%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET593+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:44:03 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 78 ( 8 unt; 6 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 215 ( 97 ~; 86 |; 19 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 72 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
=> ( subset(difference(X0,X1),X2)
& subset(difference(X0,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th52) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,union(X1,X2))
=> ( subset(difference(X0,X1),X2)
& subset(difference(X0,X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ( ~ subset(difference(X0,X1),X2)
| ~ subset(difference(X0,X2),X1) )
& subset(X0,union(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,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,[],[f9]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f16]) ).
fof(f21,plain,
( ( ~ subset(difference(sK2,sK3),sK4)
| ~ subset(difference(sK2,sK4),sK3) )
& subset(sK2,union(sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
( ~ subset(difference(sK2,sK3),sK4)
| ~ subset(difference(sK2,sK4),sK3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ member(sK0(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f49,plain,
! [X3,X0,X1] :
( subset(X0,X1)
| member(X3,X0)
| ~ member(X3,X1) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f55,plain,
( subset(difference(sK2,sK3),sK4)
| subset(difference(sK2,sK4),sK3) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f56,plain,
~ subset(sK2,union(sK3,sK4)),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f58,definition,
( spl5_1
<=> subset(difference(sK2,sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f60,plain,
( subset(difference(sK2,sK4),sK3)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl5_2
<=> subset(difference(sK2,sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f64,plain,
( subset(difference(sK2,sK3),sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f55,f62,f58]) ).
fof(f72,plain,
( ~ member(sK0(difference(sK2,sK3),sK4),difference(sK2,sK3))
| ~ spl5_2 ),
inference(resolution,[],[f48,f64]) ).
fof(f73,plain,
( member(sK0(difference(sK2,sK3),sK4),sK3)
| ~ spl5_2 ),
inference(resolution,[],[f72,f46]) ).
fof(f74,plain,
( ~ member(sK0(difference(sK2,sK3),sK4),sK2)
| ~ spl5_2 ),
inference(resolution,[],[f72,f45]) ).
fof(f75,plain,
! [X0] :
( member(X0,sK2)
| ~ member(X0,union(sK3,sK4)) ),
inference(resolution,[],[f49,f56]) ).
fof(f79,plain,
( ~ member(sK0(difference(sK2,sK3),sK4),union(sK3,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f75,f74]) ).
fof(f82,plain,
( ~ member(sK0(difference(sK2,sK3),sK4),sK4)
| ~ member(sK0(difference(sK2,sK3),sK4),sK3)
| ~ spl5_2 ),
inference(resolution,[],[f43,f79]) ).
fof(f86,definition,
( spl5_3
<=> member(sK0(difference(sK2,sK3),sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f88,plain,
( ~ member(sK0(difference(sK2,sK3),sK4),sK3)
| spl5_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl5_4
<=> member(sK0(difference(sK2,sK3),sK4),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f92,plain,
( ~ member(sK0(difference(sK2,sK3),sK4),sK4)
| spl5_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( ~ spl5_3
| ~ spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f82,f62,f90,f86]) ).
fof(f94,plain,
( $false
| ~ spl5_2
| spl5_3 ),
inference(resolution,[],[f88,f73]) ).
fof(f95,plain,
( ~ spl5_2
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f96,plain,
( ~ subset(difference(sK2,sK3),sK4)
| spl5_4 ),
inference(resolution,[],[f92,f47]) ).
fof(f97,plain,
( ~ spl5_2
| spl5_4 ),
inference(avatar_split_clause,[],[f96,f90,f62]) ).
fof(f98,plain,
( ~ member(sK0(difference(sK2,sK4),sK3),difference(sK2,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f60,f48]) ).
fof(f100,plain,
( member(sK0(difference(sK2,sK4),sK3),sK4)
| ~ spl5_1 ),
inference(resolution,[],[f98,f46]) ).
fof(f101,plain,
( ~ member(sK0(difference(sK2,sK4),sK3),sK2)
| ~ spl5_1 ),
inference(resolution,[],[f98,f45]) ).
fof(f102,plain,
( ~ member(sK0(difference(sK2,sK4),sK3),union(sK3,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f101,f75]) ).
fof(f103,plain,
( ~ member(sK0(difference(sK2,sK4),sK3),sK4)
| ~ member(sK0(difference(sK2,sK4),sK3),sK3)
| ~ spl5_1 ),
inference(resolution,[],[f102,f43]) ).
fof(f105,definition,
( spl5_5
<=> member(sK0(difference(sK2,sK4),sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f107,plain,
( ~ member(sK0(difference(sK2,sK4),sK3),sK3)
| spl5_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl5_6
<=> member(sK0(difference(sK2,sK4),sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f111,plain,
( ~ member(sK0(difference(sK2,sK4),sK3),sK4)
| spl5_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( ~ spl5_5
| ~ spl5_6
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f103,f58,f109,f105]) ).
fof(f113,plain,
( ~ subset(difference(sK2,sK4),sK3)
| spl5_5 ),
inference(resolution,[],[f107,f47]) ).
fof(f114,plain,
( ~ spl5_1
| spl5_5 ),
inference(avatar_split_clause,[],[f113,f105,f58]) ).
fof(f115,plain,
( $false
| ~ spl5_1
| spl5_6 ),
inference(resolution,[],[f111,f100]) ).
fof(f116,plain,
( ~ spl5_1
| spl5_6 ),
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f93]) ).
cnf(s3,plain,
( ~ spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f95]) ).
cnf(s4,plain,
( ~ spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f97]) ).
cnf(s5,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( ~ spl5_1
| spl5_5 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
( ~ spl5_1
| spl5_6 ),
inference(sat_conversion,[],[f116]) ).
cnf(s8,plain,
~ spl5_2,
inference(rat,[],[s2,s3,s4]) ).
cnf(s9,plain,
spl5_1,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
spl5_6,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
spl5_5,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s5,s10,s11,s9]) ).
fof(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET593+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:17:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.46 % (2603757)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (2603765)dis+10_1_sil=32000:sp=arity:random_seed=284753292:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (2603763)% WARNING: option uhcvi not known.
% 0.10/0.46 % (2603762)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2500061538_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (2603763)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3510982652:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % (2603764)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1963154030:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (2603767)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=515799781:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (2603766)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2041467326:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (2603768)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2635646744:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (2603768) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2603757-2603768"...
% 0.10/0.46 % (2603766) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2603757-2603766"...
% 0.10/0.46 % TRYING [4]
% 0.10/0.46 % (2603768)...printing done.
% 0.10/0.46 % (2603766)...printing done.
% 0.10/0.46 % (2603768)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (2603768)------------------------------
% 0.10/0.46 % (2603768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (2603768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (2603768)CaDiCaL version: 2.1.3
% 0.10/0.46 % (2603768)Termination reason: Refutation
% 0.10/0.46 % (2603768)Time elapsed: 0.004 s
% 0.10/0.46 % (2603768)Peak memory usage: 12 MB
% 0.10/0.46 % (2603768)Instructions burned: 4 (million)
% 0.10/0.46 % (2603757)Success in time 0.039 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------