%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:39:59 PM UTC 2026
% Result : Unsatisfiable 3.23s 1.37s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 24 unt; 6 def)
% Number of atoms : 195 ( 62 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 184 ( 83 ~; 95 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f30,axiom,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f53,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_set_in_its_singleton_1) ).
fof(f102,negated_conjecture,
singleton(x) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_set_in_its_singleton_2) ).
fof(f103,plain,
null_class = singleton(x),
inference(reorient_equations,[],[f102]) ).
fof(f107,plain,
! [X0] : member(singleton(X0),universal_class),
inference(superposition,[],[f11,f12]) ).
fof(f113,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f114,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[],[f113,f103]) ).
fof(f115,plain,
member(x,null_class),
inference(forward_subsumption_resolution,[],[f114,f101]) ).
fof(f194,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f199,definition,
( spl0_10
<=> inductive(null_class) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f259,plain,
! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| null_class = X1
| null_class = X0 ),
inference(resolution,[],[f8,f48]) ).
fof(f262,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f263,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f262]) ).
fof(f268,plain,
! [X0] :
( ~ member(X0,null_class)
| x = X0 ),
inference(superposition,[],[f263,f103]) ).
fof(f270,plain,
! [X0] : ordered_pair(X0,x) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)),
inference(superposition,[],[f13,f103]) ).
fof(f294,plain,
! [X0] :
( null_class != restrict(X0,null_class,universal_class)
| ~ member(x,domain_of(X0)) ),
inference(superposition,[],[f30,f103]) ).
fof(f355,plain,
ordered_pair(null_class,x) = unordered_pair(singleton(null_class),singleton(null_class)),
inference(superposition,[],[f270,f12]) ).
fof(f358,plain,
! [X0] :
( member(singleton(X0),ordered_pair(X0,x))
| ~ member(singleton(X0),universal_class) ),
inference(superposition,[],[f9,f270]) ).
fof(f360,plain,
! [X0] : member(singleton(X0),ordered_pair(X0,x)),
inference(forward_subsumption_resolution,[],[f358,f107]) ).
fof(f362,plain,
ordered_pair(null_class,x) = singleton(singleton(null_class)),
inference(forward_demodulation,[],[f355,f12]) ).
fof(f377,plain,
! [X0] :
( ~ member(X0,ordered_pair(null_class,x))
| singleton(null_class) = X0 ),
inference(superposition,[],[f263,f362]) ).
fof(f394,definition,
( spl0_21
<=> null_class = ordered_pair(null_class,x) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f395,plain,
( null_class != ordered_pair(null_class,x)
| spl0_21 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f396,plain,
( null_class = ordered_pair(null_class,x)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f407,definition,
( spl0_24
<=> null_class = singleton(null_class) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f409,plain,
( null_class = singleton(null_class)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f423,plain,
( member(singleton(null_class),null_class)
| ~ spl0_21 ),
inference(superposition,[],[f360,f396]) ).
fof(f573,plain,
! [X0] :
( member(x,X0)
| null_class = X0 ),
inference(resolution,[],[f194,f115]) ).
fof(f579,plain,
! [X0] :
( singleton(X0) = null_class
| x = X0 ),
inference(resolution,[],[f573,f263]) ).
fof(f580,plain,
( null_class = ordered_pair(null_class,x)
| x = singleton(null_class) ),
inference(resolution,[],[f573,f377]) ).
fof(f595,plain,
( x = singleton(null_class)
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f580,f395]) ).
fof(f619,plain,
( ordered_pair(null_class,x) = unordered_pair(x,unordered_pair(null_class,null_class))
| spl0_21 ),
inference(superposition,[],[f270,f595]) ).
fof(f625,plain,
( ordered_pair(null_class,x) = unordered_pair(x,singleton(null_class))
| spl0_21 ),
inference(forward_demodulation,[],[f619,f12]) ).
fof(f630,plain,
( ordered_pair(null_class,x) = unordered_pair(x,x)
| spl0_21 ),
inference(forward_demodulation,[],[f625,f595]) ).
fof(f635,plain,
( singleton(x) = ordered_pair(null_class,x)
| spl0_21 ),
inference(forward_demodulation,[],[f630,f12]) ).
fof(f637,plain,
( null_class = ordered_pair(null_class,x)
| spl0_21 ),
inference(forward_demodulation,[],[f635,f103]) ).
fof(f639,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f637,f395]) ).
fof(f640,plain,
spl0_21,
inference(avatar_contradiction_clause,[],[f639]) ).
fof(f647,definition,
( spl0_40
<=> x = singleton(null_class) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f649,plain,
( x = singleton(null_class)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f688,plain,
( x = singleton(null_class)
| ~ spl0_21 ),
inference(resolution,[],[f423,f268]) ).
fof(f689,plain,
( spl0_40
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f688,f394,f647]) ).
fof(f703,plain,
( ! [X0] :
( ~ member(X0,x)
| null_class = X0 )
| ~ spl0_40 ),
inference(superposition,[],[f263,f649]) ).
fof(f1047,plain,
( null_class = x
| null_class = x
| ~ spl0_40 ),
inference(resolution,[],[f703,f573]) ).
fof(f1050,plain,
( null_class = x
| ~ spl0_40 ),
inference(duplicate_literal_removal,[],[f1047]) ).
fof(f1053,definition,
( spl0_56
<=> null_class = x ),
introduced(definition,[new_symbols(definition,[spl0_56])],[avatar_definition]) ).
fof(f1055,plain,
( null_class = x
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1070,plain,
( spl0_56
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1050,f647,f1053]) ).
fof(f1082,plain,
( null_class = singleton(null_class)
| ~ spl0_56 ),
inference(superposition,[],[f103,f1055]) ).
fof(f1126,plain,
( spl0_24
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f1082,f1053,f407]) ).
fof(f1250,plain,
( ! [X0] :
( ~ member(X0,null_class)
| null_class = X0 )
| ~ spl0_24 ),
inference(superposition,[],[f263,f409]) ).
fof(f1686,plain,
( ! [X0] :
( singleton(X0) = null_class
| null_class = X0 )
| ~ spl0_56 ),
inference(forward_demodulation,[],[f579,f1055]) ).
fof(f1759,plain,
( ! [X0] :
( member(X0,null_class)
| ~ member(X0,universal_class)
| null_class = X0 )
| ~ spl0_56 ),
inference(superposition,[],[f113,f1686]) ).
fof(f1777,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| null_class = X0 )
| ~ spl0_24
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[],[f1759,f1250]) ).
fof(f1787,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = null_class
| ~ spl0_24
| ~ spl0_56 ),
inference(resolution,[],[f1777,f11]) ).
fof(f1794,plain,
( null_class = omega
| ~ spl0_24
| ~ spl0_56 ),
inference(resolution,[],[f1777,f53]) ).
fof(f1822,plain,
( inductive(null_class)
| ~ spl0_24
| ~ spl0_56 ),
inference(superposition,[],[f51,f1794]) ).
fof(f1838,plain,
( spl0_10
| ~ spl0_24
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f1822,f1053,f407,f199]) ).
fof(f2255,plain,
( ! [X0,X1] :
( ~ inductive(null_class)
| null_class = X1
| null_class = X0 )
| ~ spl0_24
| ~ spl0_56 ),
inference(superposition,[],[f259,f1787]) ).
fof(f2278,definition,
( spl0_95
<=> ! [X0] : null_class = X0 ),
introduced(definition,[new_symbols(definition,[spl0_95])],[avatar_definition]) ).
fof(f2279,plain,
( ! [X0] : null_class = X0
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f2280,plain,
( spl0_95
| spl0_95
| ~ spl0_10
| ~ spl0_24
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f2255,f1053,f407,f199,f2278,f2278]) ).
fof(f2302,plain,
( ! [X0,X1] :
( restrict(X1,X0,universal_class) != X0
| ~ member(x,domain_of(X1)) )
| ~ spl0_95 ),
inference(superposition,[],[f294,f2279]) ).
fof(f2996,plain,
( ! [X0,X1] :
( null_class != X0
| ~ member(x,domain_of(X1)) )
| ~ spl0_95 ),
inference(forward_demodulation,[],[f2302,f2279]) ).
fof(f3111,plain,
( ! [X1] : ~ member(x,domain_of(X1))
| ~ spl0_95 ),
inference(forward_subsumption_resolution,[],[f2996,f2279]) ).
fof(f3151,plain,
( ~ member(x,null_class)
| ~ spl0_95 ),
inference(forward_demodulation,[],[f3111,f2279]) ).
fof(f3169,plain,
( $false
| ~ spl0_95 ),
inference(forward_subsumption_resolution,[],[f3151,f115]) ).
fof(f3170,plain,
~ spl0_95,
inference(avatar_contradiction_clause,[],[f3169]) ).
cnf(s25,plain,
spl0_21,
inference(sat_conversion,[],[f640]) ).
cnf(s29,plain,
( ~ spl0_21
| spl0_40 ),
inference(sat_conversion,[],[f689]) ).
cnf(s49,plain,
( ~ spl0_40
| spl0_56 ),
inference(sat_conversion,[],[f1070]) ).
cnf(s54,plain,
( spl0_24
| ~ spl0_56 ),
inference(sat_conversion,[],[f1126]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_24
| ~ spl0_56 ),
inference(sat_conversion,[],[f1838]) ).
cnf(s106,plain,
( spl0_95
| ~ spl0_24
| ~ spl0_56
| ~ spl0_10
| spl0_95 ),
inference(sat_conversion,[],[f2280]) ).
cnf(s107,plain,
( ~ spl0_10
| ~ spl0_24
| ~ spl0_56
| spl0_95 ),
inference(rat,[],[s106]) ).
cnf(s164,plain,
~ spl0_95,
inference(sat_conversion,[],[f3170]) ).
cnf(s174,plain,
( ~ spl0_10
| ~ spl0_24
| ~ spl0_56 ),
inference(rat,[],[s107,s164]) ).
cnf(s179,plain,
spl0_40,
inference(rat,[],[s29,s25]) ).
cnf(s180,plain,
spl0_56,
inference(rat,[],[s49,s179]) ).
cnf(s184,plain,
spl0_24,
inference(rat,[],[s54,s180]) ).
cnf(s190,plain,
~ spl0_10,
inference(rat,[],[s174,s180,s184]) ).
cnf(s191,plain,
$false,
inference(rat,[],[s90,s180,s184,s190]) ).
fof(f3196,plain,
$false,
inference(avatar_sat_refutation,[],[s191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:35:39 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.23/1.37 % (2888589)Input is clausal, will run a generic CNF schedule.
% 3.23/1.37 % (2888598)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2839787644:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.23/1.37 % (2888594)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=995862659:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.23/1.37 % (2888597)lrs+10_1_sil=8000:sp=occurrence:random_seed=1419597751:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.23/1.37 % (2888597)Refutation not found, incomplete strategy
% 3.23/1.37 % (2888597)------------------------------
% 3.23/1.37 % (2888597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.37 % (2888597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.37 % (2888597)CaDiCaL version: 2.1.3
% 3.23/1.37 % (2888597)Termination reason: Refutation not found, incomplete strategy
% 3.23/1.37 % (2888597)Time elapsed: 0.001 s
% 3.23/1.37 % (2888597)Peak memory usage: 87 MB
% 3.23/1.37 % (2888595)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1444838987:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.23/1.37 % (2888596)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3230686325:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.23/1.37 % (2888598)Instruction limit reached!
% 3.23/1.37 % (2888598)------------------------------
% 3.23/1.37 % (2888598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.37 % (2888598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.37 % (2888598)CaDiCaL version: 2.1.3
% 3.23/1.37 % (2888598)Termination reason: Instruction limit
% 3.23/1.37 % (2888598)Termination phase: Saturation
% 3.23/1.37 % (2888598)Time elapsed: 0.039 s
% 3.23/1.37 % (2888598)Peak memory usage: 89 MB
% 3.23/1.37 % (2888598)Instructions burned: 117 (million)
% 3.23/1.37 % (2888599)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=223228231:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.23/1.37 % (2888600)dis-21_1_sil=8000:lcm=predicate:random_seed=2352379021:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.23/1.37 % (2888600)Instruction limit reached!
% 3.23/1.37 % (2888600)------------------------------
% 3.23/1.37 % (2888600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.37 % (2888600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.37 % (2888600)CaDiCaL version: 2.1.3
% 3.23/1.37 % (2888600)Termination reason: Instruction limit
% 3.23/1.37 % (2888600)Termination phase: Saturation
% 3.23/1.37 % (2888600)Time elapsed: 0.064 s
% 3.23/1.37 % (2888600)Peak memory usage: 88 MB
% 3.23/1.37 % (2888600)Instructions burned: 119 (million)
% 3.23/1.37 % (2888599)First to succeed.
% 3.23/1.37 % (2888599)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2888589"
% 3.23/1.37 % (2888606)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3885563122:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.23/1.37 % (2888606)Instruction limit reached!
% 3.23/1.37 % (2888606)------------------------------
% 3.23/1.37 % (2888606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.37 % (2888606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.37 % (2888606)CaDiCaL version: 2.1.3
% 3.23/1.37 % (2888606)Termination reason: Instruction limit
% 3.23/1.37 % (2888606)Termination phase: Saturation
% 3.23/1.37 % (2888606)Time elapsed: 0.054 s
% 3.23/1.37 % (2888606)Peak memory usage: 90 MB
% 3.23/1.37 % (2888606)Instructions burned: 145 (million)
% 3.23/1.37 % (2888597)------------------------------
% 3.23/1.37 % (2888597)------------------------------
% 3.23/1.37 % (2888609)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=604661959:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.23/1.37 % (2888599)Refutation found. Thanks to Tanya!
% 3.23/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.23/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.47 % (2888599)------------------------------
% 4.03/1.47 % (2888599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.47 % (2888599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.47 % (2888599)CaDiCaL version: 2.1.3
% 4.03/1.47 % (2888599)Termination reason: Refutation
% 4.03/1.47 % (2888599)Time elapsed: 0.067 s
% 4.03/1.47 % (2888599)Peak memory usage: 91 MB
% 4.03/1.47 % (2888599)Instructions burned: 92 (million)
% 4.03/1.47 % (2888599)------------------------------
% 4.03/1.47 % (2888599)------------------------------
% 4.03/1.47 % (2888589)Success in time 0.498 s
% 4.03/1.47 % Vampire exiting
%------------------------------------------------------------------------------