%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:47:29 PM UTC 2026
% Result : Theorem 0.55s 1.00s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 10 unt; 3 def)
% Number of atoms : 287 ( 83 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 330 ( 126 ~; 145 |; 45 &)
% ( 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 97 ( 1 sgn 84 !; 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(f14,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f41,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f59,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f62,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f70,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f71,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(negated_conjecture,[status(cth)],[f70]) ).
fof(f95,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f120,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f124,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f140,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f141,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f140]) ).
fof(f142,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(f143,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,[],[f142]) ).
fof(f144,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))],[f143]) ).
fof(f145,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f146,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f145]) ).
fof(f147,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))],[f146]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f165]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f166]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK11(X0,X1,X2),X0)
| ~ in(sK11(X0,X1,X2),X1)
| ~ in(sK11(X0,X1,X2),X2) )
& ( ( in(sK11(X0,X1,X2),X0)
& in(sK11(X0,X1,X2),X1) )
| in(sK11(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f167]) ).
fof(f177,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f191,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,[],[f124]) ).
fof(f192,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,[],[f191]) ).
fof(f193,plain,
( ( ( empty_set != sK19
& sK19 != singleton(sK20) )
| ~ subset(sK19,singleton(sK20)) )
& ( empty_set = sK19
| sK19 = singleton(sK20)
| subset(sK19,singleton(sK20)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X1,sK20)],[f192]) ).
fof(f204,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f205,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f144]) ).
fof(f210,plain,
! [X0] :
( in(sK1(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f238,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f168]) ).
fof(f272,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
fof(f285,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f95]) ).
fof(f295,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f299,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f312,plain,
( empty_set = sK19
| sK19 = singleton(sK20)
| subset(sK19,singleton(sK20)) ),
inference(cnf_transformation,[],[f193]) ).
fof(f313,plain,
( sK19 != singleton(sK20)
| ~ subset(sK19,singleton(sK20)) ),
inference(cnf_transformation,[],[f193]) ).
fof(f314,plain,
( empty_set != sK19
| ~ subset(sK19,singleton(sK20)) ),
inference(cnf_transformation,[],[f193]) ).
fof(f343,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f205]) ).
fof(f362,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f238]) ).
fof(f372,definition,
( spl23_1
<=> subset(sK19,singleton(sK20)) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f373,plain,
( ~ subset(sK19,singleton(sK20))
| spl23_1 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f374,plain,
( subset(sK19,singleton(sK20))
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f376,definition,
( spl23_2
<=> sK19 = singleton(sK20) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f377,plain,
( sK19 != singleton(sK20)
| spl23_2 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( sK19 = singleton(sK20)
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f380,definition,
( spl23_3
<=> empty_set = sK19 ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
fof(f381,plain,
( empty_set != sK19
| spl23_3 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f382,plain,
( empty_set = sK19
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f383,plain,
( spl23_1
| spl23_2
| spl23_3 ),
inference(avatar_split_clause,[],[f312,f380,f376,f372]) ).
fof(f384,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(avatar_split_clause,[],[f313,f376,f372]) ).
fof(f385,plain,
( ~ spl23_1
| ~ spl23_3 ),
inference(avatar_split_clause,[],[f314,f380,f372]) ).
fof(f386,plain,
( ~ subset(sK19,sK19)
| spl23_1
| ~ spl23_2 ),
inference(superposition,[],[f373,f378]) ).
fof(f387,plain,
( $false
| spl23_1
| ~ spl23_2 ),
inference(resolution,[],[f285,f386]) ).
fof(f388,plain,
( spl23_1
| ~ spl23_2 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f389,plain,
( ~ subset(empty_set,singleton(sK20))
| spl23_1
| ~ spl23_3 ),
inference(superposition,[],[f373,f382]) ).
fof(f390,plain,
( $false
| spl23_1
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f389,f299]) ).
fof(f391,plain,
( spl23_1
| ~ spl23_3 ),
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f543,plain,
( sK19 = set_intersection2(sK19,singleton(sK20))
| ~ spl23_1 ),
inference(resolution,[],[f295,f374]) ).
fof(f636,plain,
( ! [X0] :
( ~ in(X0,sK19)
| in(X0,singleton(sK20)) )
| ~ spl23_1 ),
inference(superposition,[],[f362,f543]) ).
fof(f637,plain,
( in(sK1(sK19),singleton(sK20))
| empty_set = sK19
| ~ spl23_1 ),
inference(resolution,[],[f636,f210]) ).
fof(f639,plain,
( in(sK1(sK19),singleton(sK20))
| ~ spl23_1
| spl23_3 ),
inference(forward_subsumption_resolution,[],[f637,f381]) ).
fof(f645,plain,
( sK20 = sK1(sK19)
| ~ spl23_1
| spl23_3 ),
inference(resolution,[],[f639,f343]) ).
fof(f655,plain,
( in(sK20,sK19)
| empty_set = sK19
| ~ spl23_1
| spl23_3 ),
inference(superposition,[],[f210,f645]) ).
fof(f656,plain,
( in(sK20,sK19)
| ~ spl23_1
| spl23_3 ),
inference(forward_subsumption_resolution,[],[f655,f381]) ).
fof(f775,plain,
( sK19 = singleton(sK20)
| ~ subset(singleton(sK20),sK19)
| ~ spl23_1 ),
inference(resolution,[],[f204,f374]) ).
fof(f778,plain,
( ~ subset(singleton(sK20),sK19)
| ~ spl23_1
| spl23_2 ),
inference(forward_subsumption_resolution,[],[f775,f377]) ).
fof(f779,plain,
( ~ in(sK20,sK19)
| ~ spl23_1
| spl23_2 ),
inference(resolution,[],[f778,f272]) ).
fof(f780,plain,
( $false
| ~ spl23_1
| spl23_2
| spl23_3 ),
inference(forward_subsumption_resolution,[],[f779,f656]) ).
fof(f781,plain,
( ~ spl23_1
| spl23_2
| spl23_3 ),
inference(avatar_contradiction_clause,[],[f780]) ).
cnf(s1,plain,
( spl23_1
| spl23_2
| spl23_3 ),
inference(sat_conversion,[],[f383]) ).
cnf(s2,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f384]) ).
cnf(s3,plain,
( ~ spl23_1
| ~ spl23_3 ),
inference(sat_conversion,[],[f385]) ).
cnf(s4,plain,
( spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f388]) ).
cnf(s5,plain,
( spl23_1
| ~ spl23_3 ),
inference(sat_conversion,[],[f391]) ).
cnf(s7,plain,
( ~ spl23_1
| spl23_2
| spl23_3 ),
inference(sat_conversion,[],[f781]) ).
cnf(s8,plain,
spl23_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s9,plain,
~ spl23_3,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
~ spl23_2,
inference(rat,[],[s2,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s9,s8,s10]) ).
fof(f782,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:48:15 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/1.00 % (2643529)Detected formulas, will run a generic FOF schedule.
% 0.55/1.00 % (2643539)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4128212790:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.55/1.00 % (2643534)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4066398724:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.55/1.00 % (2643538)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2974071560:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.55/1.00 % (2643540)dis-21_1_sil=8000:lcm=predicate:random_seed=3272040047:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.55/1.00 % (2643535)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1448693352:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.55/1.00 % (2643536)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1331274165:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.55/1.00 % (2643537)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=360235340:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.55/1.00 % (2643539)First to succeed.
% 0.55/1.00 % (2643537)Also succeeded, but the first one will report.
% 0.55/1.00 % (2643539)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2643529"
% 0.55/1.00 % (2643538)Also succeeded, but the first one will report.
% 0.55/1.00 % (2643540)Instruction limit reached!
% 0.55/1.00 % (2643540)------------------------------
% 0.55/1.00 % (2643540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.55/1.00 % (2643540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/1.00 % (2643540)CaDiCaL version: 2.1.3
% 0.55/1.00 % (2643540)Termination reason: Instruction limit
% 0.55/1.00 % (2643540)Termination phase: Saturation
% 0.55/1.00 % (2643540)Time elapsed: 0.083 s
% 0.55/1.00 % (2643540)Peak memory usage: 89 MB
% 0.55/1.00 % (2643540)Instructions burned: 129 (million)
% 0.55/1.00 % (2643548)lrs+10_1_sil=8000:sp=occurrence:random_seed=2680152423:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.55/1.00 % (2643548)Also succeeded, but the first one will report.
% 0.55/1.00 % (2643539)Refutation found. Thanks to Tanya!
% 0.55/1.00 % SZS status Theorem for theBenchmark
% 0.55/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 3.18/1.20 % (2643539)------------------------------
% 3.18/1.20 % (2643539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.20 % (2643539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.20 % (2643539)CaDiCaL version: 2.1.3
% 3.18/1.20 % (2643539)Termination reason: Refutation
% 3.18/1.20 % (2643539)Time elapsed: 0.016 s
% 3.18/1.20 % (2643539)Peak memory usage: 90 MB
% 3.18/1.20 % (2643539)Instructions burned: 21 (million)
% 3.18/1.20 % (2643539)------------------------------
% 3.18/1.20 % (2643539)------------------------------
% 3.18/1.20 % (2643529)Success in time 0.404 s
% 3.18/1.20 % Vampire exiting
%------------------------------------------------------------------------------