%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET013+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:42:34 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 11 unt; 4 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 92 ( 36 ~; 43 |; 3 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(intersection(X0,X1),intersection(X1,X0)),
file('/export/starexec/sandbox/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] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
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(f19,plain,
? [X0,X1] : ~ equal_set(intersection(X0,X1),intersection(X1,X0)),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f4]) ).
fof(f47,plain,
~ equal_set(intersection(sK3,sK4),intersection(sK4,sK3)),
inference(cnf_transformation,[],[f19]) ).
fof(f58,plain,
( ~ subset(intersection(sK3,sK4),intersection(sK4,sK3))
| ~ subset(intersection(sK4,sK3),intersection(sK3,sK4)) ),
inference(resolution,[],[f23,f47]) ).
fof(f60,definition,
( spl5_1
<=> subset(intersection(sK4,sK3),intersection(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f62,plain,
( ~ subset(intersection(sK4,sK3),intersection(sK3,sK4))
| spl5_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl5_2
<=> subset(intersection(sK3,sK4),intersection(sK4,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f66,plain,
( ~ subset(intersection(sK3,sK4),intersection(sK4,sK3))
| spl5_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f58,f64,f60]) ).
fof(f68,plain,
( ~ member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),intersection(sK3,sK4))
| spl5_1 ),
inference(resolution,[],[f62,f22]) ).
fof(f69,plain,
( member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),intersection(sK4,sK3))
| spl5_1 ),
inference(resolution,[],[f62,f21]) ).
fof(f83,plain,
( member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),sK4)
| spl5_1 ),
inference(resolution,[],[f69,f27]) ).
fof(f84,plain,
( member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),sK3)
| spl5_1 ),
inference(resolution,[],[f69,f26]) ).
fof(f151,plain,
( ~ member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),sK3)
| ~ member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),sK4)
| spl5_1 ),
inference(resolution,[],[f28,f68]) ).
fof(f152,plain,
( ~ member(sK0(intersection(sK4,sK3),intersection(sK3,sK4)),sK4)
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f151,f84]) ).
fof(f153,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f152,f83]) ).
fof(f154,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f153]) ).
fof(f162,plain,
( ~ member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),intersection(sK4,sK3))
| spl5_2 ),
inference(resolution,[],[f66,f22]) ).
fof(f163,plain,
( member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),intersection(sK3,sK4))
| spl5_2 ),
inference(resolution,[],[f66,f21]) ).
fof(f190,plain,
( ~ member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK4)
| ~ member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK3)
| spl5_2 ),
inference(resolution,[],[f162,f28]) ).
fof(f193,definition,
( spl5_3
<=> member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f195,plain,
( ~ member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK3)
| spl5_3 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f197,definition,
( spl5_4
<=> member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f200,plain,
( ~ spl5_3
| ~ spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f190,f64,f197,f193]) ).
fof(f216,plain,
( member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK3)
| spl5_2 ),
inference(resolution,[],[f163,f27]) ).
fof(f217,plain,
( member(sK0(intersection(sK3,sK4),intersection(sK4,sK3)),sK4)
| spl5_2 ),
inference(resolution,[],[f163,f26]) ).
fof(f221,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f217,f64,f197]) ).
fof(f222,plain,
( $false
| spl5_2
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f216,f195]) ).
fof(f223,plain,
( spl5_2
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f222]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f154]) ).
cnf(s3,plain,
( spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f200]) ).
cnf(s4,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f221]) ).
cnf(s5,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f223]) ).
cnf(s6,plain,
~ spl5_2,
inference(rat,[],[s1,s2]) ).
cnf(s7,plain,
spl5_3,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl5_4,
inference(rat,[],[s4,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7,s6]) ).
fof(f224,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:05:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.15/0.46 % (1067390)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (1067396)% WARNING: option uhcvi not known.
% 0.15/0.46 % (1067396)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3919071712:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (1067395)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3153023731_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (1067397)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2419976292:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (1067398)dis+10_1_sil=32000:sp=arity:random_seed=2083946996:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (1067400)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=495181657:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (1067399)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1248045792:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (1067401)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2148239489:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % TRYING [4]
% 0.15/0.46 % (1067399) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1067390-1067399"...
% 0.15/0.46 % TRYING [5]
% 0.15/0.46 % (1067399)...printing done.
% 0.15/0.46 % (1067399)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (1067399)------------------------------
% 0.15/0.46 % (1067399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (1067399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (1067399)CaDiCaL version: 2.1.3
% 0.15/0.46 % (1067399)Termination reason: Refutation
% 0.15/0.46 % (1067399)Time elapsed: 0.008 s
% 0.15/0.46 % (1067399)Peak memory usage: 12 MB
% 0.15/0.46 % (1067399)Instructions burned: 10 (million)
% 0.15/0.46 % (1067390)Success in time 0.054 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------