%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM625+1 : 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 : n002.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 12:25:04 PM UTC 2026
% Result : ContradictoryAxioms 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 25 unt; 6 def)
% Number of atoms : 272 ( 38 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 319 ( 121 ~; 115 |; 63 &)
% ( 15 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 89 ( 0 sgn 83 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f113,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).
fof(f120,axiom,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5496) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f147,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(f148,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,[],[f147]) ).
fof(f257,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f258,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f259,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f148,f258,f257]) ).
fof(f264,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,[],[f137]) ).
fof(f265,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,[],[f264]) ).
fof(f266,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,[],[f265]) ).
fof(f267,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f266]) ).
fof(f274,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP2(X2,X0,X1) )
& ( sP2(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f258]) ).
fof(f275,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f274]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ( sP2(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) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f257]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ( sP2(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) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(flattening,[],[f276]) ).
fof(f278,plain,
! [X0,X1,X2] :
( ( sP2(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) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f277]) ).
fof(f279,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK7(X0,X1,X2))
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X0) )
& ( ( aElement0(sK7(X0,X1,X2))
& aElementOf0(sK7(X0,X1,X2),X1)
& sK7(X0,X1,X2) != X2 )
| aElementOf0(sK7(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) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f278]) ).
fof(f323,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f331,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f350,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f352,plain,
! [X2,X0,X1,X4] :
( X2 != X4
| ~ aElementOf0(X4,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f361,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f369,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f525,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f527,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f528,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f529,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f540,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f550,plain,
xp = xx,
inference(cnf_transformation,[],[f120]) ).
fof(f551,plain,
szmzizndt0(xQ) = xx,
inference(definition_unfolding,[],[f527,f550]) ).
fof(f561,plain,
! [X0,X1] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f350]) ).
fof(f562,plain,
! [X0,X1,X4] :
( ~ sP2(X0,X1,X4)
| ~ aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f352]) ).
fof(f624,plain,
xP = sdtmndt0(xQ,xx),
inference(forward_demodulation,[],[f528,f551]) ).
fof(f759,plain,
( aElement0(xx)
| ~ aSet0(xP) ),
inference(resolution,[],[f323,f540]) ).
fof(f760,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f759,f529]) ).
fof(f762,definition,
( spl29_20
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl29_20])],[avatar_definition]) ).
fof(f763,plain,
( aSet0(xQ)
| ~ spl29_20 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f766,definition,
( spl29_21
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl29_21])],[avatar_definition]) ).
fof(f768,plain,
( aElement0(xx)
| ~ spl29_21 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f812,plain,
spl29_21,
inference(avatar_split_clause,[],[f760,f766]) ).
fof(f821,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f331,f525]) ).
fof(f825,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f821,f369]) ).
fof(f835,plain,
spl29_20,
inference(avatar_split_clause,[],[f825,f762]) ).
fof(f1044,plain,
( sP2(xP,xQ,xx)
| ~ sP3(xx,xQ) ),
inference(superposition,[],[f561,f624]) ).
fof(f1046,definition,
( spl29_43
<=> sP3(xx,xQ) ),
introduced(definition,[new_symbols(definition,[spl29_43])],[avatar_definition]) ).
fof(f1048,plain,
( ~ sP3(xx,xQ)
| spl29_43 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f1050,definition,
( spl29_44
<=> sP2(xP,xQ,xx) ),
introduced(definition,[new_symbols(definition,[spl29_44])],[avatar_definition]) ).
fof(f1052,plain,
( sP2(xP,xQ,xx)
| ~ spl29_44 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f1053,plain,
( ~ spl29_43
| spl29_44 ),
inference(avatar_split_clause,[],[f1044,f1050,f1046]) ).
fof(f1055,plain,
( ~ aSet0(xQ)
| ~ aElement0(xx)
| spl29_43 ),
inference(resolution,[],[f1048,f361]) ).
fof(f1056,plain,
( ~ aElement0(xx)
| ~ spl29_20
| spl29_43 ),
inference(forward_subsumption_resolution,[],[f1055,f763]) ).
fof(f1057,plain,
( $false
| ~ spl29_20
| ~ spl29_21
| spl29_43 ),
inference(forward_subsumption_resolution,[],[f1056,f768]) ).
fof(f1058,plain,
( ~ spl29_20
| ~ spl29_21
| spl29_43 ),
inference(avatar_contradiction_clause,[],[f1057]) ).
fof(f2374,plain,
( ~ aElementOf0(xx,xP)
| ~ spl29_44 ),
inference(resolution,[],[f1052,f562]) ).
fof(f2376,plain,
( $false
| ~ spl29_44 ),
inference(forward_subsumption_resolution,[],[f2374,f540]) ).
fof(f2377,plain,
~ spl29_44,
inference(avatar_contradiction_clause,[],[f2376]) ).
cnf(s18,plain,
spl29_21,
inference(sat_conversion,[],[f812]) ).
cnf(s23,plain,
spl29_20,
inference(sat_conversion,[],[f835]) ).
cnf(s45,plain,
( ~ spl29_43
| spl29_44 ),
inference(sat_conversion,[],[f1053]) ).
cnf(s46,plain,
( ~ spl29_20
| ~ spl29_21
| spl29_43 ),
inference(sat_conversion,[],[f1058]) ).
cnf(s104,plain,
~ spl29_44,
inference(sat_conversion,[],[f2377]) ).
cnf(s114,plain,
~ spl29_43,
inference(rat,[],[s45,s104]) ).
cnf(s127,plain,
~ spl29_21,
inference(rat,[],[s46,s114,s23]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s18,s127]) ).
fof(f2378,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:52:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.17/0.48 % (3862793)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3862801)dis+10_1_sil=32000:sp=arity:random_seed=1609556740:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3862799)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3862798)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2886011358_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3862799)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3796208128:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3862800)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1810995433:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3862802)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2461185834:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3862803)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=610191603:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3862804)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=497417541:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3862801) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3862793-3862801"...
% 0.17/0.48 % (3862801)...printing done.
% 0.17/0.48 % (3862801)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status ContradictoryAxioms for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3862801)------------------------------
% 0.17/0.48 % (3862801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3862801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3862801)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3862801)Termination reason: Refutation
% 0.17/0.48 % (3862801)Time elapsed: 0.021 s
% 0.17/0.48 % (3862801)Peak memory usage: 13 MB
% 0.17/0.48 % (3862801)Instructions burned: 54 (million)
% 0.17/0.48 % (3862793)Success in time 0.057 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------