%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU146+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 : n015.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 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 90 ( 12 unt; 3 def)
% Number of atoms : 301 ( 93 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 345 ( 134 ~; 153 |; 44 &)
% ( 12 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 1 sgn 92 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_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(f29,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f32,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f47,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f62,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f72,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f85,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f87,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f108,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f109,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f111,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f111]) ).
fof(f113,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f114,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ( X0 = empty_set
| in(sK1(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f114]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK3(X0,X1,X2),X0)
& ~ in(sK3(X0,X1,X2),X1) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( in(sK3(X0,X1,X2),X0)
| in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f122]) ).
fof(f136,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f138,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f139,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
( ( ( empty_set != sK7
& sK7 != singleton(sK8) )
| ~ subset(sK7,singleton(sK8)) )
& ( empty_set = sK7
| sK7 = singleton(sK8)
| subset(sK7,singleton(sK8)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f139]) ).
fof(f156,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f157,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f112]) ).
fof(f162,plain,
! [X0] :
( in(sK1(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f115]) ).
fof(f171,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f201,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f205,plain,
( empty_set = sK7
| sK7 = singleton(sK8)
| subset(sK7,singleton(sK8)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f206,plain,
( sK7 != singleton(sK8)
| ~ subset(sK7,singleton(sK8)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f207,plain,
( empty_set != sK7
| ~ subset(sK7,singleton(sK8)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f210,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f72]) ).
fof(f212,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f222,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f241,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f253,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f157,f241]) ).
fof(f264,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f201,f241]) ).
fof(f267,plain,
( empty_set != sK7
| ~ subset(sK7,unordered_pair(sK8,sK8)) ),
inference(definition_unfolding,[],[f207,f241]) ).
fof(f268,plain,
( sK7 != unordered_pair(sK8,sK8)
| ~ subset(sK7,unordered_pair(sK8,sK8)) ),
inference(definition_unfolding,[],[f206,f241,f241]) ).
fof(f269,plain,
( empty_set = sK7
| sK7 = unordered_pair(sK8,sK8)
| subset(sK7,unordered_pair(sK8,sK8)) ),
inference(definition_unfolding,[],[f205,f241,f241]) ).
fof(f281,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f253]) ).
fof(f288,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f298,definition,
( spl14_1
<=> subset(sK7,unordered_pair(sK8,sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f299,plain,
( ~ subset(sK7,unordered_pair(sK8,sK8))
| spl14_1 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( subset(sK7,unordered_pair(sK8,sK8))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f302,definition,
( spl14_2
<=> sK7 = unordered_pair(sK8,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f303,plain,
( sK7 != unordered_pair(sK8,sK8)
| spl14_2 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f304,plain,
( sK7 = unordered_pair(sK8,sK8)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f306,definition,
( spl14_3
<=> empty_set = sK7 ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f307,plain,
( empty_set != sK7
| spl14_3 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( empty_set = sK7
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f309,plain,
( spl14_1
| spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f269,f306,f302,f298]) ).
fof(f310,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f268,f302,f298]) ).
fof(f311,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f267,f306,f298]) ).
fof(f312,plain,
( ~ subset(sK7,sK7)
| spl14_1
| ~ spl14_2 ),
inference(superposition,[],[f299,f304]) ).
fof(f313,plain,
( $false
| spl14_1
| ~ spl14_2 ),
inference(resolution,[],[f210,f312]) ).
fof(f314,plain,
( spl14_1
| ~ spl14_2 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f315,plain,
( ~ subset(empty_set,unordered_pair(sK8,sK8))
| spl14_1
| ~ spl14_3 ),
inference(superposition,[],[f299,f308]) ).
fof(f316,plain,
( $false
| spl14_1
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f315,f222]) ).
fof(f317,plain,
( spl14_1
| ~ spl14_3 ),
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f417,plain,
( unordered_pair(sK8,sK8) = set_union2(sK7,unordered_pair(sK8,sK8))
| ~ spl14_1 ),
inference(resolution,[],[f212,f300]) ).
fof(f492,plain,
( ! [X0] :
( in(X0,unordered_pair(sK8,sK8))
| ~ in(X0,sK7) )
| ~ spl14_1 ),
inference(superposition,[],[f288,f417]) ).
fof(f493,plain,
( ! [X0] :
( ~ in(X0,sK7)
| sK8 = X0 )
| ~ spl14_1 ),
inference(resolution,[],[f492,f281]) ).
fof(f512,plain,
( sK8 = sK1(sK7)
| empty_set = sK7
| ~ spl14_1 ),
inference(resolution,[],[f493,f162]) ).
fof(f516,plain,
( sK8 = sK1(sK7)
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f512,f307]) ).
fof(f526,plain,
( in(sK8,sK7)
| empty_set = sK7
| ~ spl14_1
| spl14_3 ),
inference(superposition,[],[f162,f516]) ).
fof(f527,plain,
( in(sK8,sK7)
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f526,f307]) ).
fof(f601,plain,
( ~ subset(unordered_pair(sK8,sK8),sK7)
| sK7 = unordered_pair(sK8,sK8)
| ~ spl14_1 ),
inference(resolution,[],[f156,f300]) ).
fof(f604,plain,
( ~ subset(unordered_pair(sK8,sK8),sK7)
| ~ spl14_1
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f601,f303]) ).
fof(f605,plain,
( ~ in(sK8,sK7)
| ~ spl14_1
| spl14_2 ),
inference(resolution,[],[f604,f264]) ).
fof(f607,plain,
( $false
| ~ spl14_1
| spl14_2
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f605,f527]) ).
fof(f608,plain,
( ~ spl14_1
| spl14_2
| spl14_3 ),
inference(avatar_contradiction_clause,[],[f607]) ).
cnf(s1,plain,
( spl14_1
| spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f309]) ).
cnf(s2,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f310]) ).
cnf(s3,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(sat_conversion,[],[f311]) ).
cnf(s4,plain,
( spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f314]) ).
cnf(s5,plain,
( spl14_1
| ~ spl14_3 ),
inference(sat_conversion,[],[f317]) ).
cnf(s6,plain,
( ~ spl14_1
| spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f608]) ).
cnf(s7,plain,
spl14_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s8,plain,
~ spl14_3,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
~ spl14_2,
inference(rat,[],[s2,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s7,s9]) ).
fof(f609,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:47:31 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
% 0.15/0.47 % (2238538)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (2238545)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2421319059:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (2238544)% WARNING: option uhcvi not known.
% 0.15/0.47 % (2238543)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3833936665_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (2238544)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3024047169:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (2238546)dis+10_1_sil=32000:sp=arity:random_seed=2093035797:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (2238547)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2563704747:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (2238549)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=391378516:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (2238548)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1016757916:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (2238546) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2238538-2238546"...
% 0.15/0.47 % (2238546)...printing done.
% 0.15/0.47 % (2238546)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2238546)------------------------------
% 0.15/0.47 % (2238546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2238546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2238546)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2238546)Termination reason: Refutation
% 0.15/0.47 % (2238546)Time elapsed: 0.012 s
% 0.15/0.47 % (2238546)Peak memory usage: 12 MB
% 0.15/0.47 % (2238546)Instructions burned: 15 (million)
% 0.15/0.47 % (2238538)Success in time 0.047 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------