%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM582+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:24:54 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 8 unt; 2 def)
% Number of atoms : 181 ( 18 equ)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 210 ( 59 ~; 47 |; 83 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [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)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(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)
=> ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f85,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(f88,conjecture,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f89,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f99,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [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)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f138,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f207,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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,[],[f99]) ).
fof(f208,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(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(flattening,[],[f207]) ).
fof(f210,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f211,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f210]) ).
fof(f216,plain,
( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(ennf_transformation,[],[f89]) ).
fof(f228,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f229,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f230,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(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(definition_folding,[],[f208,f229,f228]) ).
fof(f311,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f230]) ).
fof(f318,plain,
( ~ aElementOf0(sK41,xS)
& aElementOf0(sK41,sdtlpdtrp0(xN,xi))
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X0,sK41)],[f216]) ).
fof(f366,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f373,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f534,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f311]) ).
fof(f541,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f548,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f85]) ).
fof(f569,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(cnf_transformation,[],[f318]) ).
fof(f1214,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(superposition,[],[f541,f534]) ).
fof(f1215,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1214,f373]) ).
fof(f1217,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1215,f366]) ).
fof(f1244,plain,
~ aElementOf0(xi,szNzAzT0),
inference(resolution,[],[f1217,f569]) ).
fof(f1247,plain,
$false,
inference(forward_subsumption_resolution,[],[f1244,f548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM582+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:35:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.33 Running first-order model finding
% 0.08/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.39 % (2713838)Will run a generic schedule for satisfiability detection.
% 0.08/0.39 % (2713844)% WARNING: option uhcvi not known.
% 0.08/0.39 % (2713843)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1658536140_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.39 % (2713845)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=631317112:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.39 % (2713844)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3236710829:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.39 % (2713846)dis+10_1_sil=32000:sp=arity:random_seed=1639556003:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.39 % (2713847)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2620337855:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.39 % (2713848)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3236534736:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.39 % (2713849)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3166403288:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.39 % (2713845) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2713838-2713845"...
% 0.08/0.39 % TRYING [1]
% 0.08/0.39 % (2713845)...printing done.
% 0.08/0.39 % TRYING [2]
% 0.08/0.39 % (2713845)Refutation found. Thanks to Tanya!
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.39 % (2713845)------------------------------
% 0.08/0.39 % (2713845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.39 % (2713845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.39 % (2713845)CaDiCaL version: 2.1.3
% 0.08/0.39 % (2713845)Termination reason: Refutation
% 0.08/0.39 % (2713845)Time elapsed: 0.014 s
% 0.08/0.39 % (2713845)Peak memory usage: 12 MB
% 0.08/0.39 % (2713845)Instructions burned: 33 (million)
% 0.08/0.39 % (2713838)Success in time 0.049 s
% 0.08/0.39 % Vampire exiting
%------------------------------------------------------------------------------