%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET091+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:40:03 PM UTC 2026
% Result : Theorem 3.50s 1.53s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 11 unt; 1 def)
% Number of atoms : 53 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 23 ~; 13 |; 10 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [X0] :
( member(member_of(X0),universal_class)
| member_of(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_universal_self) ).
fof(f47,axiom,
! [X0] :
( singleton(member_of(X0)) = X0
| member_of(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_self) ).
fof(f48,conjecture,
! [X0,X1] :
( ( ~ ? [X2] :
( member(X2,universal_class)
& X0 = singleton(X2) )
& X0 = X1 )
=> member_of(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_when_not_a_singleton) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( ( ~ ? [X2] :
( member(X2,universal_class)
& X0 = singleton(X2) )
& X0 = X1 )
=> member_of(X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f66,plain,
? [X0,X1] :
( member_of(X0) != X1
& ! [X2] :
( ~ member(X2,universal_class)
| singleton(X2) != X0 )
& X0 = X1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f67,plain,
? [X0,X1] :
( member_of(X0) != X1
& ! [X2] :
( ~ member(X2,universal_class)
| singleton(X2) != X0 )
& X0 = X1 ),
inference(flattening,[],[f66]) ).
fof(f110,plain,
( sK7 != member_of(sK6)
& ! [X2] :
( ~ member(X2,universal_class)
| singleton(X2) != sK6 )
& sK6 = sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f67]) ).
fof(f200,plain,
! [X0] :
( member(member_of(X0),universal_class)
| member_of(X0) = X0 ),
inference(cnf_transformation,[],[f46]) ).
fof(f201,plain,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f202,plain,
sK6 = sK7,
inference(cnf_transformation,[],[f110]) ).
fof(f203,plain,
! [X2] :
( singleton(X2) != sK6
| ~ member(X2,universal_class) ),
inference(cnf_transformation,[],[f110]) ).
fof(f204,plain,
sK7 != member_of(sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f211,plain,
sK6 != member_of(sK6),
inference(forward_demodulation,[],[f204,f202]) ).
fof(f307,plain,
( sK6 != sK6
| sK6 = singleton(member_of(sK6)) ),
inference(superposition,[],[f211,f201]) ).
fof(f309,plain,
sK6 = singleton(member_of(sK6)),
inference(trivial_inequality_removal,[],[f307]) ).
fof(f316,plain,
( sK6 != sK6
| ~ member(member_of(sK6),universal_class) ),
inference(superposition,[],[f203,f309]) ).
fof(f317,plain,
~ member(member_of(sK6),universal_class),
inference(trivial_inequality_removal,[],[f316]) ).
fof(f319,definition,
( spl8_10
<=> member(member_of(sK6),universal_class) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f321,plain,
( ~ member(member_of(sK6),universal_class)
| spl8_10 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f329,plain,
~ spl8_10,
inference(avatar_split_clause,[],[f317,f319]) ).
fof(f331,plain,
( sK6 = member_of(sK6)
| spl8_10 ),
inference(resolution,[],[f321,f200]) ).
fof(f339,plain,
( $false
| spl8_10 ),
inference(forward_subsumption_resolution,[],[f331,f211]) ).
fof(f340,plain,
spl8_10,
inference(avatar_contradiction_clause,[],[f339]) ).
cnf(s7,plain,
~ spl8_10,
inference(sat_conversion,[],[f329]) ).
cnf(s8,plain,
spl8_10,
inference(sat_conversion,[],[f340]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s7,s8]) ).
fof(f341,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET091+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n001.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 28 00:44:34 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 3.50/1.53 % (4114893)Detected formulas, will run a generic FOF schedule.
% 3.50/1.53 % (4114905)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2807731050:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.53 % (4114906)dis-21_1_sil=8000:lcm=predicate:random_seed=3224012951: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)
% 3.50/1.53 % (4114905)First to succeed.
% 3.50/1.53 % (4114906)Also succeeded, but the first one will report.
% 3.50/1.53 % (4114905)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4114893"
% 3.50/1.53 % (4114900)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=475687316:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.53 % (4114901)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=1305481008:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.53 % (4114902)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=1323740083:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.53 % (4114904)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3487939396:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.53 % (4114903)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2881756763:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.53 % (4114904)Also succeeded, but the first one will report.
% 3.50/1.53 % (4114903)Also succeeded, but the first one will report.
% 3.50/1.53 % (4114905)Refutation found. Thanks to Tanya!
% 3.50/1.53 % SZS status Theorem for theBenchmark
% 3.50/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.53 % (4114905)------------------------------
% 3.50/1.53 % (4114905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.53 % (4114905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.53 % (4114905)CaDiCaL version: 2.1.3
% 3.50/1.53 % (4114905)Termination reason: Refutation
% 3.50/1.53 % (4114905)Time elapsed: 0.007 s
% 3.50/1.53 % (4114905)Peak memory usage: 90 MB
% 3.50/1.53 % (4114905)Instructions burned: 10 (million)
% 3.50/1.53 % (4114905)------------------------------
% 3.50/1.53 % (4114905)------------------------------
% 3.50/1.53 % (4114893)Success in time 0.407 s
% 3.50/1.53 % Vampire exiting
%------------------------------------------------------------------------------