%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU032+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:47:06 PM UTC 2026
% Result : Theorem 2.78s 1.26s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 78 ( 18 unt; 4 def)
% Number of atoms : 251 ( 60 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 305 ( 132 ~; 127 |; 28 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 32 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f36,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f38,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f39,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f40,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_rng(X0) = relation_dom(X1)
& relation_composition(X0,X1) = identity_relation(relation_dom(X0)) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
fof(f41,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(function_inverse(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(function_inverse(X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f55,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f55]) ).
fof(f78,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f78]) ).
fof(f81,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f84,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( X1 = function_inverse(X0)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( X1 = function_inverse(X0)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f88,plain,
? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f87]) ).
fof(f103,plain,
( sK11 != function_inverse(function_inverse(sK11))
& one_to_one(sK11)
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f88]) ).
fof(f110,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f111,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f159,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f160,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f162,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f164,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f165,plain,
! [X0,X1] :
( relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f166,plain,
function(sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
relation(sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f169,plain,
sK11 != function_inverse(function_inverse(sK11)),
inference(cnf_transformation,[],[f103]) ).
fof(f222,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f159,f168]) ).
fof(f223,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f222,f167]) ).
fof(f227,plain,
relation_dom(sK11) = relation_rng(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f223,f166]) ).
fof(f251,definition,
( spl12_4
<=> relation(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f253,plain,
( ~ relation(function_inverse(sK11))
| spl12_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f264,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f160,f168]) ).
fof(f265,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f264,f167]) ).
fof(f269,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f265,f166]) ).
fof(f276,plain,
( relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f162,f168]) ).
fof(f277,plain,
( relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f276,f167]) ).
fof(f281,plain,
relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11)),
inference(forward_subsumption_resolution,[],[f277,f166]) ).
fof(f285,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_4 ),
inference(resolution,[],[f253,f111]) ).
fof(f287,plain,
( ~ function(sK11)
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f285,f167]) ).
fof(f288,plain,
( $false
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f287,f166]) ).
fof(f289,plain,
spl12_4,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f310,plain,
! [X0] :
( identity_relation(relation_rng(sK11)) != relation_composition(function_inverse(sK11),X0)
| ~ one_to_one(function_inverse(sK11))
| relation_dom(X0) != relation_rng(function_inverse(sK11))
| function_inverse(function_inverse(sK11)) = X0
| ~ relation(X0)
| ~ function(X0)
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(superposition,[],[f165,f269]) ).
fof(f316,plain,
! [X0] :
( relation_dom(X0) != relation_dom(sK11)
| identity_relation(relation_rng(sK11)) != relation_composition(function_inverse(sK11),X0)
| ~ one_to_one(function_inverse(sK11))
| function_inverse(function_inverse(sK11)) = X0
| ~ relation(X0)
| ~ function(X0)
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11)) ),
inference(forward_demodulation,[],[f310,f227]) ).
fof(f323,definition,
( spl12_7
<=> function(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f325,plain,
( ~ function(function_inverse(sK11))
| spl12_7 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f327,definition,
( spl12_8
<=> one_to_one(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f329,plain,
( ~ one_to_one(function_inverse(sK11))
| spl12_8 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f331,definition,
( spl12_9
<=> ! [X0] :
( relation_dom(X0) != relation_dom(sK11)
| ~ function(X0)
| ~ relation(X0)
| function_inverse(function_inverse(sK11)) = X0
| identity_relation(relation_rng(sK11)) != relation_composition(function_inverse(sK11),X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f332,plain,
( ! [X0] :
( identity_relation(relation_rng(sK11)) != relation_composition(function_inverse(sK11),X0)
| ~ function(X0)
| ~ relation(X0)
| function_inverse(function_inverse(sK11)) = X0
| relation_dom(X0) != relation_dom(sK11) )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( ~ spl12_7
| ~ spl12_4
| ~ spl12_8
| spl12_9 ),
inference(avatar_split_clause,[],[f316,f331,f327,f251,f323]) ).
fof(f378,plain,
( ~ one_to_one(sK11)
| ~ relation(sK11)
| ~ function(sK11)
| spl12_8 ),
inference(resolution,[],[f329,f164]) ).
fof(f380,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_8 ),
inference(forward_subsumption_resolution,[],[f378,f168]) ).
fof(f381,plain,
( ~ function(sK11)
| spl12_8 ),
inference(forward_subsumption_resolution,[],[f380,f167]) ).
fof(f382,plain,
( $false
| spl12_8 ),
inference(forward_subsumption_resolution,[],[f381,f166]) ).
fof(f383,plain,
spl12_8,
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f420,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_7 ),
inference(resolution,[],[f325,f110]) ).
fof(f422,plain,
( ~ function(sK11)
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f420,f167]) ).
fof(f423,plain,
( $false
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f422,f166]) ).
fof(f424,plain,
spl12_7,
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f886,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_rng(sK11))
| ~ function(sK11)
| ~ relation(sK11)
| sK11 = function_inverse(function_inverse(sK11))
| relation_dom(sK11) != relation_dom(sK11)
| ~ spl12_9 ),
inference(superposition,[],[f332,f281]) ).
fof(f887,plain,
( ~ function(sK11)
| ~ relation(sK11)
| sK11 = function_inverse(function_inverse(sK11))
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f886]) ).
fof(f888,plain,
( ~ relation(sK11)
| sK11 = function_inverse(function_inverse(sK11))
| ~ spl12_9 ),
inference(forward_subsumption_resolution,[],[f887,f166]) ).
fof(f889,plain,
( sK11 = function_inverse(function_inverse(sK11))
| ~ spl12_9 ),
inference(forward_subsumption_resolution,[],[f888,f167]) ).
fof(f890,plain,
( $false
| ~ spl12_9 ),
inference(forward_subsumption_resolution,[],[f889,f169]) ).
fof(f891,plain,
~ spl12_9,
inference(avatar_contradiction_clause,[],[f890]) ).
cnf(s6,plain,
spl12_4,
inference(sat_conversion,[],[f289]) ).
cnf(s8,plain,
( ~ spl12_4
| ~ spl12_7
| ~ spl12_8
| spl12_9 ),
inference(sat_conversion,[],[f333]) ).
cnf(s14,plain,
spl12_8,
inference(sat_conversion,[],[f383]) ).
cnf(s21,plain,
spl12_7,
inference(sat_conversion,[],[f424]) ).
cnf(s42,plain,
~ spl12_9,
inference(sat_conversion,[],[f891]) ).
cnf(s43,plain,
~ spl12_4,
inference(rat,[],[s8,s42,s14,s21]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s6,s43]) ).
fof(f892,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU032+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:25:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.78/1.26 % (405310)Detected formulas, will run a generic FOF schedule.
% 2.78/1.26 % (405316)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=963831172:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.26 % (405320)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2177059320:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.26 % (405317)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=2219271940:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.26 % (405315)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=587738601:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.26 % (405318)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2665553646:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.26 % (405319)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4255323227:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.26 % (405318)Refutation not found, incomplete strategy
% 2.78/1.26 % (405318)------------------------------
% 2.78/1.26 % (405318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.26 % (405319)Refutation not found, incomplete strategy
% 2.78/1.26 % (405319)------------------------------
% 2.78/1.26 % (405319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.26 % (405318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.26 % (405318)CaDiCaL version: 2.1.3
% 2.78/1.26 % (405320)First to succeed.
% 2.78/1.26 % (405319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.26 % (405318)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.26 % (405318)Time elapsed: 0.001 s
% 2.78/1.26 % (405318)Peak memory usage: 88 MB
% 2.78/1.26 % (405319)CaDiCaL version: 2.1.3
% 2.78/1.26 % (405319)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.26 % (405319)Time elapsed: 0.002 s
% 2.78/1.26 % (405319)Peak memory usage: 88 MB
% 2.78/1.26 % (405319)Instructions burned: 1 (million)
% 2.78/1.26 % (405320)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-405310"
% 2.78/1.26 % (405321)dis-21_1_sil=8000:lcm=predicate:random_seed=3640135737: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)
% 2.78/1.26 % (405321)Instruction limit reached!
% 2.78/1.26 % (405321)------------------------------
% 2.78/1.26 % (405321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.26 % (405321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.26 % (405321)CaDiCaL version: 2.1.3
% 2.78/1.26 % (405321)Termination reason: Instruction limit
% 2.78/1.26 % (405321)Termination phase: Saturation
% 2.78/1.26 % (405321)Time elapsed: 0.079 s
% 2.78/1.26 % (405321)Peak memory usage: 89 MB
% 2.78/1.26 % (405321)Instructions burned: 130 (million)
% 2.78/1.26 % (405329)lrs+10_1_sil=8000:sp=occurrence:random_seed=356663646:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.78/1.26 % (405329)Also succeeded, but the first one will report.
% 2.78/1.26 % (405319)------------------------------
% 2.78/1.26 % (405319)------------------------------
% 2.78/1.26 % (405318)------------------------------
% 2.78/1.26 % (405318)------------------------------
% 2.78/1.26 % (405320)Refutation found. Thanks to Tanya!
% 2.78/1.26 % SZS status Theorem for theBenchmark
% 2.78/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.35 % (405320)------------------------------
% 3.38/1.35 % (405320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.35 % (405320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.35 % (405320)CaDiCaL version: 2.1.3
% 3.38/1.35 % (405320)Termination reason: Refutation
% 3.38/1.35 % (405320)Time elapsed: 0.017 s
% 3.38/1.35 % (405320)Peak memory usage: 90 MB
% 3.38/1.35 % (405320)Instructions burned: 22 (million)
% 3.38/1.35 % (405320)------------------------------
% 3.38/1.35 % (405320)------------------------------
% 3.38/1.35 % (405310)Success in time 0.411 s
% 3.38/1.35 % Vampire exiting
%------------------------------------------------------------------------------