%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 11:52:36 AM UTC 2026
% Result : Theorem 3.07s 1.35s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 98 ( 34 unt; 12 def)
% Number of atoms : 204 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 191 ( 85 ~; 79 |; 2 &)
% ( 17 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 81 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
fof(f45,conjecture,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f46,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ or_1,
inference(flattening,[],[f46]) ).
fof(f48,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f55,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f56,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f55]) ).
fof(f57,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f56]) ).
fof(f59,plain,
( or_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f61,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f50]) ).
fof(f64,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f48]) ).
fof(f68,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f57]) ).
fof(f73,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f75,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f78,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f64]) ).
fof(f82,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f68]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f97,plain,
~ or_1,
inference(cnf_transformation,[],[f47]) ).
fof(f107,definition,
( spl2_3
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f111,definition,
( spl2_4
<=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f112,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f82,f111,f107]) ).
fof(f139,definition,
( spl2_11
<=> r5 ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f143,definition,
( spl2_12
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f144,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( ~ spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f78,f143,f139]) ).
fof(f155,definition,
( spl2_15
<=> r3 ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f159,definition,
( spl2_16
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f160,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f161,plain,
( ~ spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f76,f159,f155]) ).
fof(f163,definition,
( spl2_17
<=> r2 ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f167,definition,
( spl2_18
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f168,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f169,plain,
( ~ spl2_17
| spl2_18 ),
inference(avatar_split_clause,[],[f75,f167,f163]) ).
fof(f179,definition,
( spl2_21
<=> is_a_theorem(implies(sK0,or(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_21])],[avatar_definition]) ).
fof(f181,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| spl2_21 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,definition,
( spl2_22
<=> or_1 ),
introduced(definition,[new_symbols(definition,[spl2_22])],[avatar_definition]) ).
fof(f186,plain,
( ~ spl2_21
| spl2_22 ),
inference(avatar_split_clause,[],[f73,f183,f179]) ).
fof(f196,definition,
( spl2_25
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_25])],[avatar_definition]) ).
fof(f200,definition,
( spl2_26
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_26])],[avatar_definition]) ).
fof(f201,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f202,plain,
( ~ spl2_25
| spl2_26 ),
inference(avatar_split_clause,[],[f71,f200,f196]) ).
fof(f203,plain,
~ spl2_22,
inference(avatar_split_clause,[],[f97,f183]) ).
fof(f206,plain,
spl2_3,
inference(avatar_split_clause,[],[f84,f107]) ).
fof(f216,plain,
spl2_25,
inference(avatar_split_clause,[],[f87,f196]) ).
fof(f222,plain,
spl2_17,
inference(avatar_split_clause,[],[f89,f163]) ).
fof(f225,plain,
spl2_15,
inference(avatar_split_clause,[],[f90,f155]) ).
fof(f231,plain,
spl2_11,
inference(avatar_split_clause,[],[f92,f139]) ).
fof(f245,plain,
( ! [X0] :
( ~ is_a_theorem(implies(X0,implies(sK0,or(sK0,sK1))))
| ~ is_a_theorem(X0) )
| spl2_21
| ~ spl2_26 ),
inference(resolution,[],[f201,f181]) ).
fof(f275,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X1),implies(or(not(X0),X2),implies(X0,X1))))
| ~ spl2_4
| ~ spl2_12 ),
inference(superposition,[],[f144,f112]) ).
fof(f276,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X1),implies(implies(X0,X2),implies(X0,X1))))
| ~ spl2_4
| ~ spl2_12 ),
inference(forward_demodulation,[],[f275,f112]) ).
fof(f301,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,implies(sK0,or(sK0,sK1)))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| spl2_21
| ~ spl2_26 ),
inference(resolution,[],[f245,f201]) ).
fof(f2080,plain,
( ! [X0] :
( ~ is_a_theorem(implies(sK0,X0))
| ~ is_a_theorem(implies(X0,or(sK0,sK1))) )
| ~ spl2_4
| ~ spl2_12
| spl2_21
| ~ spl2_26 ),
inference(resolution,[],[f301,f276]) ).
fof(f2192,plain,
( ! [X0] : ~ is_a_theorem(implies(or(X0,sK0),or(sK0,sK1)))
| ~ spl2_4
| ~ spl2_12
| ~ spl2_18
| spl2_21
| ~ spl2_26 ),
inference(resolution,[],[f2080,f168]) ).
fof(f2229,plain,
( $false
| ~ spl2_4
| ~ spl2_12
| ~ spl2_16
| ~ spl2_18
| spl2_21
| ~ spl2_26 ),
inference(resolution,[],[f2192,f160]) ).
fof(f2234,plain,
( ~ spl2_4
| ~ spl2_12
| ~ spl2_16
| ~ spl2_18
| spl2_21
| ~ spl2_26 ),
inference(avatar_contradiction_clause,[],[f2229]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s6,plain,
( ~ spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f145]) ).
cnf(s8,plain,
( ~ spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f161]) ).
cnf(s9,plain,
( ~ spl2_17
| spl2_18 ),
inference(sat_conversion,[],[f169]) ).
cnf(s11,plain,
( ~ spl2_21
| spl2_22 ),
inference(sat_conversion,[],[f186]) ).
cnf(s13,plain,
( ~ spl2_25
| spl2_26 ),
inference(sat_conversion,[],[f202]) ).
cnf(s14,plain,
~ spl2_22,
inference(sat_conversion,[],[f203]) ).
cnf(s16,plain,
spl2_3,
inference(sat_conversion,[],[f206]) ).
cnf(s22,plain,
spl2_25,
inference(sat_conversion,[],[f216]) ).
cnf(s26,plain,
spl2_17,
inference(sat_conversion,[],[f222]) ).
cnf(s28,plain,
spl2_15,
inference(sat_conversion,[],[f225]) ).
cnf(s32,plain,
spl2_11,
inference(sat_conversion,[],[f231]) ).
cnf(s39,plain,
( ~ spl2_4
| ~ spl2_12
| ~ spl2_16
| ~ spl2_18
| spl2_21
| ~ spl2_26 ),
inference(sat_conversion,[],[f2234]) ).
cnf(s40,plain,
spl2_26,
inference(rat,[],[s13,s22]) ).
cnf(s42,plain,
~ spl2_21,
inference(rat,[],[s11,s14]) ).
cnf(s44,plain,
spl2_18,
inference(rat,[],[s9,s26]) ).
cnf(s45,plain,
spl2_16,
inference(rat,[],[s8,s28]) ).
cnf(s47,plain,
spl2_12,
inference(rat,[],[s6,s32]) ).
cnf(s48,plain,
~ spl2_4,
inference(rat,[],[s39,s40,s42,s44,s45,s47]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s2,s48,s16]) ).
fof(f2235,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.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 : Sun Sep 27 15:50:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.07/1.35 % (2206813)Detected formulas, will run a generic FOF schedule.
% 3.07/1.35 % (2206819)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=4250475153:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.07/1.35 % (2206820)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=3845469529:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.07/1.35 % (2206818)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=2975747615:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.07/1.35 % (2206821)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=378715804:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.07/1.35 % (2206822)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2234556626:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.07/1.35 % (2206823)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3002624349:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.07/1.35 % (2206822)Refutation not found, incomplete strategy
% 3.07/1.35 % (2206822)------------------------------
% 3.07/1.35 % (2206822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.35 % (2206822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.35 % (2206821)Refutation not found, incomplete strategy
% 3.07/1.35 % (2206821)------------------------------
% 3.07/1.35 % (2206821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.35 % (2206822)CaDiCaL version: 2.1.3
% 3.07/1.35 % (2206822)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.35 % (2206822)Time elapsed: 0.001 s
% 3.07/1.35 % (2206821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.35 % (2206822)Peak memory usage: 86 MB
% 3.07/1.35 % (2206821)CaDiCaL version: 2.1.3
% 3.07/1.35 % (2206821)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.35 % (2206821)Time elapsed: 0.001 s
% 3.07/1.35 % (2206821)Peak memory usage: 86 MB
% 3.07/1.35 % (2206824)dis-21_1_sil=8000:lcm=predicate:random_seed=3955759507: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)
% 3.07/1.35 % (2206824)Refutation not found, incomplete strategy
% 3.07/1.35 % (2206824)------------------------------
% 3.07/1.35 % (2206824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.35 % (2206824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.35 % (2206824)CaDiCaL version: 2.1.3
% 3.07/1.35 % (2206824)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.35 % (2206824)Time elapsed: 0.002 s
% 3.07/1.35 % (2206824)Peak memory usage: 88 MB
% 3.07/1.35 % (2206824)Instructions burned: 1 (million)
% 3.07/1.35 % (2206823)First to succeed.
% 3.07/1.35 % (2206823)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2206813"
% 3.07/1.35 % (2206821)------------------------------
% 3.07/1.35 % (2206821)------------------------------
% 3.07/1.35 % (2206822)------------------------------
% 3.07/1.35 % (2206822)------------------------------
% 3.07/1.35 % (2206824)------------------------------
% 3.07/1.35 % (2206824)------------------------------
% 3.07/1.35 % (2206823)Refutation found. Thanks to Tanya!
% 3.07/1.35 % SZS status Theorem for theBenchmark
% 3.07/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.47 % (2206823)------------------------------
% 3.93/1.47 % (2206823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.47 % (2206823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.47 % (2206823)CaDiCaL version: 2.1.3
% 3.93/1.47 % (2206823)Termination reason: Refutation
% 3.93/1.47 % (2206823)Time elapsed: 0.054 s
% 3.93/1.47 % (2206823)Peak memory usage: 91 MB
% 3.93/1.47 % (2206823)Instructions burned: 79 (million)
% 3.93/1.47 % (2206823)------------------------------
% 3.93/1.47 % (2206823)------------------------------
% 3.93/1.47 % (2206813)Success in time 0.486 s
% 3.93/1.47 % Vampire exiting
%------------------------------------------------------------------------------