%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU261+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 : n013.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 12:52:38 PM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 77 ( 19 unt; 0 def)
% Number of atoms : 326 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 431 ( 182 ~; 176 |; 53 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 46 ( 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f3,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> ( ( reflexive(X0)
=> reflexive(X1) )
& ( transitive(X0)
=> transitive(X1) )
& ( connected(X0)
=> connected(X1) )
& ( antisymmetric(X0)
=> antisymmetric(X1) )
& ( well_founded_relation(X0)
=> well_founded_relation(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f4,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( well_ordering(X0)
& relation_isomorphism(X0,X1,X2) )
=> well_ordering(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f5,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( well_ordering(X0)
& relation_isomorphism(X0,X1,X2) )
=> well_ordering(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( reflexive(X1)
| ~ reflexive(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( well_founded_relation(X1)
| ~ well_founded_relation(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( reflexive(X1)
| ~ reflexive(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( well_founded_relation(X1)
| ~ well_founded_relation(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& well_ordering(X0)
& relation_isomorphism(X0,X1,X2)
& relation(X2)
& function(X2) )
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& well_ordering(X0)
& relation_isomorphism(X0,X1,X2)
& relation(X2)
& function(X2) )
& relation(X1) )
& relation(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,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,[],[f6]) ).
fof(f12,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,[],[f11]) ).
fof(f14,plain,
( ~ well_ordering(sK2)
& well_ordering(sK1)
& relation_isomorphism(sK1,sK2,sK3)
& relation(sK3)
& function(sK3)
& relation(sK2)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f10]) ).
fof(f15,plain,
! [X0] :
( ~ well_ordering(X0)
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0] :
( ~ well_ordering(X0)
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0] :
( ~ well_ordering(X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ well_ordering(X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0] :
( ~ well_ordering(X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ well_founded_relation(X0)
| well_founded_relation(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ antisymmetric(X0)
| antisymmetric(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ connected(X0)
| connected(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ transitive(X0)
| transitive(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ reflexive(X0)
| reflexive(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f28,plain,
relation(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
relation(sK2),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
function(sK3),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
relation(sK3),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
relation_isomorphism(sK1,sK2,sK3),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
well_ordering(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
~ well_ordering(sK2),
inference(cnf_transformation,[],[f14]) ).
fof(f44,plain,
( well_founded_relation(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f15,f33]) ).
fof(f45,plain,
well_founded_relation(sK1),
inference(forward_subsumption_resolution,[],[f44,f28]) ).
fof(f59,plain,
( connected(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f16,f33]) ).
fof(f60,plain,
connected(sK1),
inference(forward_subsumption_resolution,[],[f59,f28]) ).
fof(f64,plain,
( antisymmetric(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f17,f33]) ).
fof(f65,plain,
antisymmetric(sK1),
inference(forward_subsumption_resolution,[],[f64,f28]) ).
fof(f69,plain,
( transitive(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f18,f33]) ).
fof(f70,plain,
transitive(sK1),
inference(forward_subsumption_resolution,[],[f69,f28]) ).
fof(f74,plain,
( reflexive(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f19,f33]) ).
fof(f75,plain,
reflexive(sK1),
inference(forward_subsumption_resolution,[],[f74,f28]) ).
fof(f112,plain,
( ~ transitive(sK1)
| transitive(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolution,[],[f26,f32]) ).
fof(f113,plain,
( transitive(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f112,f70]) ).
fof(f114,plain,
( transitive(sK2)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f113,f31]) ).
fof(f115,plain,
( transitive(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f114,f30]) ).
fof(f116,plain,
( transitive(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f115,f29]) ).
fof(f117,plain,
transitive(sK2),
inference(forward_subsumption_resolution,[],[f116,f28]) ).
fof(f133,plain,
( ~ antisymmetric(sK1)
| antisymmetric(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolution,[],[f24,f32]) ).
fof(f134,plain,
( antisymmetric(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f133,f65]) ).
fof(f135,plain,
( antisymmetric(sK2)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f134,f31]) ).
fof(f136,plain,
( antisymmetric(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f135,f30]) ).
fof(f137,plain,
( antisymmetric(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f136,f29]) ).
fof(f138,plain,
antisymmetric(sK2),
inference(forward_subsumption_resolution,[],[f137,f28]) ).
fof(f161,plain,
( ~ reflexive(sK1)
| reflexive(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolution,[],[f27,f32]) ).
fof(f162,plain,
( reflexive(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f161,f75]) ).
fof(f170,plain,
( reflexive(sK2)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f162,f31]) ).
fof(f172,plain,
( reflexive(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f170,f30]) ).
fof(f173,plain,
( reflexive(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f172,f29]) ).
fof(f174,plain,
reflexive(sK2),
inference(forward_subsumption_resolution,[],[f173,f28]) ).
fof(f195,plain,
( ~ well_founded_relation(sK1)
| well_founded_relation(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolution,[],[f23,f32]) ).
fof(f196,plain,
( well_founded_relation(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f195,f45]) ).
fof(f197,plain,
( well_founded_relation(sK2)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f196,f31]) ).
fof(f198,plain,
( well_founded_relation(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f197,f30]) ).
fof(f199,plain,
( well_founded_relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f198,f29]) ).
fof(f200,plain,
well_founded_relation(sK2),
inference(forward_subsumption_resolution,[],[f199,f28]) ).
fof(f215,plain,
( ~ connected(sK1)
| connected(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolution,[],[f25,f32]) ).
fof(f216,plain,
( connected(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f215,f60]) ).
fof(f217,plain,
( connected(sK2)
| ~ function(sK3)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f216,f31]) ).
fof(f218,plain,
( connected(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f217,f30]) ).
fof(f219,plain,
( connected(sK2)
| ~ relation(sK1) ),
inference(forward_subsumption_resolution,[],[f218,f29]) ).
fof(f220,plain,
connected(sK2),
inference(forward_subsumption_resolution,[],[f219,f28]) ).
fof(f229,plain,
( ~ reflexive(sK2)
| ~ transitive(sK2)
| ~ antisymmetric(sK2)
| ~ connected(sK2)
| well_ordering(sK2)
| ~ relation(sK2) ),
inference(resolution,[],[f20,f200]) ).
fof(f230,plain,
( ~ transitive(sK2)
| ~ antisymmetric(sK2)
| ~ connected(sK2)
| well_ordering(sK2)
| ~ relation(sK2) ),
inference(forward_subsumption_resolution,[],[f229,f174]) ).
fof(f231,plain,
( ~ antisymmetric(sK2)
| ~ connected(sK2)
| well_ordering(sK2)
| ~ relation(sK2) ),
inference(forward_subsumption_resolution,[],[f230,f117]) ).
fof(f232,plain,
( ~ connected(sK2)
| well_ordering(sK2)
| ~ relation(sK2) ),
inference(forward_subsumption_resolution,[],[f231,f138]) ).
fof(f233,plain,
( well_ordering(sK2)
| ~ relation(sK2) ),
inference(forward_subsumption_resolution,[],[f232,f220]) ).
fof(f234,plain,
~ relation(sK2),
inference(forward_subsumption_resolution,[],[f233,f34]) ).
fof(f235,plain,
$false,
inference(forward_subsumption_resolution,[],[f234,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 04:21:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.43 % (797671)Will run a generic schedule for satisfiability detection.
% 0.09/0.43 % (797678)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1570952963:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.43 % (797678) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-797671-797678"...
% 0.09/0.43 % (797677)% WARNING: option uhcvi not known.
% 0.09/0.43 % (797678)...printing done.
% 0.09/0.43 % (797678)Refutation found. Thanks to Tanya!
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (797678)------------------------------
% 0.09/0.44 % (797678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (797678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (797678)CaDiCaL version: 2.1.3
% 0.09/0.44 % (797678)Termination reason: Refutation
% 0.09/0.44 % (797678)Time elapsed: 0.003 s
% 0.09/0.44 % (797678)Peak memory usage: 12 MB
% 0.09/0.44 % (797678)Instructions burned: 5 (million)
% 0.09/0.44 % (797671)Success in time 0.035 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------