%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:42:19 PM UTC 2026
% Result : Theorem 5.44s 2.00s
% Output : Refutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 9 unt; 3 def)
% Number of atoms : 59 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 28 ~; 19 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
fof(f5,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f7,plain,
? [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<~> ~ in(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f9,plain,
? [X0,X1] :
( ( in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) )
& ( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f10,plain,
( ( in(sK0,sK1)
| singleton(sK0) != set_difference(singleton(sK0),sK1) )
& ( ~ in(sK0,sK1)
| singleton(sK0) = set_difference(singleton(sK0),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),X1) = singleton(X0)
| in(X0,X1) )
& ( ~ in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
( ~ in(sK0,sK1)
| singleton(sK0) = set_difference(singleton(sK0),sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f13,plain,
( in(sK0,sK1)
| singleton(sK0) != set_difference(singleton(sK0),sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,definition,
~ sP2(singleton(sK0)),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f18,plain,
( in(sK0,sK1)
| sP2(set_difference(singleton(sK0),sK1)) ),
inference(inequality_splitting,[],[f13,f17]) ).
fof(f19,plain,
singleton(sK0) = set_difference(singleton(sK0),sK1),
inference(forward_subsumption_resolution,[],[f12,f15]) ).
fof(f21,definition,
( spl3_1
<=> sP2(set_difference(singleton(sK0),sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f23,plain,
( sP2(set_difference(singleton(sK0),sK1))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl3_2
<=> in(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f27,plain,
( in(sK0,sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f18,f25,f21]) ).
fof(f30,plain,
( singleton(sK0) != singleton(sK0)
| ~ in(sK0,sK1) ),
inference(superposition,[],[f14,f19]) ).
fof(f31,plain,
~ in(sK0,sK1),
inference(trivial_inequality_removal,[],[f30]) ).
fof(f32,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f31,f27]) ).
fof(f33,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f32]) ).
fof(f34,plain,
( sP2(singleton(sK0))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f23,f19]) ).
fof(f35,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f34,f17]) ).
fof(f36,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f35]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f37,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 28 03:08:25 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 5.44/2.00 % (1990105)Detected formulas, will run a generic FOF schedule.
% 5.44/2.00 % (1990112)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=1171833954:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.44/2.00 % (1990113)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=4292450455:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.44/2.00 % (1990115)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=89638138:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.44/2.00 % (1990115)First to succeed.
% 5.44/2.00 % (1990115)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1990105"
% 5.44/2.00 % (1990114)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=2495342905:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.44/2.00 % (1990118)dis-21_1_sil=8000:lcm=predicate:random_seed=1406391672: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)
% 5.44/2.00 % (1990117)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2900486428:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.44/2.00 % (1990116)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1161254330:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.44/2.00 % (1990116)Also succeeded, but the first one will report.
% 5.44/2.00 % (1990118)Also succeeded, but the first one will report.
% 5.44/2.00 % (1990117)Also succeeded, but the first one will report.
% 5.44/2.00 % (1990115)Refutation found. Thanks to Tanya!
% 5.44/2.00 % SZS status Theorem for theBenchmark
% 5.44/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 5.44/2.00 % (1990115)------------------------------
% 5.44/2.00 % (1990115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/2.00 % (1990115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/2.00 % (1990115)CaDiCaL version: 2.1.3
% 5.44/2.00 % (1990115)Termination reason: Refutation
% 5.44/2.00 % (1990115)Time elapsed: 0.004 s
% 5.44/2.00 % (1990115)Peak memory usage: 89 MB
% 5.44/2.00 % (1990115)Instructions burned: 1 (million)
% 5.44/2.00 % (1990115)------------------------------
% 5.44/2.00 % (1990115)------------------------------
% 5.44/2.00 % (1990105)Success in time 0.65 s
% 5.44/2.00 % Vampire exiting
%------------------------------------------------------------------------------