%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:58 PM UTC 2026
% Result : Theorem 2.97s 1.25s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 103 ( 9 unt; 0 def)
% Number of atoms : 398 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 535 ( 240 ~; 221 |; 48 &)
% ( 16 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 70 ( 67 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f3,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( well_orders(X0,X1)
<=> ( is_reflexive_in(X0,X1)
& is_transitive_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_connected_in(X0,X1)
& is_well_founded_in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_wellord1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f14,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f15,conjecture,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
fof(f16,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
? [X0] :
( ( well_orders(X0,relation_field(X0))
<~> well_ordering(X0) )
& relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f19,plain,
! [X0] :
( ! [X1] :
( well_orders(X0,X1)
<=> ( is_reflexive_in(X0,X1)
& is_transitive_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_connected_in(X0,X1)
& is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0] :
( ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0] :
( ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
? [X0] :
( ( ~ well_ordering(X0)
| ~ well_orders(X0,relation_field(X0)) )
& ( well_ordering(X0)
| well_orders(X0,relation_field(X0)) )
& relation(X0) ),
inference(nnf_transformation,[],[f17]) ).
fof(f26,plain,
? [X0] :
( ( ~ well_ordering(X0)
| ~ well_orders(X0,relation_field(X0)) )
& ( well_ordering(X0)
| well_orders(X0,relation_field(X0)) )
& relation(X0) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( ( ~ well_ordering(sK0)
| ~ well_orders(sK0,relation_field(sK0)) )
& ( well_ordering(sK0)
| well_orders(sK0,relation_field(sK0)) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f26]) ).
fof(f28,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,[],[f18]) ).
fof(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( well_orders(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_well_founded_in(X0,X1) )
& ( ( is_reflexive_in(X0,X1)
& is_transitive_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_connected_in(X0,X1)
& is_well_founded_in(X0,X1) )
| ~ well_orders(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ( well_orders(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_well_founded_in(X0,X1) )
& ( ( is_reflexive_in(X0,X1)
& is_transitive_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_connected_in(X0,X1)
& is_well_founded_in(X0,X1) )
| ~ well_orders(X0,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) )
& ( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0] :
( ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X0] :
( ( ( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0)) )
& ( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) )
& ( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f24]) ).
fof(f37,plain,
relation(sK0),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
( well_orders(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
( ~ well_orders(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
! [X0] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X0] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
! [X0] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X0] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0] :
( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X0,X1] :
( well_orders(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X0] :
( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f54,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0] :
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
! [X0] :
( ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f64,plain,
! [X0] :
( antisymmetric(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(resolution,[],[f53,f48]) ).
fof(f65,plain,
! [X0] :
( ~ well_orders(X0,relation_field(X0))
| ~ relation(X0)
| antisymmetric(X0) ),
inference(duplicate_literal_removal,[],[f64]) ).
fof(f68,plain,
! [X0] :
( connected(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(resolution,[],[f55,f47]) ).
fof(f69,plain,
! [X0] :
( ~ well_orders(X0,relation_field(X0))
| ~ relation(X0)
| connected(X0) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f72,plain,
! [X0] :
( transitive(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(resolution,[],[f57,f49]) ).
fof(f73,plain,
! [X0] :
( ~ well_orders(X0,relation_field(X0))
| ~ relation(X0)
| transitive(X0) ),
inference(duplicate_literal_removal,[],[f72]) ).
fof(f76,plain,
! [X0] :
( reflexive(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(resolution,[],[f59,f50]) ).
fof(f77,plain,
! [X0] :
( ~ well_orders(X0,relation_field(X0))
| ~ relation(X0)
| reflexive(X0) ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f80,plain,
! [X0] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(resolution,[],[f61,f46]) ).
fof(f81,plain,
! [X0] :
( ~ well_orders(X0,relation_field(X0))
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f83,plain,
( ~ relation(sK0)
| antisymmetric(sK0)
| well_ordering(sK0) ),
inference(resolution,[],[f65,f38]) ).
fof(f84,plain,
( ~ relation(sK0)
| antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f83,f42]) ).
fof(f85,plain,
antisymmetric(sK0),
inference(forward_subsumption_resolution,[],[f84,f37]) ).
fof(f86,plain,
( ~ is_reflexive_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| ~ well_ordering(sK0) ),
inference(resolution,[],[f51,f39]) ).
fof(f89,plain,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_reflexive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(forward_subsumption_resolution,[],[f86,f37]) ).
fof(f90,plain,
( ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_reflexive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f89,f60]) ).
fof(f92,plain,
( ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_reflexive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f90,f40]) ).
fof(f93,plain,
( ~ is_reflexive_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(forward_subsumption_resolution,[],[f92,f37]) ).
fof(f94,plain,
( ~ relation(sK0)
| connected(sK0)
| well_ordering(sK0) ),
inference(resolution,[],[f69,f38]) ).
fof(f97,plain,
( ~ relation(sK0)
| connected(sK0) ),
inference(forward_subsumption_resolution,[],[f94,f41]) ).
fof(f98,plain,
connected(sK0),
inference(forward_subsumption_resolution,[],[f97,f37]) ).
fof(f99,plain,
( ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ reflexive(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f93,f58]) ).
fof(f101,plain,
( ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f99,f44]) ).
fof(f102,plain,
( ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(forward_subsumption_resolution,[],[f101,f37]) ).
fof(f103,plain,
( ~ relation(sK0)
| transitive(sK0)
| well_ordering(sK0) ),
inference(resolution,[],[f73,f38]) ).
fof(f106,plain,
( ~ relation(sK0)
| transitive(sK0) ),
inference(forward_subsumption_resolution,[],[f103,f43]) ).
fof(f107,plain,
transitive(sK0),
inference(forward_subsumption_resolution,[],[f106,f37]) ).
fof(f108,plain,
( ~ relation(sK0)
| reflexive(sK0)
| well_ordering(sK0) ),
inference(resolution,[],[f77,f38]) ).
fof(f111,plain,
( ~ relation(sK0)
| reflexive(sK0) ),
inference(forward_subsumption_resolution,[],[f108,f44]) ).
fof(f112,plain,
reflexive(sK0),
inference(forward_subsumption_resolution,[],[f111,f37]) ).
fof(f113,plain,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ transitive(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f102,f56]) ).
fof(f115,plain,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f113,f43]) ).
fof(f116,plain,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(forward_subsumption_resolution,[],[f115,f37]) ).
fof(f117,plain,
( ~ relation(sK0)
| well_founded_relation(sK0)
| well_ordering(sK0) ),
inference(resolution,[],[f81,f38]) ).
fof(f120,plain,
( ~ relation(sK0)
| well_founded_relation(sK0) ),
inference(forward_subsumption_resolution,[],[f117,f40]) ).
fof(f121,plain,
well_founded_relation(sK0),
inference(forward_subsumption_resolution,[],[f120,f37]) ).
fof(f122,plain,
( ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ connected(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f116,f54]) ).
fof(f124,plain,
( ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f122,f41]) ).
fof(f125,plain,
( ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(forward_subsumption_resolution,[],[f124,f37]) ).
fof(f126,plain,
( ~ well_ordering(sK0)
| ~ antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f125,f52]) ).
fof(f128,plain,
( ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f126,f42]) ).
fof(f129,plain,
~ well_ordering(sK0),
inference(forward_subsumption_resolution,[],[f128,f37]) ).
fof(f130,plain,
( ~ reflexive(sK0)
| ~ transitive(sK0)
| ~ antisymmetric(sK0)
| ~ connected(sK0)
| ~ well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f129,f45]) ).
fof(f131,plain,
( ~ transitive(sK0)
| ~ antisymmetric(sK0)
| ~ connected(sK0)
| ~ well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f130,f112]) ).
fof(f132,plain,
( ~ antisymmetric(sK0)
| ~ connected(sK0)
| ~ well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f131,f107]) ).
fof(f133,plain,
( ~ connected(sK0)
| ~ well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f132,f85]) ).
fof(f134,plain,
( ~ well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f133,f98]) ).
fof(f135,plain,
~ relation(sK0),
inference(forward_subsumption_resolution,[],[f134,f121]) ).
fof(f136,plain,
$false,
inference(forward_subsumption_resolution,[],[f135,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n015.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:20:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.97/1.25 % (2254790)Detected formulas, will run a generic FOF schedule.
% 2.97/1.25 % (2254795)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=1289723456:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.97/1.25 % (2254799)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1996937575:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.97/1.25 % (2254797)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=3070978417:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.97/1.25 % (2254798)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2867129592:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.97/1.25 % (2254796)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=2369974799:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.97/1.25 % (2254801)dis-21_1_sil=8000:lcm=predicate:random_seed=3383348945: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)
% 2.97/1.25 % (2254800)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2360040191:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.97/1.25 % (2254798)Refutation not found, incomplete strategy
% 2.97/1.25 % (2254798)------------------------------
% 2.97/1.25 % (2254798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.25 % (2254798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.25 % (2254798)CaDiCaL version: 2.1.3
% 2.97/1.25 % (2254798)Termination reason: Refutation not found, incomplete strategy
% 2.97/1.25 % (2254798)Time elapsed: 0.001 s
% 2.97/1.25 % (2254798)Peak memory usage: 87 MB
% 2.97/1.25 % (2254799)First to succeed.
% 2.97/1.25 % (2254801)Also succeeded, but the first one will report.
% 2.97/1.25 % (2254799)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2254790"
% 2.97/1.25 % (2254800)Also succeeded, but the first one will report.
% 2.97/1.25 % (2254798)------------------------------
% 2.97/1.25 % (2254798)------------------------------
% 2.97/1.25 % (2254799)Refutation found. Thanks to Tanya!
% 2.97/1.25 % SZS status Theorem for theBenchmark
% 2.97/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.40 % (2254799)------------------------------
% 0.16/1.40 % (2254799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (2254799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (2254799)CaDiCaL version: 2.1.3
% 0.16/1.40 % (2254799)Termination reason: Refutation
% 0.16/1.40 % (2254799)Time elapsed: 0.004 s
% 0.16/1.40 % (2254799)Peak memory usage: 88 MB
% 0.16/1.40 % (2254799)Instructions burned: 4 (million)
% 0.16/1.40 % (2254799)------------------------------
% 0.16/1.40 % (2254799)------------------------------
% 0.16/1.40 % (2254790)Success in time 0.41 s
% 0.16/1.40 % Vampire exiting
%------------------------------------------------------------------------------