%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU275+1 : 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 : n008.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 12:48:07 PM UTC 2026
% Result : Theorem 2.68s 1.37s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 16 unt; 2 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 134 ( 57 ~; 48 |; 20 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f4,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f6,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f7,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f8,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f9,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f10,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f11,conjecture,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f12,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f16,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
? [X0] :
( ~ well_ordering(inclusion_relation(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0) )
& ( ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0) )
& ( ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f20]) ).
fof(f23,plain,
( ~ well_ordering(inclusion_relation(sK1))
& ordinal(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f19]) ).
fof(f32,plain,
! [X0] :
( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f42,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
~ well_ordering(inclusion_relation(sK1)),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
( ~ reflexive(inclusion_relation(sK1))
| ~ transitive(inclusion_relation(sK1))
| ~ antisymmetric(inclusion_relation(sK1))
| ~ connected(inclusion_relation(sK1))
| ~ well_founded_relation(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(resolution,[],[f32,f43]) ).
fof(f45,plain,
( ~ transitive(inclusion_relation(sK1))
| ~ antisymmetric(inclusion_relation(sK1))
| ~ connected(inclusion_relation(sK1))
| ~ well_founded_relation(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f44,f37]) ).
fof(f46,plain,
( ~ antisymmetric(inclusion_relation(sK1))
| ~ connected(inclusion_relation(sK1))
| ~ well_founded_relation(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f45,f38]) ).
fof(f47,plain,
( ~ connected(inclusion_relation(sK1))
| ~ well_founded_relation(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f46,f40]) ).
fof(f48,plain,
( ~ connected(inclusion_relation(sK1))
| ~ well_founded_relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f47,f33]) ).
fof(f50,definition,
( spl2_1
<=> well_founded_relation(inclusion_relation(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f52,plain,
( ~ well_founded_relation(inclusion_relation(sK1))
| spl2_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl2_2
<=> connected(inclusion_relation(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f56,plain,
( ~ connected(inclusion_relation(sK1))
| spl2_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f48,f54,f50]) ).
fof(f58,plain,
( ~ ordinal(sK1)
| spl2_1 ),
inference(resolution,[],[f52,f41]) ).
fof(f60,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f58,f42]) ).
fof(f61,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f62,plain,
( ~ ordinal(sK1)
| spl2_2 ),
inference(resolution,[],[f56,f39]) ).
fof(f64,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f62,f42]) ).
fof(f65,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n008.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 04:26:55 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.68/1.37 % (1871144)Detected formulas, will run a generic FOF schedule.
% 2.68/1.37 % (1871154)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1005808281:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.37 % (1871154)First to succeed.
% 2.68/1.37 % (1871154)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1871144"
% 2.68/1.37 % (1871149)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=2701222917:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.37 % (1871153)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2199119749:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.37 % (1871151)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=2038021405:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.37 % (1871150)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=1531466666:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.37 % (1871152)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2272291670:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.37 % (1871152)Refutation not found, incomplete strategy
% 2.68/1.37 % (1871152)------------------------------
% 2.68/1.37 % (1871152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.37 % (1871152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.37 % (1871152)CaDiCaL version: 2.1.3
% 2.68/1.37 % (1871152)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.37 % (1871152)Time elapsed: 0.001 s
% 2.68/1.37 % (1871152)Peak memory usage: 86 MB
% 2.68/1.37 % (1871153)Also succeeded, but the first one will report.
% 2.68/1.37 % (1871155)dis-21_1_sil=8000:lcm=predicate:random_seed=1211143143: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)
% 2.68/1.37 % (1871155)Also succeeded, but the first one will report.
% 2.68/1.37 % (1871154)Refutation found. Thanks to Tanya!
% 2.68/1.37 % SZS status Theorem for theBenchmark
% 2.68/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.37 % (1871154)------------------------------
% 2.68/1.37 % (1871154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.37 % (1871154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.37 % (1871154)CaDiCaL version: 2.1.3
% 2.68/1.37 % (1871154)Termination reason: Refutation
% 2.68/1.37 % (1871154)Time elapsed: 0.002 s
% 2.68/1.37 % (1871154)Peak memory usage: 89 MB
% 2.68/1.37 % (1871154)Instructions burned: 2 (million)
% 2.68/1.37 % (1871154)------------------------------
% 2.68/1.37 % (1871154)------------------------------
% 2.68/1.37 % (1871144)Success in time 0.293 s
% 2.68/1.37 % Vampire exiting
%------------------------------------------------------------------------------