%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU159+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:52:10 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 7 unt; 5 def)
% Number of atoms : 157 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 149 ( 58 ~; 75 |; 3 &)
% ( 11 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 49 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f68,conjecture,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f69,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f100,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f123,plain,
? [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<~> ( in(X0,X2)
& in(X1,X2) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| X0 = X3
| ~ in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f10]) ).
fof(f161,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f10]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( X0 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f10]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f178,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f179,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f250,plain,
( ~ in(sK20,sK21)
| ~ in(sK19,sK21)
| ~ subset(unordered_pair(sK19,sK20),sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f251,plain,
( in(sK20,sK21)
| subset(unordered_pair(sK19,sK20),sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f252,plain,
( in(sK19,sK21)
| subset(unordered_pair(sK19,sK20),sK21) ),
inference(cnf_transformation,[],[f123]) ).
fof(f334,plain,
! [X2,X3,X1] :
( in(X3,X2)
| unordered_pair(X3,X1) != X2 ),
inference(equality_resolution,[],[f162]) ).
fof(f335,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f334]) ).
fof(f336,plain,
! [X2,X3,X0] :
( in(X3,X2)
| unordered_pair(X0,X3) != X2 ),
inference(equality_resolution,[],[f161]) ).
fof(f337,plain,
! [X3,X0] : in(X3,unordered_pair(X0,X3)),
inference(equality_resolution,[],[f336]) ).
fof(f338,plain,
! [X3,X0,X1] :
( ~ in(X3,unordered_pair(X0,X1))
| X0 = X3
| X1 = X3 ),
inference(equality_resolution,[],[f160]) ).
fof(f359,definition,
( spl24_1
<=> subset(unordered_pair(sK19,sK20),sK21) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f360,plain,
( subset(unordered_pair(sK19,sK20),sK21)
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f361,plain,
( ~ subset(unordered_pair(sK19,sK20),sK21)
| spl24_1 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f363,definition,
( spl24_2
<=> in(sK19,sK21) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f364,plain,
( in(sK19,sK21)
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( ~ in(sK19,sK21)
| spl24_2 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f367,definition,
( spl24_3
<=> in(sK20,sK21) ),
introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition]) ).
fof(f368,plain,
( in(sK20,sK21)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f369,plain,
( ~ in(sK20,sK21)
| spl24_3 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f370,plain,
( ~ spl24_1
| ~ spl24_2
| ~ spl24_3 ),
inference(avatar_split_clause,[],[f250,f367,f363,f359]) ).
fof(f371,plain,
( spl24_1
| spl24_3 ),
inference(avatar_split_clause,[],[f251,f367,f359]) ).
fof(f372,plain,
( spl24_1
| spl24_2 ),
inference(avatar_split_clause,[],[f252,f363,f359]) ).
fof(f552,plain,
( in(sK10(unordered_pair(sK19,sK20),sK21),unordered_pair(sK19,sK20))
| spl24_1 ),
inference(resolution,[],[f178,f361]) ).
fof(f560,plain,
( ~ in(sK10(unordered_pair(sK19,sK20),sK21),sK21)
| spl24_1 ),
inference(resolution,[],[f179,f361]) ).
fof(f1183,plain,
( sK19 = sK10(unordered_pair(sK19,sK20),sK21)
| sK20 = sK10(unordered_pair(sK19,sK20),sK21)
| spl24_1 ),
inference(resolution,[],[f338,f552]) ).
fof(f1191,definition,
( spl24_10
<=> sK20 = sK10(unordered_pair(sK19,sK20),sK21) ),
introduced(definition,[new_symbols(definition,[spl24_10])],[avatar_definition]) ).
fof(f1193,plain,
( sK20 = sK10(unordered_pair(sK19,sK20),sK21)
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f1195,definition,
( spl24_11
<=> sK19 = sK10(unordered_pair(sK19,sK20),sK21) ),
introduced(definition,[new_symbols(definition,[spl24_11])],[avatar_definition]) ).
fof(f1197,plain,
( sK19 = sK10(unordered_pair(sK19,sK20),sK21)
| ~ spl24_11 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1198,plain,
( spl24_10
| spl24_11
| spl24_1 ),
inference(avatar_split_clause,[],[f1183,f359,f1195,f1191]) ).
fof(f1248,plain,
( ~ in(sK20,sK21)
| spl24_1
| ~ spl24_10 ),
inference(superposition,[],[f560,f1193]) ).
fof(f1250,plain,
( $false
| spl24_1
| ~ spl24_3
| ~ spl24_10 ),
inference(forward_subsumption_resolution,[],[f1248,f368]) ).
fof(f1251,plain,
( spl24_1
| ~ spl24_3
| ~ spl24_10 ),
inference(avatar_contradiction_clause,[],[f1250]) ).
fof(f1280,plain,
( ~ in(sK19,sK21)
| spl24_1
| ~ spl24_11 ),
inference(superposition,[],[f560,f1197]) ).
fof(f1282,plain,
( $false
| spl24_1
| ~ spl24_2
| ~ spl24_11 ),
inference(forward_subsumption_resolution,[],[f1280,f364]) ).
fof(f1283,plain,
( spl24_1
| ~ spl24_2
| ~ spl24_11 ),
inference(avatar_contradiction_clause,[],[f1282]) ).
fof(f1286,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(sK19,sK20))
| in(X0,sK21) )
| ~ spl24_1 ),
inference(resolution,[],[f360,f177]) ).
fof(f1695,plain,
( in(sK19,sK21)
| ~ spl24_1 ),
inference(resolution,[],[f1286,f335]) ).
fof(f1696,plain,
( in(sK20,sK21)
| ~ spl24_1 ),
inference(resolution,[],[f1286,f337]) ).
fof(f1715,plain,
( $false
| ~ spl24_1
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f1696,f369]) ).
fof(f1716,plain,
( ~ spl24_1
| spl24_3 ),
inference(avatar_contradiction_clause,[],[f1715]) ).
fof(f1717,plain,
( $false
| ~ spl24_1
| spl24_2 ),
inference(forward_subsumption_resolution,[],[f1695,f365]) ).
fof(f1718,plain,
( ~ spl24_1
| spl24_2 ),
inference(avatar_contradiction_clause,[],[f1717]) ).
cnf(s1,plain,
( ~ spl24_1
| ~ spl24_2
| ~ spl24_3 ),
inference(sat_conversion,[],[f370]) ).
cnf(s2,plain,
( spl24_1
| spl24_3 ),
inference(sat_conversion,[],[f371]) ).
cnf(s3,plain,
( spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f372]) ).
cnf(s9,plain,
( spl24_1
| spl24_10
| spl24_11 ),
inference(sat_conversion,[],[f1198]) ).
cnf(s10,plain,
( spl24_1
| ~ spl24_3
| ~ spl24_10 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s11,plain,
( spl24_1
| ~ spl24_2
| ~ spl24_11 ),
inference(sat_conversion,[],[f1283]) ).
cnf(s15,plain,
( ~ spl24_1
| spl24_3 ),
inference(sat_conversion,[],[f1716]) ).
cnf(s16,plain,
( ~ spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f1718]) ).
cnf(s17,plain,
spl24_1,
inference(rat,[],[s9,s10,s11,s2,s3]) ).
cnf(s18,plain,
spl24_2,
inference(rat,[],[s16,s17]) ).
cnf(s19,plain,
spl24_3,
inference(rat,[],[s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s18,s19,s17]) ).
fof(f1719,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU159+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:48:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.16/0.48 % (417444)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (417453)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4108910481:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (417450)% WARNING: option uhcvi not known.
% 0.16/0.48 % (417449)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2794681073_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (417450)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1442477320:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (417452)dis+10_1_sil=32000:sp=arity:random_seed=631460897:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (417451)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1781185542:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (417454)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=996569058:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (417455)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1887101131:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (417453) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-417444-417453"...
% 0.16/0.48 % (417453)...printing done.
% 0.16/0.48 % (417453)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (417453)------------------------------
% 0.16/0.48 % (417453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (417453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (417453)CaDiCaL version: 2.1.3
% 0.16/0.48 % (417453)Termination reason: Refutation
% 0.16/0.48 % (417453)Time elapsed: 0.026 s
% 0.16/0.48 % (417453)Peak memory usage: 13 MB
% 0.16/0.48 % (417453)Instructions burned: 69 (million)
% 0.16/0.48 % (417444)Success in time 0.055 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------