%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 : Fri Sep 25 02:56:20 PM UTC 2026
% Result : Theorem 1.53s 1.53s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 111 ( 3 unt; 0 def)
% Number of atoms : 497 ( 14 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 699 ( 313 ~; 312 |; 48 &)
% ( 16 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 127 ( 0 sgn 124 !; 3 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f3,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f15,conjecture,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox2/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(f18,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0] :
( ~ relation(X0)
| ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f25,plain,
! [X0] :
( ~ relation(X0)
| ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f26,plain,
? [X0] :
( relation(X0)
& ( well_orders(X0,relation_field(X0))
<~> well_ordering(X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) )
& ( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) )
& ( ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) )
& ( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ well_orders(X0,X1)
| ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) )
& ( ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ well_orders(X0,X1)
| ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) )
& ( ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1) ) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) )
& ( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0] :
( ~ relation(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) ) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f36,plain,
? [X0] :
( relation(X0)
& ( well_orders(X0,relation_field(X0))
| well_ordering(X0) )
& ( ~ well_orders(X0,relation_field(X0))
| ~ well_ordering(X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f37,plain,
? [X0] :
( relation(X0)
& ( well_orders(X0,relation_field(X0))
| well_ordering(X0) )
& ( ~ well_orders(X0,relation_field(X0))
| ~ well_ordering(X0) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
( relation(sK0)
& ( well_orders(sK0,relation_field(sK0))
| well_ordering(sK0) )
& ( ~ well_orders(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f37]) ).
fof(f40,plain,
! [X0] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f43,plain,
! [X0] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X0] :
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f54,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f64,plain,
relation(sK0),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
( well_orders(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f66,plain,
( ~ well_orders(sK0,relation_field(sK0))
| ~ well_ordering(sK0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_50,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_51,plain,
! [X0: $i] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ antisymmetric(X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_52,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_53,plain,
! [X0: $i] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_54,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_55,plain,
! [X0: $i] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_56,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ connected(X0)
| ~ relation(X0)
| ~ antisymmetric(X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_57,plain,
! [X0: $i] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_58,plain,
! [X0: $i] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_59,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( well_orders(X0,X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_69,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_70,plain,
! [X0: $i] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_72,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_73,plain,
! [X0: $i] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_74,negated_conjecture,
( ~ well_ordering(sK0)
| ~ well_orders(sK0,relation_field(sK0)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_75,negated_conjecture,
( well_ordering(sK0)
| well_orders(sK0,relation_field(sK0)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_76,negated_conjecture,
relation(sK0),
inference(cnf_transformation,[],[f64]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X1,relation_field(X1))
| ~ well_ordering(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_51]) ).
tcf(c_495,plain,
! [X0: $i] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_494]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i] :
( well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ connected(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_507,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ connected(X0)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_506]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X1,relation_field(X1))
| ~ well_ordering(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_53]) ).
tcf(c_545,plain,
! [X0: $i] :
( is_connected_in(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_544]) ).
tcf(c_546,plain,
( is_connected_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(instantiation,[status(thm)],[c_545]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i] :
( well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_507]) ).
tcf(c_557,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_556]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X1,relation_field(X1))
| ~ well_ordering(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_55]) ).
tcf(c_595,plain,
! [X0: $i] :
( is_transitive_in(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_594]) ).
tcf(c_596,plain,
( is_transitive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(instantiation,[status(thm)],[c_595]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] :
( well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_557]) ).
tcf(c_607,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X0,relation_field(X0))
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_606]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i] :
( well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ is_transitive_in(X1,relation_field(X1))
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_607]) ).
tcf(c_643,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X0,relation_field(X0))
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_642]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X1,relation_field(X1))
| ~ well_ordering(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_70]) ).
tcf(c_671,plain,
! [X0: $i] :
( is_reflexive_in(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_670]) ).
tcf(c_672,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(instantiation,[status(thm)],[c_671]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] :
( well_ordering(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ is_transitive_in(X1,relation_field(X1))
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_643]) ).
tcf(c_693,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X0,relation_field(X0))
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_692]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X1,relation_field(X1))
| ~ well_ordering(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_73]) ).
tcf(c_721,plain,
! [X0: $i] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_720]) ).
tcf(c_722,plain,
( is_well_founded_in(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0) ),
inference(instantiation,[status(thm)],[c_721]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i] :
( well_orders(X2,X1)
| ~ well_ordering(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ is_well_founded_in(X2,X1)
| ~ is_reflexive_in(X2,X1)
| ~ is_transitive_in(X2,X1)
| ~ is_connected_in(X2,X1)
| ( X0 != X2 )
| ( relation_field(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_495,c_62]) ).
tcf(c_747,plain,
! [X0: $i] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_746]) ).
tcf(c_748,plain,
( well_orders(sK0,relation_field(sK0))
| ~ well_ordering(sK0)
| ~ relation(sK0)
| ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ is_reflexive_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0)) ),
inference(instantiation,[status(thm)],[c_747]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i] :
( well_ordering(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ well_orders(X2,X1)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X0,relation_field(X0))
| ( X0 != X2 )
| ( relation_field(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_693,c_65]) ).
tcf(c_762,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ well_orders(X0,relation_field(X0))
| ~ is_transitive_in(X0,relation_field(X0))
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(unflattening,[status(thm)],[c_761]) ).
tcf(c_778,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_762,c_67,c_63,c_64,c_66]) ).
tcf(c_782,plain,
( well_ordering(sK0)
| ~ relation(sK0)
| ~ well_orders(sK0,relation_field(sK0)) ),
inference(instantiation,[status(thm)],[c_778]) ).
tcf(c_793,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_782,c_748,c_722,c_672,c_596,c_546,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.60 % Computer : n017.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Thu Sep 24 13:18:03 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.64 Running first-order theorem proving
% 0.16/0.64 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.66
% 0.16/0.66 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.66
% 0.16/0.66 % Detected problem language: tptp
% 0.16/0.67 % Proving...
% 1.53/1.53 % SZS status Started for theBenchmark.p
% 1.53/1.53 % SZS status Theorem for theBenchmark.p
% 1.53/1.53
% 1.53/1.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.53/1.53
% 1.53/1.53 % ------ iProver source info
% 1.53/1.53
% 1.53/1.53 % git: date: 2026-07-19 20:42:38 +0200
% 1.53/1.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.53/1.53 % git: non_committed_changes: false
% 1.53/1.53
% 1.53/1.53 % ------ Parsing...
% 1.53/1.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.53/1.53
% 1.53/1.53 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s%
% 1.53/1.53
% 1.53/1.53 % SZS status Theorem for theBenchmark.p
% 1.53/1.53
% 1.53/1.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.53/1.53
% 1.53/1.53
%------------------------------------------------------------------------------