%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM590+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 : n017.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 12:15:53 PM UTC 2026
% Result : Theorem 4.89s 1.83s
% Output : Refutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 2 def)
% Number of atoms : 120 ( 17 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 124 ( 37 ~; 29 |; 47 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(f90,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448) ).
fof(f91,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(xY)
& ! [X0] :
( aElementOf0(X0,xY)
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
fof(f92,conjecture,
( ! [X0] :
( aElementOf0(X0,xY)
=> aElementOf0(X0,szNzAzT0) )
| aSubsetOf0(xY,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f93,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,xY)
=> aElementOf0(X0,szNzAzT0) )
| aSubsetOf0(xY,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f92]) ).
fof(f109,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(rectify,[],[f91]) ).
fof(f216,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(f228,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(ennf_transformation,[],[f109]) ).
fof(f229,plain,
( ? [X0] :
( ~ aElementOf0(X0,szNzAzT0)
& aElementOf0(X0,xY) )
& ~ aSubsetOf0(xY,szNzAzT0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f383,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( ( aElementOf0(X1,xY)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,xY) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(nnf_transformation,[],[f228]) ).
fof(f384,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( ( aElementOf0(X1,xY)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,xY) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(flattening,[],[f383]) ).
fof(f385,plain,
( ~ aElementOf0(sK59,szNzAzT0)
& aElementOf0(sK59,xY)
& ~ aSubsetOf0(xY,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(X0,sK59)],[f229]) ).
fof(f606,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f712,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f90]) ).
fof(f716,plain,
! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,xY) ),
inference(cnf_transformation,[],[f384]) ).
fof(f723,plain,
aElementOf0(sK59,xY),
inference(cnf_transformation,[],[f385]) ).
fof(f724,plain,
~ aElementOf0(sK59,szNzAzT0),
inference(cnf_transformation,[],[f385]) ).
fof(f1143,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(X0,xY) ),
inference(resolution,[],[f606,f716]) ).
fof(f1146,definition,
( spl61_28
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl61_28])],[avatar_definition]) ).
fof(f1147,plain,
( ~ aElementOf0(xi,szNzAzT0)
| spl61_28 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f1153,definition,
( spl61_30
<=> ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xY) ) ),
introduced(definition,[new_symbols(definition,[spl61_30])],[avatar_definition]) ).
fof(f1154,plain,
( ! [X0] :
( ~ aElementOf0(X0,xY)
| aElementOf0(X0,szNzAzT0) )
| ~ spl61_30 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f1155,plain,
( ~ spl61_28
| spl61_30 ),
inference(avatar_split_clause,[],[f1143,f1153,f1146]) ).
fof(f1156,plain,
( $false
| spl61_28 ),
inference(resolution,[],[f1147,f712]) ).
fof(f1157,plain,
spl61_28,
inference(avatar_contradiction_clause,[],[f1156]) ).
fof(f1158,plain,
( aElementOf0(sK59,szNzAzT0)
| ~ spl61_30 ),
inference(resolution,[],[f1154,f723]) ).
fof(f1159,plain,
( $false
| ~ spl61_30 ),
inference(resolution,[],[f1158,f724]) ).
fof(f1160,plain,
~ spl61_30,
inference(avatar_contradiction_clause,[],[f1159]) ).
cnf(s24,plain,
( ~ spl61_28
| spl61_30 ),
inference(sat_conversion,[],[f1155]) ).
cnf(s25,plain,
spl61_28,
inference(sat_conversion,[],[f1157]) ).
cnf(s26,plain,
~ spl61_30,
inference(sat_conversion,[],[f1160]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s24,s26,s25]) ).
fof(f1161,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM590+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:34:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 4.89/1.83 % (2921138)Detected formulas, will run a generic FOF schedule.
% 4.89/1.83 % (2921163)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=3951776541:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.89/1.83 % (2921170)dis-21_1_sil=8000:lcm=predicate:random_seed=346201072: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)
% 4.89/1.83 % (2921167)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1674540381:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.89/1.83 % (2921170)First to succeed.
% 4.89/1.83 % (2921170)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2921138"
% 4.89/1.83 % (2921166)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=3587946140:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.89/1.83 % (2921168)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=786684030:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.89/1.83 % (2921169)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=694347778:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.89/1.83 % (2921164)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=3068577802:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.89/1.83 % (2921168)Also succeeded, but the first one will report.
% 4.89/1.83 % (2921169)Also succeeded, but the first one will report.
% 4.89/1.83 % (2921167)Also succeeded, but the first one will report.
% 4.89/1.83 % (2921170)Refutation found. Thanks to Tanya!
% 4.89/1.83 % SZS status Theorem for theBenchmark
% 4.89/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 4.89/1.83 % (2921170)------------------------------
% 4.89/1.83 % (2921170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.89/1.83 % (2921170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.83 % (2921170)CaDiCaL version: 2.1.3
% 4.89/1.83 % (2921170)Termination reason: Refutation
% 4.89/1.83 % (2921170)Time elapsed: 0.018 s
% 4.89/1.83 % (2921170)Peak memory usage: 90 MB
% 4.89/1.83 % (2921170)Instructions burned: 25 (million)
% 4.89/1.83 % (2921170)------------------------------
% 4.89/1.83 % (2921170)------------------------------
% 4.89/1.83 % (2921138)Success in time 0.577 s
% 4.89/1.83 % Vampire exiting
%------------------------------------------------------------------------------