%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n019.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 12:52:41 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 18 unt; 2 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 103 ( 43 ~; 42 |; 9 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 24 ( 0 sgn 23 !; 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(f28,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f33,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f37,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
~ well_ordering(inclusion_relation(sK1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0] :
( ~ well_ordering(X0)
| well_founded_relation(X0)
| connected(X0)
| ~ antisymmetric(X0)
| transitive(X0)
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f49,plain,
! [X0] : ~ transitive(inclusion_relation(X0)),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f50,plain,
! [X0] :
( ~ connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f51,plain,
! [X0] :
( ~ well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f52,plain,
well_ordering(inclusion_relation(sK1)),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f57,plain,
( well_founded_relation(inclusion_relation(sK1))
| connected(inclusion_relation(sK1))
| ~ antisymmetric(inclusion_relation(sK1))
| transitive(inclusion_relation(sK1))
| ~ reflexive(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(resolution,[],[f42,f52]) ).
fof(f58,plain,
( well_founded_relation(inclusion_relation(sK1))
| connected(inclusion_relation(sK1))
| transitive(inclusion_relation(sK1))
| ~ reflexive(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f57,f36]) ).
fof(f59,plain,
( well_founded_relation(inclusion_relation(sK1))
| connected(inclusion_relation(sK1))
| ~ reflexive(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f58,f49]) ).
fof(f60,plain,
( well_founded_relation(inclusion_relation(sK1))
| connected(inclusion_relation(sK1))
| ~ relation(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f59,f33]) ).
fof(f61,plain,
( well_founded_relation(inclusion_relation(sK1))
| connected(inclusion_relation(sK1)) ),
inference(forward_subsumption_resolution,[],[f60,f29]) ).
fof(f63,definition,
( spl2_1
<=> connected(inclusion_relation(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f65,plain,
( connected(inclusion_relation(sK1))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl2_2
<=> well_founded_relation(inclusion_relation(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f69,plain,
( well_founded_relation(inclusion_relation(sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f61,f67,f63]) ).
fof(f71,plain,
( ~ ordinal(sK1)
| ~ spl2_2 ),
inference(resolution,[],[f69,f51]) ).
fof(f73,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f71,f38]) ).
fof(f74,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f73]) ).
fof(f75,plain,
( ~ ordinal(sK1)
| ~ spl2_1 ),
inference(resolution,[],[f65,f50]) ).
fof(f77,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f75,f38]) ).
fof(f78,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f77]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f74]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f78]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f79,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n019.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
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:26:19 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 % (3657343)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (3657349)% WARNING: option uhcvi not known.
% 0.11/0.44 % (3657349)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3452309890:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % (3657349) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3657343-3657349"...
% 0.11/0.44 % (3657349)...printing done.
% 0.11/0.44 % (3657349)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (3657349)------------------------------
% 0.11/0.44 % (3657349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (3657349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (3657349)CaDiCaL version: 2.1.3
% 0.11/0.44 % (3657349)Termination reason: Refutation
% 0.11/0.44 % (3657349)Time elapsed: 0.001 s
% 0.11/0.44 % (3657349)Peak memory usage: 12 MB
% 0.11/0.44 % (3657349)Instructions burned: 2 (million)
% 0.11/0.44 % (3657343)Success in time 0.024 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------