%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU144+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 : n007.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 12:52:05 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 12 unt; 2 def)
% Number of atoms : 124 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 44 ~; 48 |; 0 &)
% ( 11 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f11,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f28,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f29,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f36,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f60,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f76,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f81,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f83,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f107,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f113,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f116,plain,
! [X0] :
( in(sK1(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f8]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f10]) ).
fof(f131,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f132,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f154,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f28]) ).
fof(f155,plain,
( in(sK7,sK8)
| subset(singleton(sK7),sK8) ),
inference(cnf_transformation,[],[f81]) ).
fof(f156,plain,
( ~ in(sK7,sK8)
| ~ subset(singleton(sK7),sK8) ),
inference(cnf_transformation,[],[f81]) ).
fof(f163,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f83]) ).
fof(f192,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f60]) ).
fof(f203,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f113,f192]) ).
fof(f214,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f154,f192]) ).
fof(f215,plain,
( ~ in(sK7,sK8)
| ~ subset(unordered_pair(sK7,sK7),sK8) ),
inference(definition_unfolding,[],[f156,f192]) ).
fof(f216,plain,
( in(sK7,sK8)
| subset(unordered_pair(sK7,sK7),sK8) ),
inference(definition_unfolding,[],[f155,f192]) ).
fof(f226,plain,
! [X2,X0] :
( ~ in(X2,unordered_pair(X0,X0))
| X0 = X2 ),
inference(equality_resolution,[],[f203]) ).
fof(f236,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X0,X1))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f128]) ).
fof(f246,definition,
( spl14_1
<=> subset(unordered_pair(sK7,sK7),sK8) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f247,plain,
( ~ subset(unordered_pair(sK7,sK7),sK8)
| spl14_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( subset(unordered_pair(sK7,sK7),sK8)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl14_2
<=> in(sK7,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f251,plain,
( ~ in(sK7,sK8)
| spl14_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( in(sK7,sK8)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f216,f250,f246]) ).
fof(f254,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f215,f250,f246]) ).
fof(f387,plain,
! [X0] :
( sK1(unordered_pair(X0,X0)) = X0
| empty_set = unordered_pair(X0,X0) ),
inference(resolution,[],[f226,f116]) ).
fof(f388,plain,
! [X0] : sK1(unordered_pair(X0,X0)) = X0,
inference(forward_subsumption_resolution,[],[f387,f214]) ).
fof(f392,plain,
( in(sK4(unordered_pair(sK7,sK7),sK8),unordered_pair(sK7,sK7))
| spl14_1 ),
inference(resolution,[],[f131,f247]) ).
fof(f396,plain,
( sK7 = sK4(unordered_pair(sK7,sK7),sK8)
| spl14_1 ),
inference(resolution,[],[f392,f226]) ).
fof(f399,plain,
( ~ in(sK4(unordered_pair(sK7,sK7),sK8),sK8)
| spl14_1 ),
inference(resolution,[],[f132,f247]) ).
fof(f403,plain,
( ~ in(sK7,sK8)
| spl14_1 ),
inference(forward_demodulation,[],[f399,f396]) ).
fof(f404,plain,
( $false
| spl14_1
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f403,f252]) ).
fof(f405,plain,
( spl14_1
| ~ spl14_2 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f407,plain,
( sK8 = set_union2(unordered_pair(sK7,sK7),sK8)
| ~ spl14_1 ),
inference(resolution,[],[f248,f163]) ).
fof(f408,plain,
( sK8 = set_union2(sK8,unordered_pair(sK7,sK7))
| ~ spl14_1 ),
inference(forward_demodulation,[],[f407,f107]) ).
fof(f445,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(sK7,sK7))
| in(X0,sK8) )
| ~ spl14_1 ),
inference(superposition,[],[f236,f408]) ).
fof(f457,plain,
( in(sK1(unordered_pair(sK7,sK7)),sK8)
| empty_set = unordered_pair(sK7,sK7)
| ~ spl14_1 ),
inference(resolution,[],[f445,f116]) ).
fof(f458,plain,
( in(sK1(unordered_pair(sK7,sK7)),sK8)
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f457,f214]) ).
fof(f463,plain,
( in(sK7,sK8)
| ~ spl14_1 ),
inference(forward_demodulation,[],[f458,f388]) ).
fof(f464,plain,
( $false
| ~ spl14_1
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f463,f251]) ).
fof(f465,plain,
( ~ spl14_1
| spl14_2 ),
inference(avatar_contradiction_clause,[],[f464]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s2,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f254]) ).
cnf(s3,plain,
( spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f405]) ).
cnf(s7,plain,
( ~ spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f465]) ).
cnf(s8,plain,
spl14_1,
inference(rat,[],[s1,s3]) ).
cnf(s9,plain,
spl14_2,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
fof(f466,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:41:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.46 % (2005678)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (2005683)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1685129517_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % (2005684)% WARNING: option uhcvi not known.
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % (2005685)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1264121046:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (2005684)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1022309762:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (2005686)dis+10_1_sil=32000:sp=arity:random_seed=545699435:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (2005687)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2813398898:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (2005688)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=99171620:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (2005689)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2212001555:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % TRYING [4]
% 0.17/0.46 % (2005687) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2005678-2005687"...
% 0.17/0.46 % (2005687)...printing done.
% 0.17/0.46 % TRYING [5]
% 0.17/0.46 % (2005687)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (2005687)------------------------------
% 0.17/0.46 % (2005687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (2005687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (2005687)CaDiCaL version: 2.1.3
% 0.17/0.46 % (2005687)Termination reason: Refutation
% 0.17/0.46 % (2005687)Time elapsed: 0.010 s
% 0.17/0.46 % (2005687)Peak memory usage: 12 MB
% 0.17/0.46 % (2005687)Instructions burned: 14 (million)
% 0.17/0.46 % (2005678)Success in time 0.035 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------