%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM561+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:24:49 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 16 unt; 1 def)
% Number of atoms : 146 ( 31 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 181 ( 74 ~; 70 |; 28 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 50 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911_02) ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f80,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(flattening,[],[f72]) ).
fof(f91,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f167,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 ) ) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f230,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(nnf_transformation,[],[f173]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f230]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( aElementOf0(X5,X1)
& sdtlpdtrp0(X0,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6 ) )
& ( ? [X8] :
( aElementOf0(X8,X1)
& sdtlpdtrp0(X0,X8) = X6 )
| ~ aElementOf0(X6,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(rectify,[],[f231]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != sK17(X0,X1,X2) )
| ~ aElementOf0(sK17(X0,X1,X2),X2) )
& ( ( aElementOf0(sK18(X0,X1,X2),X1)
& sK17(X0,X1,X2) = sdtlpdtrp0(X0,sK18(X0,X1,X2)) )
| aElementOf0(sK17(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6 ) )
& ( ( aElementOf0(sK19(X0,X1,X6),X1)
& sdtlpdtrp0(X0,sK19(X0,X1,X6)) = X6 )
| ~ aElementOf0(X6,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X3,sK17(X0,X1,X2)),skolemize(X5,sK18(X0,X1,X2)),skolemize(X8,sK19(X0,X1,X6))],[f232]) ).
fof(f246,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f347,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f359,plain,
! [X2,X0,X1,X6,X7] :
( aElementOf0(X6,X2)
| ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f364,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f365,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f366,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f80]) ).
fof(f395,plain,
! [X2,X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),X2)
| ~ aElementOf0(X7,X1)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f359]) ).
fof(f396,plain,
! [X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),sdtlcdtrc0(X0,X1))
| ~ aElementOf0(X7,X1)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f395]) ).
fof(f428,definition,
( spl20_4
<=> aSet0(szDzozmdt0(xF)) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f429,plain,
( aSet0(szDzozmdt0(xF))
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f430,plain,
( ~ aSet0(szDzozmdt0(xF))
| spl20_4 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f438,plain,
( ~ aFunction0(xF)
| spl20_4 ),
inference(resolution,[],[f430,f347]) ).
fof(f439,plain,
( $false
| spl20_4 ),
inference(forward_subsumption_resolution,[],[f438,f364]) ).
fof(f440,plain,
spl20_4,
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f1312,plain,
( ~ aElementOf0(xx,szDzozmdt0(xF))
| ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(resolution,[],[f396,f366]) ).
fof(f1320,plain,
( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(forward_subsumption_resolution,[],[f1312,f365]) ).
fof(f1321,plain,
~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
inference(forward_subsumption_resolution,[],[f1320,f364]) ).
fof(f1322,plain,
~ aSet0(szDzozmdt0(xF)),
inference(resolution,[],[f1321,f246]) ).
fof(f1323,plain,
( $false
| ~ spl20_4 ),
inference(forward_subsumption_resolution,[],[f1322,f429]) ).
fof(f1324,plain,
~ spl20_4,
inference(avatar_contradiction_clause,[],[f1323]) ).
cnf(s5,plain,
spl20_4,
inference(sat_conversion,[],[f440]) ).
cnf(s52,plain,
~ spl20_4,
inference(sat_conversion,[],[f1324]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s5,s52]) ).
fof(f1325,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM561+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:32:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.48 % (3185297)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3185305)dis+10_1_sil=32000:sp=arity:random_seed=3401977735:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3185303)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3185302)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=55874528_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (3185303)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=743993668:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3185304)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1382364999:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3185306)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1078519159:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3185307)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1477140739:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3185308)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4079429878:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (3185305) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3185297-3185305"...
% 0.16/0.48 % (3185305)...printing done.
% 0.16/0.48 % (3185305)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3185305)------------------------------
% 0.16/0.48 % (3185305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3185305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3185305)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3185305)Termination reason: Refutation
% 0.16/0.48 % (3185305)Time elapsed: 0.014 s
% 0.16/0.48 % (3185305)Peak memory usage: 13 MB
% 0.16/0.48 % (3185305)Instructions burned: 33 (million)
% 0.16/0.48 % (3185297)Success in time 0.049 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------