738,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f739,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f744,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f820,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f911,plain,
xp != xx,
inference(forward_demodulation,[],[f731,f705]) ).
fof(f1101,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(xx,X0) ),
inference(resolution,[],[f739,f744]) ).
fof(f1256,plain,
( ~ aElementOf0(xn,szNzAzT0)
| sdtlseqdt0(xx,sdtlpdtrp0(xe,xn)) ),
inference(resolution,[],[f649,f1101]) ).
fof(f1260,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xn))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f649,f724]) ).
fof(f1270,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(forward_subsumption_resolution,[],[f1260,f725]) ).
fof(f1274,plain,
sdtlseqdt0(xx,sdtlpdtrp0(xe,xn)),
inference(forward_subsumption_resolution,[],[f1256,f725]) ).
fof(f1277,plain,
sdtlseqdt0(xx,xp),
inference(forward_demodulation,[],[f1274,f724]) ).
fof(f1498,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ),
inference(resolution,[],[f518,f744]) ).
fof(f1514,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1498,f738]) ).
fof(f1518,plain,
aElementOf0(xp,szNzAzT0),
inference(resolution,[],[f1514,f1270]) ).
fof(f3369,plain,
( ~ sdtlseqdt0(xp,xx)
| xp = xx
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(resolution,[],[f820,f1277]) ).
fof(f3386,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f3369,f911]) ).
fof(f3403,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f3386,f1518]) ).
fof(f3411,plain,
~ sdtlseqdt0(xp,xx),
inference(forward_subsumption_resolution,[],[f3403,f736]) ).
fof(f3414,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[],[f3411,f706]) ).
fof(f3415,plain,
$false,
inference(forward_subsumption_resolution,[],[f3414,f732]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM621+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 20:47:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 2.95/1.34 % (3862732)Detected formulas, will run a generic FOF schedule.
% 2.95/1.34 % (3862740)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2676354392:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.95/1.34 % (3862740)Instruction limit reached!
% 2.95/1.34 % (3862740)------------------------------
% 2.95/1.34 % (3862740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.34 % (3862740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.34 % (3862740)CaDiCaL version: 2.1.3
% 2.95/1.34 % (3862740)Termination reason: Instruction limit
% 2.95/1.34 % (3862740)Termination phase: Saturation
% 2.95/1.34 % (3862740)Time elapsed: 0.038 s
% 2.95/1.34 % (3862740)Peak memory usage: 90 MB
% 2.95/1.34 % (3862740)Instructions burned: 109 (million)
% 2.95/1.34 % (3862741)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1308401531:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.95/1.34 % (3862743)dis-21_1_sil=8000:lcm=predicate:random_seed=3338337479: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)
% 2.95/1.34 % (3862737)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=3920985205:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.95/1.34 % (3862739)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=2395782825:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.95/1.34 % (3862742)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1023802543:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.95/1.34 % (3862738)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=3092910914:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.95/1.34 % (3862743)Instruction limit reached!
% 2.95/1.34 % (3862743)------------------------------
% 2.95/1.34 % (3862743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.34 % (3862743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.34 % (3862743)CaDiCaL version: 2.1.3
% 2.95/1.34 % (3862743)Termination reason: Instruction limit
% 2.95/1.34 % (3862743)Termination phase: Saturation
% 2.95/1.34 % (3862743)Time elapsed: 0.069 s
% 2.95/1.34 % (3862743)Peak memory usage: 90 MB
% 2.95/1.34 % (3862743)Instructions burned: 129 (million)
% 2.95/1.34 % (3862741)First to succeed.
% 2.95/1.34 % (3862741)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3862732"
% 2.95/1.34 % (3862742)Instruction limit reached!
% 2.95/1.34 % (3862742)------------------------------
% 2.95/1.34 % (3862742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.34 % (3862742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.34 % (3862742)CaDiCaL version: 2.1.3
% 2.95/1.34 % (3862742)Termination reason: Instruction limit
% 2.95/1.34 % (3862742)Termination phase: Saturation
% 2.95/1.34 % (3862742)Time elapsed: 0.099 s
% 2.95/1.34 % (3862742)Peak memory usage: 90 MB
% 2.95/1.34 % (3862742)Instructions burned: 139 (million)
% 2.95/1.34 % (3862745)lrs+10_1_sil=8000:sp=occurrence:random_seed=457928193:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.95/1.34 % (3862745)Also succeeded, but the first one will report.
% 2.95/1.34 % (3862752)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2284656193:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.95/1.34 % (3862752)Refutation not found, incomplete strategy
% 2.95/1.34 % (3862752)------------------------------
% 2.95/1.34 % (3862752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.34 % (3862752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.34 % (3862752)CaDiCaL version: 2.1.3
% 2.95/1.34 % (3862752)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.34 % (3862752)Time elapsed: 0.007 s
% 2.95/1.34 % (3862752)Peak memory usage: 89 MB
% 2.95/1.34 % (3862752)Instructions burned: 9 (million)
% 2.95/1.34 % (3862753)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1590708811:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.95/1.34 % (3862741)Refutation found. Thanks to Tanya!
% 2.95/1.34 % SZS status Theorem for theBenchmark
% 4.00/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/1.44 % (3862741)------------------------------
% 4.00/1.44 % (3862741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.44 % (3862741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.44 % (3862741)CaDiCaL version: 2.1.3
% 4.00/1.44 % (3862741)Termination reason: Refutation
% 4.00/1.44 % (3862741)Time elapsed: 0.070 s
% 4.00/1.44 % (3862741)Peak memory usage: 89 MB
% 4.00/1.44 % (3862741)Instructions burned: 113 (million)
% 4.00/1.44 % (3862741)------------------------------
% 4.00/1.44 % (3862741)------------------------------
% 4.00/1.44 % (3862732)Success in time 0.502 s
% 4.00/1.44 % Vampire exiting
%------------------------------------------------------------------------------