%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET013+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:39:31 PM UTC 2026
% Result : Theorem 3.43s 11.49s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 11 unt; 6 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 58 ~; 73 |; 13 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 51 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(intersection(X0,X1),intersection(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI06) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : equal_set(intersection(X0,X1),intersection(X1,X0)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
? [X0,X1] : ~ equal_set(intersection(X0,X1),intersection(X1,X0)),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f19,plain,
~ equal_set(intersection(sK0,sK1),intersection(sK1,sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f23]) ).
fof(f26,plain,
~ equal_set(intersection(sK0,sK1),intersection(sK1,sK0)),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
( ~ subset(intersection(sK0,sK1),intersection(sK1,sK0))
| ~ subset(intersection(sK1,sK0),intersection(sK0,sK1)) ),
inference(resolution,[],[f30,f26]) ).
fof(f41,definition,
( spl3_1
<=> subset(intersection(sK1,sK0),intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f42,plain,
( ~ subset(intersection(sK1,sK0),intersection(sK0,sK1))
| spl3_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,definition,
( spl3_2
<=> subset(intersection(sK0,sK1),intersection(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f45,plain,
( ~ subset(intersection(sK0,sK1),intersection(sK1,sK0))
| spl3_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f39,f44,f41]) ).
fof(f47,plain,
( ~ member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),intersection(sK0,sK1))
| spl3_1 ),
inference(resolution,[],[f42,f33]) ).
fof(f48,plain,
( member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),intersection(sK1,sK0))
| spl3_1 ),
inference(resolution,[],[f42,f32]) ).
fof(f50,plain,
( member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK1)
| spl3_1 ),
inference(resolution,[],[f48,f28]) ).
fof(f51,plain,
( member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK0)
| spl3_1 ),
inference(resolution,[],[f48,f27]) ).
fof(f57,plain,
( ~ member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK0)
| ~ member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK1)
| spl3_1 ),
inference(resolution,[],[f29,f47]) ).
fof(f59,definition,
( spl3_3
<=> member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f60,plain,
( ~ member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK1)
| spl3_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,definition,
( spl3_4
<=> member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f63,plain,
( ~ member(sK2(intersection(sK1,sK0),intersection(sK0,sK1)),sK0)
| spl3_4 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f57,f41,f62,f59]) ).
fof(f65,plain,
( $false
| spl3_1
| spl3_3 ),
inference(resolution,[],[f60,f50]) ).
fof(f66,plain,
( spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f69,plain,
( $false
| spl3_1
| spl3_4 ),
inference(resolution,[],[f63,f51]) ).
fof(f70,plain,
( spl3_1
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f71,plain,
( ~ member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),intersection(sK1,sK0))
| spl3_2 ),
inference(resolution,[],[f45,f33]) ).
fof(f72,plain,
( member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),intersection(sK0,sK1))
| spl3_2 ),
inference(resolution,[],[f45,f32]) ).
fof(f74,plain,
( ~ member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK1)
| ~ member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK0)
| spl3_2 ),
inference(resolution,[],[f71,f29]) ).
fof(f76,definition,
( spl3_5
<=> member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f77,plain,
( ~ member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK0)
| spl3_5 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,definition,
( spl3_6
<=> member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f80,plain,
( ~ member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK1)
| spl3_6 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( ~ spl3_5
| ~ spl3_6
| spl3_2 ),
inference(avatar_split_clause,[],[f74,f44,f79,f76]) ).
fof(f82,plain,
( member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK0)
| spl3_2 ),
inference(resolution,[],[f72,f28]) ).
fof(f83,plain,
( member(sK2(intersection(sK0,sK1),intersection(sK1,sK0)),sK1)
| spl3_2 ),
inference(resolution,[],[f72,f27]) ).
fof(f84,plain,
( $false
| spl3_2
| spl3_5 ),
inference(resolution,[],[f82,f77]) ).
fof(f85,plain,
( spl3_2
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f86,plain,
( $false
| spl3_2
| spl3_6 ),
inference(resolution,[],[f83,f80]) ).
fof(f87,plain,
( spl3_2
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f86]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
( spl3_2
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f81]) ).
cnf(s6,plain,
( spl3_2
| spl3_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
( spl3_2
| spl3_6 ),
inference(sat_conversion,[],[f87]) ).
cnf(s8,plain,
spl3_1,
inference(rat,[],[s2,s3,s4]) ).
cnf(s9,plain,
~ spl3_2,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
spl3_6,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
spl3_5,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s5,s10,s11,s9]) ).
fof(f88,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/10.40 % Computer : n017.cluster.edu
% 0.10/10.40 % Model : x86_64 x86_64
% 0.10/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.40 % Memory : 8046.5625MB
% 0.10/10.40 % OS : Linux 6.8.0-71-generic
% 0.10/10.40 % CPULimit : 300
% 0.10/10.40 % WCLimit : 300
% 0.10/10.40 % DateTime : Sun Sep 27 23:59:02 UTC 2026
% 0.10/10.41 % CPUTime :
% 0.10/10.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/10.44 Running first-order theorem proving
% 0.10/10.44 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
% 3.43/11.49 % (3093428)Detected formulas, will run a generic FOF schedule.
% 3.43/11.49 % (3093435)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=2940227465:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/11.49 % (3093434)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=3053213796:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/11.49 % (3093439)dis-21_1_sil=8000:lcm=predicate:random_seed=2932579732: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)
% 3.43/11.49 % (3093439)First to succeed.
% 3.43/11.49 % (3093439)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3093428"
% 3.43/11.49 % (3093433)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=2350540236:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/11.49 % (3093438)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3794021869:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/11.49 % (3093436)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4094552550:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/11.49 % (3093437)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=581853348:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/11.49 % (3093436)Refutation not found, incomplete strategy
% 3.43/11.49 % (3093436)------------------------------
% 3.43/11.49 % (3093436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/11.49 % (3093436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/11.49 % (3093436)CaDiCaL version: 2.1.3
% 3.43/11.49 % (3093436)Termination reason: Refutation not found, incomplete strategy
% 3.43/11.49 % (3093436)Time elapsed: 0.001 s
% 3.43/11.49 % (3093436)Peak memory usage: 87 MB
% 3.43/11.49 % (3093437)Also succeeded, but the first one will report.
% 3.43/11.49 % (3093438)Also succeeded, but the first one will report.
% 3.43/11.49 % (3093436)------------------------------
% 3.43/11.49 % (3093436)------------------------------
% 3.43/11.49 % (3093439)Refutation found. Thanks to Tanya!
% 3.43/11.49 % SZS status Theorem for theBenchmark
% 3.43/11.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/11.49 % (3093439)------------------------------
% 3.43/11.49 % (3093439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/11.49 % (3093439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/11.49 % (3093439)CaDiCaL version: 2.1.3
% 3.43/11.49 % (3093439)Termination reason: Refutation
% 3.43/11.49 % (3093439)Time elapsed: 0.003 s
% 3.43/11.49 % (3093439)Peak memory usage: 89 MB
% 3.43/11.49 % (3093439)Instructions burned: 2 (million)
% 3.43/11.49 % (3093439)------------------------------
% 3.43/11.49 % (3093439)------------------------------
% 3.43/11.49 % (3093428)Success in time 0.42 s
% 3.43/11.49 % Vampire exiting
%------------------------------------------------------------------------------