%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:39:40 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 190 ( 36 unt; 0 def)
% Number of atoms : 658 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 904 ( 436 ~; 370 |; 50 &)
% ( 36 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 119 ( 0 sgn 89 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ) ).
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_reflexive_in(A,B)
& is_transitive_in(A,B)
& is_antisymmetric_in(A,B)
& is_connected_in(A,B)
& is_well_founded_in(A,B) ) ) ) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ) ).
fof(t5_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ) ).
fof(t8_wellord1,conjecture,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& well_orders(A,relation_field(A)) )
=> well_ordering(A) ),
inference(strip,[],[t8_wellord1]) ).
fof(subgoal_1,plain,
! [A] :
( ( relation(A)
& well_ordering(A) )
=> well_orders(A,relation_field(A)) ),
inference(strip,[],[t8_wellord1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& well_orders(A,relation_field(A)) )
=> well_ordering(A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ relation(A)
| ( ~ is_well_founded_in(A,relation_field(A))
<=> ~ well_founded_relation(A) ) ),
inference(canonicalize,[],[t5_wellord1]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ relation(A)
| ( ~ is_well_founded_in(A,relation_field(A))
<=> ~ well_founded_relation(A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ( ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A)
| well_founded_relation(A) )
& ( ~ relation(A)
| ~ well_founded_relation(A)
| is_well_founded_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A)
| well_founded_relation(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A] :
( ~ well_ordering(A)
& relation(A)
& well_orders(A,relation_field(A)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ well_ordering(skolemFOFtoCNF_A)
& relation(skolemFOFtoCNF_A)
& well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ well_orders(A,B)
<=> ( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B) ) ) ),
inference(canonicalize,[],[d5_wellord1]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ well_orders(A,B)
<=> ( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B) ) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ( ~ relation(A)
| ~ well_orders(A,B)
| is_antisymmetric_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_connected_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_reflexive_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_transitive_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_well_founded_in(A,B) )
& ( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B)
| ~ relation(A)
| well_orders(A,B) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ relation(A)
| ~ well_orders(A,B)
| is_well_founded_in(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
relation(skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(canonicalize,[],[d4_wellord1]) ).
fof(normalize_0_13,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] :
( ( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| connected(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) )
& ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A] :
( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] :
( ~ relation(A)
| ( ~ antisymmetric(A)
<=> ~ is_antisymmetric_in(A,relation_field(A)) ) ),
inference(canonicalize,[],[d12_relat_2]) ).
fof(normalize_0_17,plain,
! [A] :
( ~ relation(A)
| ( ~ antisymmetric(A)
<=> ~ is_antisymmetric_in(A,relation_field(A)) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A] :
( ( ~ antisymmetric(A)
| ~ relation(A)
| is_antisymmetric_in(A,relation_field(A)) )
& ( ~ is_antisymmetric_in(A,relation_field(A))
| ~ relation(A)
| antisymmetric(A) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] :
( ~ is_antisymmetric_in(A,relation_field(A))
| ~ relation(A)
| antisymmetric(A) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ~ relation(A)
| ~ well_orders(A,B)
| is_antisymmetric_in(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_21,plain,
! [A] :
( ~ relation(A)
| ( ~ connected(A)
<=> ~ is_connected_in(A,relation_field(A)) ) ),
inference(canonicalize,[],[d14_relat_2]) ).
fof(normalize_0_22,plain,
! [A] :
( ~ relation(A)
| ( ~ connected(A)
<=> ~ is_connected_in(A,relation_field(A)) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A] :
( ( ~ connected(A)
| ~ relation(A)
| is_connected_in(A,relation_field(A)) )
& ( ~ is_connected_in(A,relation_field(A))
| ~ relation(A)
| connected(A) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A] :
( ~ is_connected_in(A,relation_field(A))
| ~ relation(A)
| connected(A) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B] :
( ~ relation(A)
| ~ well_orders(A,B)
| is_connected_in(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_26,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(canonicalize,[],[d9_relat_2]) ).
fof(normalize_0_27,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A] :
( ( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) )
& ( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A] :
( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B] :
( ~ relation(A)
| ~ well_orders(A,B)
| is_reflexive_in(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_31,plain,
! [A] :
( ~ relation(A)
| ( ~ is_transitive_in(A,relation_field(A))
<=> ~ transitive(A) ) ),
inference(canonicalize,[],[d16_relat_2]) ).
fof(normalize_0_32,plain,
! [A] :
( ~ relation(A)
| ( ~ is_transitive_in(A,relation_field(A))
<=> ~ transitive(A) ) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A] :
( ( ~ is_transitive_in(A,relation_field(A))
| ~ relation(A)
| transitive(A) )
& ( ~ relation(A)
| ~ transitive(A)
| is_transitive_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [A] :
( ~ is_transitive_in(A,relation_field(A))
| ~ relation(A)
| transitive(A) ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [A,B] :
( ~ relation(A)
| ~ well_orders(A,B)
| is_transitive_in(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_36,plain,
~ well_ordering(skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A)
| well_founded_relation(A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ is_well_founded_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| ~ relation(skolemFOFtoCNF_A)
| well_founded_relation(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_2,plain,
well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ relation(A)
| ~ well_orders(A,B)
| is_well_founded_in(A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ relation(skolemFOFtoCNF_A)
| ~ well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| is_well_founded_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(relation_field(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_5,plain,
( ~ relation(skolemFOFtoCNF_A)
| is_well_founded_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
relation(skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
is_well_founded_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ relation(skolemFOFtoCNF_A)
| well_founded_relation(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( is_well_founded_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
well_founded_relation(skolemFOFtoCNF_A),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ antisymmetric(skolemFOFtoCNF_A)
| ~ connected(skolemFOFtoCNF_A)
| ~ reflexive(skolemFOFtoCNF_A)
| ~ relation(skolemFOFtoCNF_A)
| ~ transitive(skolemFOFtoCNF_A)
| ~ well_founded_relation(skolemFOFtoCNF_A)
| well_ordering(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_12,plain,
( ~ antisymmetric(skolemFOFtoCNF_A)
| ~ connected(skolemFOFtoCNF_A)
| ~ reflexive(skolemFOFtoCNF_A)
| ~ relation(skolemFOFtoCNF_A)
| ~ transitive(skolemFOFtoCNF_A)
| well_ordering(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( well_founded_relation(skolemFOFtoCNF_A) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ is_antisymmetric_in(A,relation_field(A))
| ~ relation(A)
| antisymmetric(A) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_14,plain,
( ~ is_antisymmetric_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| ~ relation(skolemFOFtoCNF_A)
| antisymmetric(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_15,plain,
( ~ relation(A)
| ~ well_orders(A,B)
| is_antisymmetric_in(A,B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_16,plain,
( ~ relation(skolemFOFtoCNF_A)
| ~ well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| is_antisymmetric_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(relation_field(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_17,plain,
( ~ relation(skolemFOFtoCNF_A)
| is_antisymmetric_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
is_antisymmetric_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ relation(skolemFOFtoCNF_A)
| antisymmetric(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( is_antisymmetric_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
antisymmetric(skolemFOFtoCNF_A),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ connected(skolemFOFtoCNF_A)
| ~ reflexive(skolemFOFtoCNF_A)
| ~ relation(skolemFOFtoCNF_A)
| ~ transitive(skolemFOFtoCNF_A)
| well_ordering(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( antisymmetric(skolemFOFtoCNF_A) )],[refute_0_20,refute_0_12]) ).
cnf(refute_0_22,plain,
( ~ is_connected_in(A,relation_field(A))
| ~ relation(A)
| connected(A) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_23,plain,
( ~ is_connected_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| ~ relation(skolemFOFtoCNF_A)
| connected(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_24,plain,
( ~ relation(A)
| ~ well_orders(A,B)
| is_connected_in(A,B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_25,plain,
( ~ relation(skolemFOFtoCNF_A)
| ~ well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| is_connected_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(relation_field(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_26,plain,
( ~ relation(skolemFOFtoCNF_A)
| is_connected_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_2,refute_0_25]) ).
cnf(refute_0_27,plain,
is_connected_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ relation(skolemFOFtoCNF_A)
| connected(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( is_connected_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
connected(skolemFOFtoCNF_A),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ reflexive(skolemFOFtoCNF_A)
| ~ relation(skolemFOFtoCNF_A)
| ~ transitive(skolemFOFtoCNF_A)
| well_ordering(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( connected(skolemFOFtoCNF_A) )],[refute_0_29,refute_0_21]) ).
cnf(refute_0_31,plain,
( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_32,plain,
( ~ is_reflexive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| ~ relation(skolemFOFtoCNF_A)
| reflexive(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_33,plain,
( ~ relation(A)
| ~ well_orders(A,B)
| is_reflexive_in(A,B) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_34,plain,
( ~ relation(skolemFOFtoCNF_A)
| ~ well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| is_reflexive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(relation_field(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_35,plain,
( ~ relation(skolemFOFtoCNF_A)
| is_reflexive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
is_reflexive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ relation(skolemFOFtoCNF_A)
| reflexive(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( is_reflexive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_36,refute_0_32]) ).
cnf(refute_0_38,plain,
reflexive(skolemFOFtoCNF_A),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ relation(skolemFOFtoCNF_A)
| ~ transitive(skolemFOFtoCNF_A)
| well_ordering(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( reflexive(skolemFOFtoCNF_A) )],[refute_0_38,refute_0_30]) ).
cnf(refute_0_40,plain,
( ~ transitive(skolemFOFtoCNF_A)
| well_ordering(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ is_transitive_in(A,relation_field(A))
| ~ relation(A)
| transitive(A) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_42,plain,
( ~ is_transitive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| ~ relation(skolemFOFtoCNF_A)
| transitive(skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_41:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_43,plain,
( ~ relation(A)
| ~ well_orders(A,B)
| is_transitive_in(A,B) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_44,plain,
( ~ relation(skolemFOFtoCNF_A)
| ~ well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A))
| is_transitive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_43:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(relation_field(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_45,plain,
( ~ relation(skolemFOFtoCNF_A)
| is_transitive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( well_orders(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_2,refute_0_44]) ).
cnf(refute_0_46,plain,
is_transitive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ relation(skolemFOFtoCNF_A)
| transitive(skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( is_transitive_in(skolemFOFtoCNF_A,relation_field(skolemFOFtoCNF_A)) )],[refute_0_46,refute_0_42]) ).
cnf(refute_0_48,plain,
transitive(skolemFOFtoCNF_A),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A) )],[refute_0_6,refute_0_47]) ).
cnf(refute_0_49,plain,
well_ordering(skolemFOFtoCNF_A),
inference(resolve,[$cnf( transitive(skolemFOFtoCNF_A) )],[refute_0_48,refute_0_40]) ).
cnf(refute_0_50,plain,
~ well_ordering(skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A) )],[refute_0_49,refute_0_50]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( relation(A)
& well_ordering(A) )
=> well_orders(A,relation_field(A)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( ~ well_orders(A,relation_field(A))
& relation(A)
& well_ordering(A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
& relation(skolemFOFtoCNF_A_1)
& well_ordering(skolemFOFtoCNF_A_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
well_ordering(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(canonicalize,[],[d4_wellord1]) ).
fof(normalize_1_4,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] :
( ( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| connected(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) )
& ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
relation(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_8,plain,
! [A] :
( ~ relation(A)
| ( ~ is_well_founded_in(A,relation_field(A))
<=> ~ well_founded_relation(A) ) ),
inference(canonicalize,[],[t5_wellord1]) ).
fof(normalize_1_9,plain,
! [A] :
( ~ relation(A)
| ( ~ is_well_founded_in(A,relation_field(A))
<=> ~ well_founded_relation(A) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A] :
( ( ~ is_well_founded_in(A,relation_field(A))
| ~ relation(A)
| well_founded_relation(A) )
& ( ~ relation(A)
| ~ well_founded_relation(A)
| is_well_founded_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A] :
( ~ relation(A)
| ~ well_founded_relation(A)
| is_well_founded_in(A,relation_field(A)) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ well_orders(A,B)
<=> ( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B) ) ) ),
inference(canonicalize,[],[d5_wellord1]) ).
fof(normalize_1_13,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ well_orders(A,B)
<=> ( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B) ) ) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [A,B] :
( ( ~ relation(A)
| ~ well_orders(A,B)
| is_antisymmetric_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_connected_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_reflexive_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_transitive_in(A,B) )
& ( ~ relation(A)
| ~ well_orders(A,B)
| is_well_founded_in(A,B) )
& ( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B)
| ~ relation(A)
| well_orders(A,B) ) ),
inference(clausify,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A,B] :
( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B)
| ~ relation(A)
| well_orders(A,B) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [A] :
( ~ relation(A)
| ( ~ antisymmetric(A)
<=> ~ is_antisymmetric_in(A,relation_field(A)) ) ),
inference(canonicalize,[],[d12_relat_2]) ).
fof(normalize_1_17,plain,
! [A] :
( ~ relation(A)
| ( ~ antisymmetric(A)
<=> ~ is_antisymmetric_in(A,relation_field(A)) ) ),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [A] :
( ( ~ antisymmetric(A)
| ~ relation(A)
| is_antisymmetric_in(A,relation_field(A)) )
& ( ~ is_antisymmetric_in(A,relation_field(A))
| ~ relation(A)
| antisymmetric(A) ) ),
inference(clausify,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [A] :
( ~ antisymmetric(A)
| ~ relation(A)
| is_antisymmetric_in(A,relation_field(A)) ),
inference(conjunct,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_21,plain,
! [A] :
( ~ relation(A)
| ( ~ connected(A)
<=> ~ is_connected_in(A,relation_field(A)) ) ),
inference(canonicalize,[],[d14_relat_2]) ).
fof(normalize_1_22,plain,
! [A] :
( ~ relation(A)
| ( ~ connected(A)
<=> ~ is_connected_in(A,relation_field(A)) ) ),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [A] :
( ( ~ connected(A)
| ~ relation(A)
| is_connected_in(A,relation_field(A)) )
& ( ~ is_connected_in(A,relation_field(A))
| ~ relation(A)
| connected(A) ) ),
inference(clausify,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [A] :
( ~ connected(A)
| ~ relation(A)
| is_connected_in(A,relation_field(A)) ),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_26,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(canonicalize,[],[d9_relat_2]) ).
fof(normalize_1_27,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(specialize,[],[normalize_1_26]) ).
fof(normalize_1_28,plain,
! [A] :
( ( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) )
& ( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_1_27]) ).
fof(normalize_1_29,plain,
! [A] :
( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ),
inference(conjunct,[],[normalize_1_28]) ).
fof(normalize_1_30,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_31,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_32,plain,
! [A] :
( ~ relation(A)
| ( ~ is_transitive_in(A,relation_field(A))
<=> ~ transitive(A) ) ),
inference(canonicalize,[],[d16_relat_2]) ).
fof(normalize_1_33,plain,
! [A] :
( ~ relation(A)
| ( ~ is_transitive_in(A,relation_field(A))
<=> ~ transitive(A) ) ),
inference(specialize,[],[normalize_1_32]) ).
fof(normalize_1_34,plain,
! [A] :
( ( ~ is_transitive_in(A,relation_field(A))
| ~ relation(A)
| transitive(A) )
& ( ~ relation(A)
| ~ transitive(A)
| is_transitive_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_1_33]) ).
fof(normalize_1_35,plain,
! [A] :
( ~ relation(A)
| ~ transitive(A)
| is_transitive_in(A,relation_field(A)) ),
inference(conjunct,[],[normalize_1_34]) ).
fof(normalize_1_36,plain,
~ well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
well_ordering(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_3,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
relation(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
well_founded_relation(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
( ~ relation(A)
| ~ well_founded_relation(A)
| is_well_founded_in(A,relation_field(A)) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_7,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_founded_relation(skolemFOFtoCNF_A_1)
| is_well_founded_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_1_6:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_8,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| is_well_founded_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( well_founded_relation(skolemFOFtoCNF_A_1) )],[refute_1_5,refute_1_7]) ).
cnf(refute_1_9,plain,
is_well_founded_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ is_antisymmetric_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_reflexive_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_well_founded_in(A,B)
| ~ relation(A)
| well_orders(A,B) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_11,plain,
( ~ is_antisymmetric_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_well_founded_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ relation(skolemFOFtoCNF_A_1)
| well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(relation_field(skolemFOFtoCNF_A_1)))]]) ).
cnf(refute_1_12,plain,
( ~ is_antisymmetric_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ relation(skolemFOFtoCNF_A_1)
| well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( is_well_founded_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) )],[refute_1_9,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ antisymmetric(A)
| ~ relation(A)
| is_antisymmetric_in(A,relation_field(A)) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_14,plain,
( ~ antisymmetric(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_A_1)
| is_antisymmetric_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_1_13:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_15,plain,
( ~ antisymmetric(skolemFOFtoCNF_A_1)
| is_antisymmetric_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_14]) ).
cnf(refute_1_16,plain,
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_17,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| antisymmetric(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_1_16:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_18,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| antisymmetric(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_1_0,refute_1_17]) ).
cnf(refute_1_19,plain,
antisymmetric(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_18]) ).
cnf(refute_1_20,plain,
is_antisymmetric_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( antisymmetric(skolemFOFtoCNF_A_1) )],[refute_1_19,refute_1_15]) ).
cnf(refute_1_21,plain,
( ~ is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ relation(skolemFOFtoCNF_A_1)
| well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( is_antisymmetric_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) )],[refute_1_20,refute_1_12]) ).
cnf(refute_1_22,plain,
( ~ connected(A)
| ~ relation(A)
| is_connected_in(A,relation_field(A)) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_23,plain,
( ~ connected(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_A_1)
| is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_1_22:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_24,plain,
( ~ connected(skolemFOFtoCNF_A_1)
| is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_23]) ).
cnf(refute_1_25,plain,
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_26,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| connected(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_1_25:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_27,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| connected(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_1_0,refute_1_26]) ).
cnf(refute_1_28,plain,
connected(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_27]) ).
cnf(refute_1_29,plain,
is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( connected(skolemFOFtoCNF_A_1) )],[refute_1_28,refute_1_24]) ).
cnf(refute_1_30,plain,
( ~ is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ relation(skolemFOFtoCNF_A_1)
| well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( is_connected_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) )],[refute_1_29,refute_1_21]) ).
cnf(refute_1_31,plain,
( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ),
inference(canonicalize,[],[normalize_1_29]) ).
cnf(refute_1_32,plain,
( ~ reflexive(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_A_1)
| is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_1_31:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_33,plain,
( ~ reflexive(skolemFOFtoCNF_A_1)
| is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
inference(canonicalize,[],[normalize_1_30]) ).
cnf(refute_1_35,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| reflexive(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_1_34:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_36,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| reflexive(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_1_0,refute_1_35]) ).
cnf(refute_1_37,plain,
reflexive(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_36]) ).
cnf(refute_1_38,plain,
is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( reflexive(skolemFOFtoCNF_A_1) )],[refute_1_37,refute_1_33]) ).
cnf(refute_1_39,plain,
( ~ is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1))
| ~ relation(skolemFOFtoCNF_A_1)
| well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( is_reflexive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) )],[refute_1_38,refute_1_30]) ).
cnf(refute_1_40,plain,
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
inference(canonicalize,[],[normalize_1_31]) ).
cnf(refute_1_41,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_1_40:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_42,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_1_0,refute_1_41]) ).
cnf(refute_1_43,plain,
transitive(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ relation(A)
| ~ transitive(A)
| is_transitive_in(A,relation_field(A)) ),
inference(canonicalize,[],[normalize_1_35]) ).
cnf(refute_1_45,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ transitive(skolemFOFtoCNF_A_1)
| is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_1_44:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_1_46,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( transitive(skolemFOFtoCNF_A_1) )],[refute_1_43,refute_1_45]) ).
cnf(refute_1_47,plain,
is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_46]) ).
cnf(refute_1_48,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( is_transitive_in(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) )],[refute_1_47,refute_1_39]) ).
cnf(refute_1_49,plain,
well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_1_4,refute_1_48]) ).
cnf(refute_1_50,plain,
~ well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)),
inference(canonicalize,[],[normalize_1_36]) ).
cnf(refute_1_51,plain,
$false,
inference(resolve,[$cnf( well_orders(skolemFOFtoCNF_A_1,relation_field(skolemFOFtoCNF_A_1)) )],[refute_1_49,refute_1_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 10:10:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------