%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM538+2 : 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 : 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 12:15:39 PM UTC 2026
% Result : Theorem 0.08s 5.80s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 17 unt; 5 def)
% Number of atoms : 187 ( 23 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 218 ( 93 ~; 80 |; 27 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(f43,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
fof(f44,axiom,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522) ).
fof(f45,axiom,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522_02) ).
fof(f46,conjecture,
( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f52,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f54]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f66]) ).
fof(f73,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f74,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS)
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(flattening,[],[f73]) ).
fof(f82,plain,
aSet0(xS),
inference(cnf_transformation,[],[f44]) ).
fof(f83,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f45]) ).
fof(f85,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnf_transformation,[],[f74]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f92,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f95,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f110,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f114,definition,
~ sP3(szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f115,plain,
sP3(sbrdtbr0(xS)),
inference(inequality_splitting,[],[f90,f114]) ).
fof(f116,definition,
~ sP4(xx),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f117,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| sP4(X0) ),
inference(inequality_splitting,[],[f85,f116]) ).
fof(f126,plain,
! [X0] :
( ~ sP3(sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),X0)))
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(superposition,[],[f114,f110]) ).
fof(f127,plain,
! [X0] :
( ~ sP3(sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),X0)))
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(forward_subsumption_resolution,[],[f126,f89]) ).
fof(f137,definition,
( spl7_3
<=> isFinite0(sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f139,plain,
( ~ isFinite0(sdtmndt0(xS,xx))
| spl7_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl7_4
<=> ! [X0] :
( ~ sP3(sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f142,plain,
( ! [X0] :
( ~ sP3(sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( ~ spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f127,f141,f137]) ).
fof(f154,plain,
( ~ aSet0(xS)
| ~ isFinite0(xS)
| ~ aElement0(xx)
| spl7_3 ),
inference(resolution,[],[f139,f92]) ).
fof(f173,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f83,f91]) ).
fof(f182,plain,
( ~ isFinite0(xS)
| ~ aElement0(xx)
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f154,f82]) ).
fof(f190,definition,
( spl7_6
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f194,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f173,f82]) ).
fof(f195,plain,
( ~ aElement0(xx)
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f182,f84]) ).
fof(f196,plain,
spl7_6,
inference(avatar_split_clause,[],[f194,f190]) ).
fof(f197,plain,
( ~ spl7_6
| spl7_3 ),
inference(avatar_split_clause,[],[f195,f137,f190]) ).
fof(f209,plain,
( ~ sP3(sbrdtbr0(xS))
| ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElementOf0(xx,xS)
| ~ aSet0(xS)
| ~ spl7_4 ),
inference(superposition,[],[f142,f95]) ).
fof(f212,plain,
( ~ sP3(sbrdtbr0(xS))
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElementOf0(xx,xS)
| ~ aSet0(xS)
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f209,f91]) ).
fof(f213,plain,
( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElementOf0(xx,xS)
| ~ aSet0(xS)
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f212,f115]) ).
fof(f214,plain,
( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aSet0(xS)
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f213,f83]) ).
fof(f215,plain,
( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f214,f82]) ).
fof(f217,plain,
( sP4(xx)
| ~ spl7_4 ),
inference(resolution,[],[f215,f117]) ).
fof(f223,plain,
( $false
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f217,f116]) ).
fof(f224,plain,
~ spl7_4,
inference(avatar_contradiction_clause,[],[f223]) ).
cnf(s2,plain,
( ~ spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f143]) ).
cnf(s5,plain,
spl7_6,
inference(sat_conversion,[],[f196]) ).
cnf(s6,plain,
( spl7_3
| ~ spl7_6 ),
inference(sat_conversion,[],[f197]) ).
cnf(s7,plain,
~ spl7_4,
inference(sat_conversion,[],[f224]) ).
cnf(s8,plain,
spl7_3,
inference(rat,[],[s6,s5]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s8]) ).
fof(f226,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/5.32 % Computer : n012.cluster.edu
% 0.05/5.32 % Model : x86_64 x86_64
% 0.05/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.32 % Memory : 8046.5625MB
% 0.05/5.32 % OS : Linux 6.8.0-71-generic
% 0.05/5.32 % CPULimit : 300
% 0.05/5.32 % WCLimit : 300
% 0.05/5.32 % DateTime : Sun Sep 27 20:23:47 UTC 2026
% 0.05/5.32 % CPUTime :
% 0.05/5.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/5.34 Running first-order theorem proving
% 0.05/5.34 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
% 0.08/5.80 % (2706591)Detected formulas, will run a generic FOF schedule.
% 0.08/5.80 % (2706601)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=86979573:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.08/5.80 % (2706597)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=3761179055:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.08/5.80 % (2706602)dis-21_1_sil=8000:lcm=predicate:random_seed=1811624127: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)
% 0.08/5.80 % (2706599)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2214312609:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.08/5.80 % (2706598)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=3082565850:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.08/5.80 % (2706600)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3745999078:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.08/5.80 % (2706596)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=2745578444:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.08/5.80 % (2706599)First to succeed.
% 0.08/5.80 % (2706599)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2706591"
% 0.08/5.80 % (2706600)Also succeeded, but the first one will report.
% 0.08/5.80 % (2706602)Instruction limit reached!
% 0.08/5.80 % (2706602)------------------------------
% 0.08/5.80 % (2706602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/5.80 % (2706602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/5.80 % (2706602)CaDiCaL version: 2.1.3
% 0.08/5.80 % (2706602)Termination reason: Instruction limit
% 0.08/5.80 % (2706602)Termination phase: Saturation
% 0.08/5.80 % (2706602)Time elapsed: 0.028 s
% 0.08/5.80 % (2706602)Peak memory usage: 89 MB
% 0.08/5.80 % (2706602)Instructions burned: 132 (million)
% 0.08/5.80 % (2706601)Instruction limit reached!
% 0.08/5.80 % (2706601)------------------------------
% 0.08/5.80 % (2706601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/5.80 % (2706601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/5.80 % (2706601)CaDiCaL version: 2.1.3
% 0.08/5.80 % (2706601)Termination reason: Instruction limit
% 0.08/5.80 % (2706601)Termination phase: Saturation
% 0.08/5.80 % (2706601)Time elapsed: 0.055 s
% 0.08/5.80 % (2706601)Peak memory usage: 90 MB
% 0.08/5.80 % (2706601)Instructions burned: 142 (million)
% 0.08/5.80 % (2706610)lrs+10_1_sil=8000:sp=occurrence:random_seed=16355552:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.08/5.80 % (2706610)Also succeeded, but the first one will report.
% 0.08/5.80 % (2706611)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1923825342:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.08/5.80 % (2706611)Also succeeded, but the first one will report.
% 0.08/5.80 % (2706599)Refutation found. Thanks to Tanya!
% 0.08/5.80 % SZS status Theorem for theBenchmark
% 0.08/5.80 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/5.89 % (2706599)------------------------------
% 0.08/5.89 % (2706599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/5.89 % (2706599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/5.89 % (2706599)CaDiCaL version: 2.1.3
% 0.08/5.89 % (2706599)Termination reason: Refutation
% 0.08/5.89 % (2706599)Time elapsed: 0.003 s
% 0.08/5.89 % (2706599)Peak memory usage: 90 MB
% 0.08/5.89 % (2706599)Instructions burned: 6 (million)
% 0.08/5.89 % (2706599)------------------------------
% 0.08/5.89 % (2706599)------------------------------
% 0.08/5.89 % (2706591)Success in time 0.264 s
% 0.08/5.89 % Vampire exiting
%------------------------------------------------------------------------------