%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU275+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 : n004.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 3.58s 1.49s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 124 ( 51 ~; 46 |; 20 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 28 ( 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,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(f86,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f262,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f285,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f305,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f317,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f328,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f337,conjecture,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f338,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f337]) ).
fof(f418,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f650,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f305]) ).
fof(f681,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f328]) ).
fof(f690,plain,
? [X0] :
( ~ well_ordering(inclusion_relation(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f338]) ).
fof(f831,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,[],[f418]) ).
fof(f832,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,[],[f831]) ).
fof(f990,plain,
( ~ well_ordering(inclusion_relation(sK148))
& ordinal(sK148) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(X0,sK148)],[f690]) ).
fof(f1211,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f832]) ).
fof(f1293,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1576,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f262]) ).
fof(f1616,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f285]) ).
fof(f1644,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f650]) ).
fof(f1675,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f317]) ).
fof(f1693,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f681]) ).
fof(f1707,plain,
ordinal(sK148),
inference(cnf_transformation,[],[f990]) ).
fof(f1708,plain,
~ well_ordering(inclusion_relation(sK148)),
inference(cnf_transformation,[],[f990]) ).
fof(f1914,plain,
! [X0] :
( ~ reflexive(inclusion_relation(X0))
| ~ transitive(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(resolution,[],[f1211,f1693]) ).
fof(f1915,plain,
! [X0] :
( ~ transitive(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1914,f1576]) ).
fof(f1916,plain,
! [X0] :
( ~ antisymmetric(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1915,f1616]) ).
fof(f1917,plain,
! [X0] :
( ~ connected(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1916,f1675]) ).
fof(f1918,plain,
! [X0] :
( well_ordering(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1917,f1644]) ).
fof(f1919,plain,
! [X0] :
( well_ordering(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1918,f1293]) ).
fof(f1920,plain,
~ ordinal(sK148),
inference(resolution,[],[f1919,f1708]) ).
fof(f1931,plain,
$false,
inference(forward_subsumption_resolution,[],[f1920,f1707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:26:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.58/1.49 % (4146943)Detected formulas, will run a generic FOF schedule.
% 3.58/1.49 % (4146950)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=3192319750:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.49 % (4146951)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3966977092:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.49 % (4146948)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=1743252448:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.49 % (4146952)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2354580424:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.49 % (4146949)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=3928366082:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.49 % (4146953)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2055228814:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.49 % (4146954)dis-21_1_sil=8000:lcm=predicate:random_seed=2080131005: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)
% 3.58/1.49 % (4146953)First to succeed.
% 3.58/1.49 % (4146953)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4146943"
% 3.58/1.49 % (4146951)Instruction limit reached!
% 3.58/1.49 % (4146951)------------------------------
% 3.58/1.49 % (4146951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (4146951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (4146951)CaDiCaL version: 2.1.3
% 3.58/1.49 % (4146951)Termination reason: Instruction limit
% 3.58/1.49 % (4146951)Termination phase: Saturation
% 3.58/1.49 % (4146951)Time elapsed: 0.067 s
% 3.58/1.49 % (4146951)Peak memory usage: 90 MB
% 3.58/1.49 % (4146951)Instructions burned: 110 (million)
% 3.58/1.49 % (4146954)Instruction limit reached!
% 3.58/1.49 % (4146954)------------------------------
% 3.58/1.49 % (4146954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (4146954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (4146954)CaDiCaL version: 2.1.3
% 3.58/1.49 % (4146954)Termination reason: Instruction limit
% 3.58/1.49 % (4146954)Termination phase: Saturation
% 3.58/1.49 % (4146954)Time elapsed: 0.067 s
% 3.58/1.49 % (4146954)Peak memory usage: 90 MB
% 3.58/1.49 % (4146954)Instructions burned: 130 (million)
% 3.58/1.49 % (4146952)Instruction limit reached!
% 3.58/1.49 % (4146952)------------------------------
% 3.58/1.49 % (4146952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (4146952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (4146952)CaDiCaL version: 2.1.3
% 3.58/1.49 % (4146952)Termination reason: Instruction limit
% 3.58/1.49 % (4146952)Termination phase: Saturation
% 3.58/1.49 % (4146952)Time elapsed: 0.079 s
% 3.58/1.49 % (4146952)Peak memory usage: 90 MB
% 3.58/1.49 % (4146952)Instructions burned: 119 (million)
% 3.58/1.49 % (4146962)lrs+10_1_sil=8000:sp=occurrence:random_seed=3459607649:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.58/1.49 % (4146964)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1773535718:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.58/1.49 % (4146963)lrs+10_1_sil=32000:urr=on:br=off:random_seed=244909629:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.58/1.49 % (4146963)Also succeeded, but the first one will report.
% 3.58/1.49 % (4146953)Refutation found. Thanks to Tanya!
% 3.58/1.49 % SZS status Theorem for theBenchmark
% 3.58/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.49 % (4146953)------------------------------
% 3.58/1.49 % (4146953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (4146953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (4146953)CaDiCaL version: 2.1.3
% 3.58/1.49 % (4146953)Termination reason: Refutation
% 3.58/1.49 % (4146953)Time elapsed: 0.023 s
% 3.58/1.49 % (4146953)Peak memory usage: 90 MB
% 3.58/1.49 % (4146953)Instructions burned: 37 (million)
% 3.58/1.49 % (4146953)------------------------------
% 3.58/1.49 % (4146953)------------------------------
% 3.58/1.49 % (4146943)Success in time 0.445 s
% 3.58/1.49 % Vampire exiting
%------------------------------------------------------------------------------