TSTP Solution File: SEU248+2 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU248+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n014.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 10:26:27 EDT 2022
% Result : Theorem 2.44s 2.73s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 311
% Syntax : Number of formulae : 3527 ( 514 unt; 0 def)
% Number of atoms : 12841 (2553 equ)
% Maximal formula atoms : 130 ( 3 avg)
% Number of connectives : 16193 (6879 ~;7684 |; 864 &)
% ( 226 <=>; 540 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 28 usr; 2 prp; 0-2 aty)
% Number of functors : 245 ( 245 usr; 29 con; 0-5 aty)
% Number of variables : 8054 ( 362 sgn1995 !; 64 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('<stdin>',d8_relat_1) ).
fof(c_0_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('<stdin>',d12_relat_1) ).
fof(c_0_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
file('<stdin>',d11_relat_1) ).
fof(c_0_3,axiom,
! [X1,X2,X3,X4] :
( X4 = unordered_triple(X1,X2,X3)
<=> ! [X5] :
( in(X5,X4)
<=> ~ ( X5 != X1
& X5 != X2
& X5 != X3 ) ) ),
file('<stdin>',d1_enumset1) ).
fof(c_0_4,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
file('<stdin>',d14_relat_1) ).
fof(c_0_5,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('<stdin>',d13_relat_1) ).
fof(c_0_6,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('<stdin>',d2_zfmisc_1) ).
fof(c_0_7,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('<stdin>',d13_funct_1) ).
fof(c_0_8,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('<stdin>',d8_setfam_1) ).
fof(c_0_9,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('<stdin>',d3_xboole_0) ).
fof(c_0_10,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('<stdin>',d12_funct_1) ).
fof(c_0_11,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('<stdin>',d4_xboole_0) ).
fof(c_0_12,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
file('<stdin>',d7_relat_1) ).
fof(c_0_13,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('<stdin>',d2_relat_1) ).
fof(c_0_14,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('<stdin>',d2_xboole_0) ).
fof(c_0_15,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
file('<stdin>',d10_relat_1) ).
fof(c_0_16,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( subset(X3,X2)
& X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& disjoint(fiber(X1,X4),X3) ) ) ) ),
file('<stdin>',d3_wellord1) ).
fof(c_0_17,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_18,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('<stdin>',d5_relat_1) ).
fof(c_0_19,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('<stdin>',d4_relat_1) ).
fof(c_0_20,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_transitive_in(X1,X2)
<=> ! [X3,X4,X5] :
( ( in(X3,X2)
& in(X4,X2)
& in(X5,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X5),X1) )
=> in(ordered_pair(X3,X5),X1) ) ) ),
file('<stdin>',d8_relat_2) ).
fof(c_0_21,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('<stdin>',d3_relat_1) ).
fof(c_0_22,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_connected_in(X1,X2)
<=> ! [X3,X4] :
~ ( in(X3,X2)
& in(X4,X2)
& X3 != X4
& ~ in(ordered_pair(X3,X4),X1)
& ~ in(ordered_pair(X4,X3),X1) ) ) ),
file('<stdin>',d6_relat_2) ).
fof(c_0_23,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('<stdin>',d1_relat_2) ).
fof(c_0_24,axiom,
! [X1,X2] :
( ( X1 != empty_set
=> ( X2 = set_meet(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ! [X4] :
( in(X4,X1)
=> in(X3,X4) ) ) ) )
& ( X1 = empty_set
=> ( X2 = set_meet(X1)
<=> X2 = empty_set ) ) ),
file('<stdin>',d1_setfam_1) ).
fof(c_0_25,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_antisymmetric_in(X1,X2)
<=> ! [X3,X4] :
( ( in(X3,X2)
& in(X4,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X3),X1) )
=> X3 = X4 ) ) ),
file('<stdin>',d4_relat_2) ).
fof(c_0_26,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('<stdin>',dt_k6_subset_1) ).
fof(c_0_27,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('<stdin>',d5_funct_1) ).
fof(c_0_28,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_29,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( subset(X2,relation_field(X1))
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X1,X3),X2) ) ) ) ),
file('<stdin>',d2_wellord1) ).
fof(c_0_30,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( well_orders(X1,X2)
<=> ( is_reflexive_in(X1,X2)
& is_transitive_in(X1,X2)
& is_antisymmetric_in(X1,X2)
& is_connected_in(X1,X2)
& is_well_founded_in(X1,X2) ) ) ),
file('<stdin>',d5_wellord1) ).
fof(c_0_31,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('<stdin>',redefinition_k6_subset_1) ).
fof(c_0_32,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('<stdin>',d8_funct_1) ).
fof(c_0_33,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_34,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_35,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('<stdin>',d4_funct_1) ).
fof(c_0_36,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('<stdin>',dt_k7_setfam_1) ).
fof(c_0_37,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('<stdin>',t7_tarski) ).
fof(c_0_38,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k6_setfam_1) ).
fof(c_0_39,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k5_setfam_1) ).
fof(c_0_40,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('<stdin>',d1_relat_1) ).
fof(c_0_41,axiom,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('<stdin>',t9_tarski) ).
fof(c_0_42,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_43,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k7_setfam_1) ).
fof(c_0_44,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
file('<stdin>',d3_ordinal1) ).
fof(c_0_45,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k3_subset_1) ).
fof(c_0_46,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_47,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k3_subset_1) ).
fof(c_0_48,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
file('<stdin>',redefinition_k6_setfam_1) ).
fof(c_0_49,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('<stdin>',redefinition_k5_setfam_1) ).
fof(c_0_50,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('<stdin>',t4_subset) ).
fof(c_0_51,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_52,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('<stdin>',d6_wellord1) ).
fof(c_0_53,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('<stdin>',d5_subset_1) ).
fof(c_0_54,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_55,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('<stdin>',fc1_funct_1) ).
fof(c_0_56,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('<stdin>',fc4_subset_1) ).
fof(c_0_57,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_58,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_59,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('<stdin>',redefinition_r1_ordinal1) ).
fof(c_0_60,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('<stdin>',fc3_subset_1) ).
fof(c_0_61,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_62,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_63,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
file('<stdin>',d4_wellord1) ).
fof(c_0_64,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('<stdin>',t3_subset) ).
fof(c_0_65,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_66,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_67,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('<stdin>',fc9_relat_1) ).
fof(c_0_68,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('<stdin>',fc5_funct_1) ).
fof(c_0_69,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('<stdin>',fc4_funct_1) ).
fof(c_0_70,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
file('<stdin>',fc3_relat_1) ).
fof(c_0_71,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('<stdin>',fc2_relat_1) ).
fof(c_0_72,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('<stdin>',fc1_relat_1) ).
fof(c_0_73,axiom,
! [X1,X2] :
( ( relation(X1)
& relation_empty_yielding(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& relation_empty_yielding(relation_dom_restriction(X1,X2)) ) ),
file('<stdin>',fc13_relat_1) ).
fof(c_0_74,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
file('<stdin>',fc10_relat_1) ).
fof(c_0_75,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('<stdin>',dt_k5_relat_1) ).
fof(c_0_76,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('<stdin>',d2_ordinal1) ).
fof(c_0_77,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('<stdin>',d9_relat_2) ).
fof(c_0_78,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
file('<stdin>',d16_relat_2) ).
fof(c_0_79,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('<stdin>',d14_relat_2) ).
fof(c_0_80,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('<stdin>',d12_relat_2) ).
fof(c_0_81,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('<stdin>',connectedness_r1_ordinal1) ).
fof(c_0_82,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('<stdin>',t2_subset) ).
fof(c_0_83,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('<stdin>',d2_subset_1) ).
fof(c_0_84,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_85,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('<stdin>',dt_k8_relat_1) ).
fof(c_0_86,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('<stdin>',dt_k7_relat_1) ).
fof(c_0_87,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('<stdin>',dt_k2_wellord1) ).
fof(c_0_88,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('<stdin>',d6_relat_1) ).
fof(c_0_89,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('<stdin>',t1_subset) ).
fof(c_0_90,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_91,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_92,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
file('<stdin>',fc3_funct_1) ).
fof(c_0_93,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_94,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_95,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('<stdin>',d9_funct_1) ).
fof(c_0_96,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('<stdin>',reflexivity_r1_ordinal1) ).
fof(c_0_97,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('<stdin>',fc6_relat_1) ).
fof(c_0_98,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('<stdin>',fc5_relat_1) ).
fof(c_0_99,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_100,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_101,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_102,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_103,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('<stdin>',dt_k2_subset_1) ).
fof(c_0_104,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_105,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_106,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('<stdin>',dt_k2_funct_1) ).
fof(c_0_107,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('<stdin>',d1_ordinal1) ).
fof(c_0_108,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('<stdin>',fc3_ordinal1) ).
fof(c_0_109,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_110,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_111,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('<stdin>',d4_ordinal1) ).
fof(c_0_112,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('<stdin>',cc2_ordinal1) ).
fof(c_0_113,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('<stdin>',involutiveness_k4_relat_1) ).
fof(c_0_114,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('<stdin>',fc8_relat_1) ).
fof(c_0_115,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('<stdin>',fc7_relat_1) ).
fof(c_0_116,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
file('<stdin>',fc4_ordinal1) ).
fof(c_0_117,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
file('<stdin>',fc11_relat_1) ).
fof(c_0_118,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('<stdin>',dt_k4_relat_1) ).
fof(c_0_119,axiom,
! [X1] : ~ empty(singleton(X1)),
file('<stdin>',fc2_subset_1) ).
fof(c_0_120,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_121,axiom,
! [X1] : ~ empty(succ(X1)),
file('<stdin>',fc1_ordinal1) ).
fof(c_0_122,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_123,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_124,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_125,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_126,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_127,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_128,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_129,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_130,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
file('<stdin>',d6_ordinal1) ).
fof(c_0_131,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('<stdin>',cc3_ordinal1) ).
fof(c_0_132,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('<stdin>',cc1_relat_1) ).
fof(c_0_133,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('<stdin>',cc1_ordinal1) ).
fof(c_0_134,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('<stdin>',cc1_funct_1) ).
fof(c_0_135,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('<stdin>',fc2_funct_1) ).
fof(c_0_136,axiom,
! [X1] : relation(identity_relation(X1)),
file('<stdin>',dt_k6_relat_1) ).
fof(c_0_137,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_138,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('<stdin>',d4_subset_1) ).
fof(c_0_139,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc3_ordinal1) ).
fof(c_0_140,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_141,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_142,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('<stdin>',rc4_funct_1) ).
fof(c_0_143,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_144,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_145,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc2_ordinal1) ).
fof(c_0_146,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_147,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_148,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_149,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc1_ordinal1) ).
fof(c_0_150,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_151,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('<stdin>',fc4_relat_1) ).
fof(c_0_152,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('<stdin>',fc2_ordinal1) ).
fof(c_0_153,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_154,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('<stdin>',fc12_relat_1) ).
fof(c_0_155,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_156,axiom,
$true,
file('<stdin>',dt_k9_relat_1) ).
fof(c_0_157,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_158,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_159,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_160,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_161,axiom,
$true,
file('<stdin>',dt_k3_relat_1) ).
fof(c_0_162,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_163,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_164,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_165,axiom,
$true,
file('<stdin>',dt_k2_relat_1) ).
fof(c_0_166,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_167,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_168,axiom,
$true,
file('<stdin>',dt_k1_wellord1) ).
fof(c_0_169,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_170,axiom,
$true,
file('<stdin>',dt_k1_setfam_1) ).
fof(c_0_171,axiom,
$true,
file('<stdin>',dt_k1_relat_1) ).
fof(c_0_172,axiom,
$true,
file('<stdin>',dt_k1_ordinal1) ).
fof(c_0_173,axiom,
$true,
file('<stdin>',dt_k1_funct_1) ).
fof(c_0_174,axiom,
$true,
file('<stdin>',dt_k1_enumset1) ).
fof(c_0_175,axiom,
$true,
file('<stdin>',dt_k10_relat_1) ).
fof(c_0_176,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
c_0_0 ).
fof(c_0_177,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
c_0_1 ).
fof(c_0_178,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
c_0_2 ).
fof(c_0_179,axiom,
! [X1,X2,X3,X4] :
( X4 = unordered_triple(X1,X2,X3)
<=> ! [X5] :
( in(X5,X4)
<=> ~ ( X5 != X1
& X5 != X2
& X5 != X3 ) ) ),
c_0_3 ).
fof(c_0_180,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
c_0_4 ).
fof(c_0_181,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
c_0_5 ).
fof(c_0_182,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
c_0_6 ).
fof(c_0_183,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
c_0_7 ).
fof(c_0_184,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
c_0_8 ).
fof(c_0_185,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_9 ).
fof(c_0_186,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
c_0_10 ).
fof(c_0_187,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_188,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
c_0_12 ).
fof(c_0_189,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
c_0_13 ).
fof(c_0_190,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_14 ).
fof(c_0_191,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
c_0_15 ).
fof(c_0_192,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( subset(X3,X2)
& X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& disjoint(fiber(X1,X4),X3) ) ) ) ),
c_0_16 ).
fof(c_0_193,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_17 ).
fof(c_0_194,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
c_0_18 ).
fof(c_0_195,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
c_0_19 ).
fof(c_0_196,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_transitive_in(X1,X2)
<=> ! [X3,X4,X5] :
( ( in(X3,X2)
& in(X4,X2)
& in(X5,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X5),X1) )
=> in(ordered_pair(X3,X5),X1) ) ) ),
c_0_20 ).
fof(c_0_197,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
c_0_21 ).
fof(c_0_198,plain,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_connected_in(X1,X2)
<=> ! [X3,X4] :
~ ( in(X3,X2)
& in(X4,X2)
& X3 != X4
& ~ in(ordered_pair(X3,X4),X1)
& ~ in(ordered_pair(X4,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_199,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
c_0_23 ).
fof(c_0_200,axiom,
! [X1,X2] :
( ( X1 != empty_set
=> ( X2 = set_meet(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ! [X4] :
( in(X4,X1)
=> in(X3,X4) ) ) ) )
& ( X1 = empty_set
=> ( X2 = set_meet(X1)
<=> X2 = empty_set ) ) ),
c_0_24 ).
fof(c_0_201,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_antisymmetric_in(X1,X2)
<=> ! [X3,X4] :
( ( in(X3,X2)
& in(X4,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X3),X1) )
=> X3 = X4 ) ) ),
c_0_25 ).
fof(c_0_202,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
c_0_26 ).
fof(c_0_203,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
c_0_27 ).
fof(c_0_204,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_28 ).
fof(c_0_205,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( subset(X2,relation_field(X1))
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X1,X3),X2) ) ) ) ),
c_0_29 ).
fof(c_0_206,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( well_orders(X1,X2)
<=> ( is_reflexive_in(X1,X2)
& is_transitive_in(X1,X2)
& is_antisymmetric_in(X1,X2)
& is_connected_in(X1,X2)
& is_well_founded_in(X1,X2) ) ) ),
c_0_30 ).
fof(c_0_207,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
c_0_31 ).
fof(c_0_208,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
c_0_32 ).
fof(c_0_209,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_33 ).
fof(c_0_210,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_34 ).
fof(c_0_211,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_212,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
c_0_36 ).
fof(c_0_213,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
c_0_37 ).
fof(c_0_214,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
c_0_38 ).
fof(c_0_215,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
c_0_39 ).
fof(c_0_216,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
c_0_40 ).
fof(c_0_217,plain,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_218,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_42 ).
fof(c_0_219,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
c_0_43 ).
fof(c_0_220,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_221,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
c_0_45 ).
fof(c_0_222,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_46 ).
fof(c_0_223,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
c_0_47 ).
fof(c_0_224,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
c_0_48 ).
fof(c_0_225,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
c_0_49 ).
fof(c_0_226,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
c_0_50 ).
fof(c_0_227,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_51 ).
fof(c_0_228,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
c_0_52 ).
fof(c_0_229,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
c_0_53 ).
fof(c_0_230,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_54 ).
fof(c_0_231,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
c_0_55 ).
fof(c_0_232,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_233,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_234,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_235,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
c_0_59 ).
fof(c_0_236,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_237,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_238,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_62 ).
fof(c_0_239,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
c_0_63 ).
fof(c_0_240,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
c_0_64 ).
fof(c_0_241,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_242,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_243,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
c_0_67 ).
fof(c_0_244,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
c_0_68 ).
fof(c_0_245,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
c_0_69 ).
fof(c_0_246,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
c_0_70 ).
fof(c_0_247,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
c_0_71 ).
fof(c_0_248,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
c_0_72 ).
fof(c_0_249,axiom,
! [X1,X2] :
( ( relation(X1)
& relation_empty_yielding(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& relation_empty_yielding(relation_dom_restriction(X1,X2)) ) ),
c_0_73 ).
fof(c_0_250,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
c_0_74 ).
fof(c_0_251,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
c_0_75 ).
fof(c_0_252,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
c_0_76 ).
fof(c_0_253,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
c_0_77 ).
fof(c_0_254,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
c_0_78 ).
fof(c_0_255,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
c_0_79 ).
fof(c_0_256,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
c_0_80 ).
fof(c_0_257,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
c_0_81 ).
fof(c_0_258,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
c_0_82 ).
fof(c_0_259,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_260,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_84 ).
fof(c_0_261,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
c_0_85 ).
fof(c_0_262,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
c_0_86 ).
fof(c_0_263,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
c_0_87 ).
fof(c_0_264,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
c_0_88 ).
fof(c_0_265,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
c_0_89 ).
fof(c_0_266,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_90 ).
fof(c_0_267,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_91 ).
fof(c_0_268,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
c_0_92 ).
fof(c_0_269,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_270,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_94 ).
fof(c_0_271,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
c_0_95 ).
fof(c_0_272,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
c_0_96 ).
fof(c_0_273,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_274,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_275,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_99 ).
fof(c_0_276,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_100 ).
fof(c_0_277,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_101 ).
fof(c_0_278,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_102 ).
fof(c_0_279,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
c_0_103 ).
fof(c_0_280,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_104 ).
fof(c_0_281,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_282,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
c_0_106 ).
fof(c_0_283,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
c_0_107 ).
fof(c_0_284,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_285,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_286,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_110 ).
fof(c_0_287,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
c_0_111 ).
fof(c_0_288,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
c_0_112 ).
fof(c_0_289,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
c_0_113 ).
fof(c_0_290,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
c_0_114 ).
fof(c_0_291,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
c_0_115 ).
fof(c_0_292,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
c_0_116 ).
fof(c_0_293,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
c_0_117 ).
fof(c_0_294,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
c_0_118 ).
fof(c_0_295,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_296,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_297,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_298,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_122 ).
fof(c_0_299,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_123 ).
fof(c_0_300,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_124 ).
fof(c_0_301,axiom,
! [X1,X2] : subset(X1,X1),
c_0_125 ).
fof(c_0_302,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_126 ).
fof(c_0_303,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_127 ).
fof(c_0_304,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_128 ).
fof(c_0_305,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_129 ).
fof(c_0_306,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
c_0_130 ).
fof(c_0_307,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
c_0_131 ).
fof(c_0_308,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
c_0_132 ).
fof(c_0_309,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
c_0_133 ).
fof(c_0_310,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
c_0_134 ).
fof(c_0_311,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
c_0_135 ).
fof(c_0_312,axiom,
! [X1] : relation(identity_relation(X1)),
c_0_136 ).
fof(c_0_313,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_137 ).
fof(c_0_314,axiom,
! [X1] : cast_to_subset(X1) = X1,
c_0_138 ).
fof(c_0_315,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_316,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_317,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_318,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
c_0_142 ).
fof(c_0_319,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_143 ).
fof(c_0_320,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_144 ).
fof(c_0_321,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_145 ).
fof(c_0_322,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_146 ).
fof(c_0_323,axiom,
? [X1] : empty(X1),
c_0_147 ).
fof(c_0_324,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_148 ).
fof(c_0_325,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_149 ).
fof(c_0_326,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_150 ).
fof(c_0_327,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_151 ).
fof(c_0_328,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
c_0_152 ).
fof(c_0_329,axiom,
empty(empty_set),
c_0_153 ).
fof(c_0_330,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_154 ).
fof(c_0_331,axiom,
$true,
c_0_155 ).
fof(c_0_332,axiom,
$true,
c_0_156 ).
fof(c_0_333,axiom,
$true,
c_0_157 ).
fof(c_0_334,axiom,
$true,
c_0_158 ).
fof(c_0_335,axiom,
$true,
c_0_159 ).
fof(c_0_336,axiom,
$true,
c_0_160 ).
fof(c_0_337,axiom,
$true,
c_0_161 ).
fof(c_0_338,axiom,
$true,
c_0_162 ).
fof(c_0_339,axiom,
$true,
c_0_163 ).
fof(c_0_340,axiom,
$true,
c_0_164 ).
fof(c_0_341,axiom,
$true,
c_0_165 ).
fof(c_0_342,axiom,
$true,
c_0_166 ).
fof(c_0_343,axiom,
$true,
c_0_167 ).
fof(c_0_344,axiom,
$true,
c_0_168 ).
fof(c_0_345,axiom,
$true,
c_0_169 ).
fof(c_0_346,axiom,
$true,
c_0_170 ).
fof(c_0_347,axiom,
$true,
c_0_171 ).
fof(c_0_348,axiom,
$true,
c_0_172 ).
fof(c_0_349,axiom,
$true,
c_0_173 ).
fof(c_0_350,axiom,
$true,
c_0_174 ).
fof(c_0_351,axiom,
$true,
c_0_175 ).
fof(c_0_352,plain,
! [X7,X8,X9,X10,X11,X13,X14,X15,X18] :
( ( in(ordered_pair(X10,esk69_5(X7,X8,X9,X10,X11)),X7)
| ~ in(ordered_pair(X10,X11),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk69_5(X7,X8,X9,X10,X11),X11),X8)
| ~ in(ordered_pair(X10,X11),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(X13,X15),X7)
| ~ in(ordered_pair(X15,X14),X8)
| in(ordered_pair(X13,X14),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk70_3(X7,X8,X9),esk71_3(X7,X8,X9)),X9)
| ~ in(ordered_pair(esk70_3(X7,X8,X9),X18),X7)
| ~ in(ordered_pair(X18,esk71_3(X7,X8,X9)),X8)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk70_3(X7,X8,X9),esk72_3(X7,X8,X9)),X7)
| in(ordered_pair(esk70_3(X7,X8,X9),esk71_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk72_3(X7,X8,X9),esk71_3(X7,X8,X9)),X8)
| in(ordered_pair(esk70_3(X7,X8,X9),esk71_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_176])])])])])]) ).
fof(c_0_353,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( in(X10,X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(X9,X10),X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(X12,X6)
| ~ in(ordered_pair(X11,X12),X7)
| in(ordered_pair(X11,X12),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk8_3(X6,X7,X8),esk9_3(X6,X7,X8)),X8)
| ~ in(esk9_3(X6,X7,X8),X6)
| ~ in(ordered_pair(esk8_3(X6,X7,X8),esk9_3(X6,X7,X8)),X7)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(esk9_3(X6,X7,X8),X6)
| in(ordered_pair(esk8_3(X6,X7,X8),esk9_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk8_3(X6,X7,X8),esk9_3(X6,X7,X8)),X7)
| in(ordered_pair(esk8_3(X6,X7,X8),esk9_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])])])])])]) ).
fof(c_0_354,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( in(X9,X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(ordered_pair(X9,X10),X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( ~ in(X11,X7)
| ~ in(ordered_pair(X11,X12),X6)
| in(ordered_pair(X11,X12),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| ~ in(esk3_3(X6,X7,X8),X7)
| ~ in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X6)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(esk3_3(X6,X7,X8),X7)
| in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X6)
| in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])])])])])]) ).
fof(c_0_355,plain,
! [X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ( ~ in(X10,X9)
| X10 = X6
| X10 = X7
| X10 = X8
| X9 != unordered_triple(X6,X7,X8) )
& ( X11 != X6
| in(X11,X9)
| X9 != unordered_triple(X6,X7,X8) )
& ( X11 != X7
| in(X11,X9)
| X9 != unordered_triple(X6,X7,X8) )
& ( X11 != X8
| in(X11,X9)
| X9 != unordered_triple(X6,X7,X8) )
& ( esk17_4(X12,X13,X14,X15) != X12
| ~ in(esk17_4(X12,X13,X14,X15),X15)
| X15 = unordered_triple(X12,X13,X14) )
& ( esk17_4(X12,X13,X14,X15) != X13
| ~ in(esk17_4(X12,X13,X14,X15),X15)
| X15 = unordered_triple(X12,X13,X14) )
& ( esk17_4(X12,X13,X14,X15) != X14
| ~ in(esk17_4(X12,X13,X14,X15),X15)
| X15 = unordered_triple(X12,X13,X14) )
& ( in(esk17_4(X12,X13,X14,X15),X15)
| esk17_4(X12,X13,X14,X15) = X12
| esk17_4(X12,X13,X14,X15) = X13
| esk17_4(X12,X13,X14,X15) = X14
| X15 = unordered_triple(X12,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_179])])])])])]) ).
fof(c_0_356,plain,
! [X6,X7,X8,X9,X11,X12,X13,X14,X16] :
( ( in(ordered_pair(X9,esk14_4(X6,X7,X8,X9)),X6)
| ~ in(X9,X8)
| X8 != relation_inverse_image(X6,X7)
| ~ relation(X6) )
& ( in(esk14_4(X6,X7,X8,X9),X7)
| ~ in(X9,X8)
| X8 != relation_inverse_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(ordered_pair(X11,X12),X6)
| ~ in(X12,X7)
| in(X11,X8)
| X8 != relation_inverse_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(esk15_3(X6,X13,X14),X14)
| ~ in(ordered_pair(esk15_3(X6,X13,X14),X16),X6)
| ~ in(X16,X13)
| X14 = relation_inverse_image(X6,X13)
| ~ relation(X6) )
& ( in(ordered_pair(esk15_3(X6,X13,X14),esk16_3(X6,X13,X14)),X6)
| in(esk15_3(X6,X13,X14),X14)
| X14 = relation_inverse_image(X6,X13)
| ~ relation(X6) )
& ( in(esk16_3(X6,X13,X14),X13)
| in(esk15_3(X6,X13,X14),X14)
| X14 = relation_inverse_image(X6,X13)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_180])])])])])]) ).
fof(c_0_357,plain,
! [X6,X7,X8,X9,X11,X12,X13,X14,X16] :
( ( in(ordered_pair(esk11_4(X6,X7,X8,X9),X9),X6)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( in(esk11_4(X6,X7,X8,X9),X7)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(ordered_pair(X12,X11),X6)
| ~ in(X12,X7)
| in(X11,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(esk12_3(X6,X13,X14),X14)
| ~ in(ordered_pair(X16,esk12_3(X6,X13,X14)),X6)
| ~ in(X16,X13)
| X14 = relation_image(X6,X13)
| ~ relation(X6) )
& ( in(ordered_pair(esk13_3(X6,X13,X14),esk12_3(X6,X13,X14)),X6)
| in(esk12_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6) )
& ( in(esk13_3(X6,X13,X14),X13)
| in(esk12_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])])])])])]) ).
fof(c_0_358,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk35_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk36_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk35_4(X7,X8,X9,X10),esk36_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(X14,X7)
| ~ in(X15,X8)
| X13 != ordered_pair(X14,X15)
| in(X13,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(esk37_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk37_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk38_3(X16,X17,X18),X16)
| in(esk37_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk39_3(X16,X17,X18),X17)
| in(esk37_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk37_3(X16,X17,X18) = ordered_pair(esk38_3(X16,X17,X18),esk39_3(X16,X17,X18))
| in(esk37_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_182])])])])])]) ).
fof(c_0_359,plain,
! [X5,X6,X7,X8,X9,X10,X11] :
( ( in(X8,relation_dom(X5))
| ~ in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X5,X8),X6)
| ~ in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X9,relation_dom(X5))
| ~ in(apply(X5,X9),X6)
| in(X9,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk10_3(X5,X10,X11),X11)
| ~ in(esk10_3(X5,X10,X11),relation_dom(X5))
| ~ in(apply(X5,esk10_3(X5,X10,X11)),X10)
| X11 = relation_inverse_image(X5,X10)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk10_3(X5,X10,X11),relation_dom(X5))
| in(esk10_3(X5,X10,X11),X11)
| X11 = relation_inverse_image(X5,X10)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X5,esk10_3(X5,X10,X11)),X10)
| in(esk10_3(X5,X10,X11),X11)
| X11 = relation_inverse_image(X5,X10)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])])])])])]) ).
fof(c_0_360,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( element(esk76_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk76_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk76_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk76_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk76_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])])])])]) ).
fof(c_0_361,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X9,X5)
| ~ in(X9,X6)
| in(X9,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk47_3(X10,X11,X12),X12)
| ~ in(esk47_3(X10,X11,X12),X10)
| ~ in(esk47_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk47_3(X10,X11,X12),X10)
| in(esk47_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk47_3(X10,X11,X12),X11)
| in(esk47_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_185])])])])])]) ).
fof(c_0_362,plain,
! [X6,X7,X8,X9,X11,X12,X13,X14,X16] :
( ( in(esk5_4(X6,X7,X8,X9),relation_dom(X6))
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk5_4(X6,X7,X8,X9),X7)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6)
| ~ function(X6) )
& ( X9 = apply(X6,esk5_4(X6,X7,X8,X9))
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X12,relation_dom(X6))
| ~ in(X12,X7)
| X11 != apply(X6,X12)
| in(X11,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(esk6_3(X6,X13,X14),X14)
| ~ in(X16,relation_dom(X6))
| ~ in(X16,X13)
| esk6_3(X6,X13,X14) != apply(X6,X16)
| X14 = relation_image(X6,X13)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk7_3(X6,X13,X14),relation_dom(X6))
| in(esk6_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk7_3(X6,X13,X14),X13)
| in(esk6_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6)
| ~ function(X6) )
& ( esk6_3(X6,X13,X14) = apply(X6,esk7_3(X6,X13,X14))
| in(esk6_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])])])])])]) ).
fof(c_0_363,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X9,X5)
| in(X9,X6)
| in(X9,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk56_3(X10,X11,X12),X12)
| ~ in(esk56_3(X10,X11,X12),X10)
| in(esk56_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk56_3(X10,X11,X12),X10)
| in(esk56_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk56_3(X10,X11,X12),X11)
| in(esk56_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])])])])])]) ).
fof(c_0_364,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ in(ordered_pair(X7,X8),X6)
| in(ordered_pair(X8,X7),X5)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X10,X9),X5)
| in(ordered_pair(X9,X10),X6)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk65_2(X5,X6),esk66_2(X5,X6)),X6)
| ~ in(ordered_pair(esk66_2(X5,X6),esk65_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk65_2(X5,X6),esk66_2(X5,X6)),X6)
| in(ordered_pair(esk66_2(X5,X6),esk65_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])])])])])]) ).
fof(c_0_365,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| X5 != X6
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X10),X6)
| in(ordered_pair(X9,X10),X5)
| X5 != X6
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk29_2(X5,X6),esk30_2(X5,X6)),X5)
| ~ in(ordered_pair(esk29_2(X5,X6),esk30_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk29_2(X5,X6),esk30_2(X5,X6)),X5)
| in(ordered_pair(esk29_2(X5,X6),esk30_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])])])])])]) ).
fof(c_0_366,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X9,X5)
| in(X9,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X9,X6)
| in(X9,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk34_3(X10,X11,X12),X10)
| ~ in(esk34_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk34_3(X10,X11,X12),X11)
| ~ in(esk34_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk34_3(X10,X11,X12),X12)
| in(esk34_3(X10,X11,X12),X10)
| in(esk34_3(X10,X11,X12),X11)
| X12 = set_union2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])])])])]) ).
fof(c_0_367,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( in(X7,X5)
| ~ in(ordered_pair(X7,X8),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( X7 = X8
| ~ in(ordered_pair(X7,X8),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( ~ in(X9,X5)
| X9 != X10
| in(ordered_pair(X9,X10),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| ~ in(esk1_2(X5,X6),X5)
| esk1_2(X5,X6) != esk2_2(X5,X6)
| X6 = identity_relation(X5)
| ~ relation(X6) )
& ( in(esk1_2(X5,X6),X5)
| in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| X6 = identity_relation(X5)
| ~ relation(X6) )
& ( esk1_2(X5,X6) = esk2_2(X5,X6)
| in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| X6 = identity_relation(X5)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_191])])])])])]) ).
fof(c_0_368,plain,
! [X5,X6,X7,X9,X11] :
( ( in(esk45_3(X5,X6,X7),X7)
| X7 = empty_set
| ~ subset(X7,X6)
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( disjoint(fiber(X5,esk45_3(X5,X6,X7)),X7)
| X7 = empty_set
| ~ subset(X7,X6)
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( subset(esk46_2(X5,X9),X9)
| is_well_founded_in(X5,X9)
| ~ relation(X5) )
& ( esk46_2(X5,X9) != empty_set
| is_well_founded_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(X11,esk46_2(X5,X9))
| ~ disjoint(fiber(X5,X11),esk46_2(X5,X9))
| is_well_founded_in(X5,X9)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])])])])])]) ).
fof(c_0_369,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X9 != X5
| in(X9,X7)
| X7 != unordered_pair(X5,X6) )
& ( X9 != X6
| in(X9,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk31_3(X10,X11,X12) != X10
| ~ in(esk31_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk31_3(X10,X11,X12) != X11
| ~ in(esk31_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk31_3(X10,X11,X12),X12)
| esk31_3(X10,X11,X12) = X10
| esk31_3(X10,X11,X12) = X11
| X12 = unordered_pair(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_193])])])])])]) ).
fof(c_0_370,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk60_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X10,X9),X5)
| in(X9,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(esk61_2(X5,X11),X11)
| ~ in(ordered_pair(X13,esk61_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk61_2(X5,X11),X11)
| in(ordered_pair(esk62_2(X5,X11),esk61_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_194])])])])])]) ).
fof(c_0_371,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk48_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X10),X5)
| in(X9,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(esk49_2(X5,X11),X11)
| ~ in(ordered_pair(esk49_2(X5,X11),X13),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk49_2(X5,X11),X11)
| in(ordered_pair(esk49_2(X5,X11),esk50_2(X5,X11)),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_195])])])])])]) ).
fof(c_0_372,plain,
! [X6,X7,X8,X9,X10,X11] :
( ( ~ is_transitive_in(X6,X7)
| ~ in(X8,X7)
| ~ in(X9,X7)
| ~ in(X10,X7)
| ~ in(ordered_pair(X8,X9),X6)
| ~ in(ordered_pair(X9,X10),X6)
| in(ordered_pair(X8,X10),X6)
| ~ relation(X6) )
& ( in(esk73_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(esk74_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(esk75_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(ordered_pair(esk73_2(X6,X11),esk74_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(ordered_pair(esk74_2(X6,X11),esk75_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk73_2(X6,X11),esk75_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_196])])])])])]) ).
fof(c_0_373,plain,
! [X5,X6,X7,X8] :
( ( ~ subset(X5,X6)
| ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk42_2(X5,X6),esk43_2(X5,X6)),X5)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk42_2(X5,X6),esk43_2(X5,X6)),X6)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])])])])]) ).
fof(c_0_374,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ is_connected_in(X5,X6)
| ~ in(X7,X6)
| ~ in(X8,X6)
| X7 = X8
| in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X8,X7),X5)
| ~ relation(X5) )
& ( in(esk63_2(X5,X9),X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( in(esk64_2(X5,X9),X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( esk63_2(X5,X9) != esk64_2(X5,X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk63_2(X5,X9),esk64_2(X5,X9)),X5)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk64_2(X5,X9),esk63_2(X5,X9)),X5)
| is_connected_in(X5,X9)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])])])])])]) ).
fof(c_0_375,plain,
! [X4,X5,X6,X7] :
( ( ~ is_reflexive_in(X4,X5)
| ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ relation(X4) )
& ( in(esk21_2(X4,X7),X7)
| is_reflexive_in(X4,X7)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk21_2(X4,X7),esk21_2(X4,X7)),X4)
| is_reflexive_in(X4,X7)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_199])])])])])]) ).
fof(c_0_376,plain,
! [X5,X6,X7,X8,X9,X11,X14,X15,X16,X17] :
( ( ~ in(X7,X6)
| ~ in(X8,X5)
| in(X7,X8)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk22_3(X5,X6,X9),X5)
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( ~ in(X9,esk22_3(X5,X6,X9))
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk24_2(X5,X11),X5)
| ~ in(esk23_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( ~ in(esk23_2(X5,X11),esk24_2(X5,X11))
| ~ in(esk23_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( in(esk23_2(X5,X11),X11)
| ~ in(X14,X5)
| in(esk23_2(X5,X11),X14)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( X16 != set_meet(X15)
| X16 = empty_set
| X15 != empty_set )
& ( X17 != empty_set
| X17 = set_meet(X15)
| X15 != empty_set ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])])])])])]) ).
fof(c_0_377,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ is_antisymmetric_in(X5,X6)
| ~ in(X7,X6)
| ~ in(X8,X6)
| ~ in(ordered_pair(X7,X8),X5)
| ~ in(ordered_pair(X8,X7),X5)
| X7 = X8
| ~ relation(X5) )
& ( in(esk51_2(X5,X9),X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(esk52_2(X5,X9),X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(ordered_pair(esk51_2(X5,X9),esk52_2(X5,X9)),X5)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(ordered_pair(esk52_2(X5,X9),esk51_2(X5,X9)),X5)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( esk51_2(X5,X9) != esk52_2(X5,X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])])])]) ).
fof(c_0_378,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| element(subset_difference(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])]) ).
fof(c_0_379,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( in(esk57_3(X5,X6,X7),relation_dom(X5))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,esk57_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X10,relation_dom(X5))
| X9 != apply(X5,X10)
| in(X9,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk58_2(X5,X11),X11)
| ~ in(X13,relation_dom(X5))
| esk58_2(X5,X11) != apply(X5,X13)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk59_2(X5,X11),relation_dom(X5))
| in(esk58_2(X5,X11),X11)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk58_2(X5,X11) = apply(X5,esk59_2(X5,X11))
| in(esk58_2(X5,X11),X11)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])])])])])]) ).
fof(c_0_380,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk53_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk53_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk54_2(X11,X12),X12)
| ~ in(esk54_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk54_2(X11,X12),esk55_2(X11,X12))
| in(esk54_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk55_2(X11,X12),X11)
| in(esk54_2(X11,X12),X12)
| X12 = union(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])])])])])]) ).
fof(c_0_381,plain,
! [X4,X5,X8] :
( ( in(esk32_2(X4,X5),X5)
| X5 = empty_set
| ~ subset(X5,relation_field(X4))
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( disjoint(fiber(X4,esk32_2(X4,X5)),X5)
| X5 = empty_set
| ~ subset(X5,relation_field(X4))
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( subset(esk33_1(X4),relation_field(X4))
| well_founded_relation(X4)
| ~ relation(X4) )
& ( esk33_1(X4) != empty_set
| well_founded_relation(X4)
| ~ relation(X4) )
& ( ~ in(X8,esk33_1(X4))
| ~ disjoint(fiber(X4,X8),esk33_1(X4))
| well_founded_relation(X4)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_205])])])])]) ).
fof(c_0_382,plain,
! [X3,X4,X5] :
( ( is_reflexive_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_transitive_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_antisymmetric_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_connected_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_well_founded_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( ~ is_reflexive_in(X3,X5)
| ~ is_transitive_in(X3,X5)
| ~ is_antisymmetric_in(X3,X5)
| ~ is_connected_in(X3,X5)
| ~ is_well_founded_in(X3,X5)
| well_orders(X3,X5)
| ~ relation(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_206])])])])]) ).
fof(c_0_383,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_207])]) ).
fof(c_0_384,plain,
! [X4,X5,X6] :
( ( ~ one_to_one(X4)
| ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk67_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk68_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk67_1(X4)) = apply(X4,esk68_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk67_1(X4) != esk68_1(X4)
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_208])])])])]) ).
fof(c_0_385,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X7,X4)
| in(X7,X5)
| X5 != powerset(X4) )
& ( ~ in(esk27_2(X8,X9),X9)
| ~ subset(esk27_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk27_2(X8,X9),X9)
| subset(esk27_2(X8,X9),X8)
| X9 = powerset(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_209])])])])])]) ).
fof(c_0_386,plain,
! [X4,X5] :
( ( ~ in(esk92_2(X4,X5),X4)
| ~ in(esk92_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk92_2(X4,X5),X4)
| in(esk92_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])])])]) ).
fof(c_0_387,plain,
! [X4,X5,X6,X7,X8,X9,X10] :
( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( ~ in(ordered_pair(X5,X7),X4)
| X7 = apply(X4,X5)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X9 != apply(X4,X8)
| X9 = empty_set
| in(X8,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X10 != empty_set
| X10 = apply(X4,X8)
| in(X8,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])])])])]) ).
fof(c_0_388,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(complements_of_subsets(X3,X4),powerset(powerset(X3))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_212])]) ).
fof(c_0_389,plain,
! [X5,X6,X8] :
( ( in(esk93_2(X5,X6),X6)
| ~ in(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,esk93_2(X5,X6))
| ~ in(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_213])])])])]) ).
fof(c_0_390,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(meet_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])]) ).
fof(c_0_391,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(union_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_215])]) ).
fof(c_0_392,plain,
! [X5,X6,X9,X11,X12] :
( ( ~ relation(X5)
| ~ in(X6,X5)
| X6 = ordered_pair(esk18_2(X5,X6),esk19_2(X5,X6)) )
& ( in(esk20_1(X9),X9)
| relation(X9) )
& ( esk20_1(X9) != ordered_pair(X11,X12)
| relation(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_216])])])])])]) ).
fof(c_0_393,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk94_1(X6))
& ( ~ in(X8,esk94_1(X6))
| ~ subset(X9,X8)
| in(X9,esk94_1(X6)) )
& ( in(esk95_2(X6,X10),esk94_1(X6))
| ~ in(X10,esk94_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk95_2(X6,X10))
| ~ in(X10,esk94_1(X6)) )
& ( ~ subset(X13,esk94_1(X6))
| are_equipotent(X13,esk94_1(X6))
| in(X13,esk94_1(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_217])])])])]) ).
fof(c_0_394,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk25_2(X8,X9),X9)
| esk25_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk25_2(X8,X9),X9)
| esk25_2(X8,X9) = X8
| X9 = singleton(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_218])])])])])]) ).
fof(c_0_395,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_219])]) ).
fof(c_0_396,plain,
! [X4,X5,X6,X7] :
( ( ~ epsilon_connected(X4)
| ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5) )
& ( in(esk40_1(X7),X7)
| epsilon_connected(X7) )
& ( in(esk41_1(X7),X7)
| epsilon_connected(X7) )
& ( ~ in(esk40_1(X7),esk41_1(X7))
| epsilon_connected(X7) )
& ( esk40_1(X7) != esk41_1(X7)
| epsilon_connected(X7) )
& ( ~ in(esk41_1(X7),esk40_1(X7))
| epsilon_connected(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_220])])])])])]) ).
fof(c_0_397,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_221])]) ).
fof(c_0_398,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk44_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk44_2(X7,X8),X8)
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_222])])])])])]) ).
fof(c_0_399,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_223])]) ).
fof(c_0_400,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| meet_of_subsets(X3,X4) = set_meet(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_224])]) ).
fof(c_0_401,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| union_of_subsets(X3,X4) = union(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_225])]) ).
fof(c_0_402,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_226])]) ).
fof(c_0_403,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_227])])])]) ).
fof(c_0_404,plain,
! [X3,X4] :
( ~ relation(X3)
| relation_restriction(X3,X4) = set_intersection2(X3,cartesian_product2(X4,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_228])])]) ).
fof(c_0_405,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_229])]) ).
fof(c_0_406,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_407,plain,
! [X3,X4] :
( ( relation(relation_composition(X3,X4))
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4) )
& ( function(relation_composition(X3,X4))
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_231])])]) ).
fof(c_0_408,plain,
! [X3,X4] :
( empty(X3)
| empty(X4)
| ~ empty(cartesian_product2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_232])]) ).
fof(c_0_409,plain,
! [X3,X4] :
( empty(X3)
| ~ empty(set_union2(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_233])])])]) ).
fof(c_0_410,plain,
! [X3,X4] :
( empty(X3)
| ~ empty(set_union2(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_234])])])]) ).
fof(c_0_411,plain,
! [X3,X4] :
( ( ~ ordinal_subset(X3,X4)
| subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) )
& ( ~ subset(X3,X4)
| ordinal_subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_235])])]) ).
fof(c_0_412,plain,
! [X3,X4] : ~ empty(unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_413,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_414,plain,
! [X3,X4,X5,X6] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X5,X6)
| ~ subset(X6,X5)
| X5 = X6 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_238])])])])]) ).
fof(c_0_415,plain,
! [X2] :
( ( reflexive(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( transitive(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( antisymmetric(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( connected(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( well_founded_relation(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( ~ reflexive(X2)
| ~ transitive(X2)
| ~ antisymmetric(X2)
| ~ connected(X2)
| ~ well_founded_relation(X2)
| well_ordering(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_239])])]) ).
fof(c_0_416,plain,
! [X3,X4,X5,X6] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| element(X5,powerset(X6)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_240])])])]) ).
fof(c_0_417,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_241])]) ).
fof(c_0_418,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_242])]) ).
fof(c_0_419,plain,
! [X3,X4] :
( ( empty(relation_composition(X3,X4))
| ~ empty(X3)
| ~ relation(X4) )
& ( relation(relation_composition(X3,X4))
| ~ empty(X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_243])])]) ).
fof(c_0_420,plain,
! [X3,X4] :
( ( relation(relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(X4) )
& ( function(relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_244])])]) ).
fof(c_0_421,plain,
! [X3,X4,X5] :
( ( relation(relation_dom_restriction(X3,X4))
| ~ relation(X3)
| ~ function(X3) )
& ( function(relation_dom_restriction(X3,X5))
| ~ relation(X3)
| ~ function(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_245])])])])]) ).
fof(c_0_422,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_difference(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_246])]) ).
fof(c_0_423,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_247])]) ).
fof(c_0_424,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_248])]) ).
fof(c_0_425,plain,
! [X3,X4,X5] :
( ( relation(relation_dom_restriction(X3,X4))
| ~ relation(X3)
| ~ relation_empty_yielding(X3) )
& ( relation_empty_yielding(relation_dom_restriction(X3,X5))
| ~ relation(X3)
| ~ relation_empty_yielding(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_249])])])])]) ).
fof(c_0_426,plain,
! [X3,X4] :
( ( empty(relation_composition(X4,X3))
| ~ empty(X3)
| ~ relation(X4) )
& ( relation(relation_composition(X4,X3))
| ~ empty(X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_250])])]) ).
fof(c_0_427,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(relation_composition(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_251])]) ).
fof(c_0_428,plain,
! [X3,X4,X5] :
( ( ~ epsilon_transitive(X3)
| ~ in(X4,X3)
| subset(X4,X3) )
& ( in(esk28_1(X5),X5)
| epsilon_transitive(X5) )
& ( ~ subset(esk28_1(X5),X5)
| epsilon_transitive(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_252])])])])])]) ).
fof(c_0_429,plain,
! [X2] :
( ( ~ reflexive(X2)
| is_reflexive_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_reflexive_in(X2,relation_field(X2))
| reflexive(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_253])])]) ).
fof(c_0_430,plain,
! [X2] :
( ( ~ transitive(X2)
| is_transitive_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_transitive_in(X2,relation_field(X2))
| transitive(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_254])])]) ).
fof(c_0_431,plain,
! [X2] :
( ( ~ connected(X2)
| is_connected_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_connected_in(X2,relation_field(X2))
| connected(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_255])])]) ).
fof(c_0_432,plain,
! [X2] :
( ( ~ antisymmetric(X2)
| is_antisymmetric_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_antisymmetric_in(X2,relation_field(X2))
| antisymmetric(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_256])])]) ).
fof(c_0_433,plain,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| ordinal_subset(X3,X4)
| ordinal_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_257])]) ).
fof(c_0_434,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_258])]) ).
fof(c_0_435,plain,
! [X3,X4,X5,X6,X7,X8] :
( ( ~ element(X4,X3)
| in(X4,X3)
| empty(X3) )
& ( ~ in(X5,X3)
| element(X5,X3)
| empty(X3) )
& ( ~ element(X7,X6)
| empty(X7)
| ~ empty(X6) )
& ( ~ empty(X8)
| element(X8,X6)
| ~ empty(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_259])])])])]) ).
fof(c_0_436,plain,
! [X3,X4,X5,X6] :
( ( subset(X3,X4)
| ~ proper_subset(X3,X4) )
& ( X3 != X4
| ~ proper_subset(X3,X4) )
& ( ~ subset(X5,X6)
| X5 = X6
| proper_subset(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_260])])])])]) ).
fof(c_0_437,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_261])]) ).
fof(c_0_438,plain,
! [X3,X4] :
( ~ relation(X3)
| relation(relation_dom_restriction(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_262])])])]) ).
fof(c_0_439,plain,
! [X3,X4] :
( ~ relation(X3)
| relation(relation_restriction(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_263])])])]) ).
fof(c_0_440,plain,
! [X2] :
( ~ relation(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_264])]) ).
fof(c_0_441,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_265])]) ).
fof(c_0_442,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_266])]) ).
fof(c_0_443,plain,
! [X3,X4,X5,X6] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X5,X6) != empty_set
| disjoint(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_267])])])]) ).
fof(c_0_444,plain,
! [X2] :
( ( relation(relation_inverse(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2) )
& ( function(relation_inverse(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_268])])]) ).
fof(c_0_445,plain,
! [X3] :
( ( element(esk81_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk81_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_269])])])]) ).
fof(c_0_446,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_270])]) ).
fof(c_0_447,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| function_inverse(X2) = relation_inverse(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_271])]) ).
fof(c_0_448,plain,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| ordinal_subset(X3,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_272])])])]) ).
fof(c_0_449,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_273])]) ).
fof(c_0_450,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_274])]) ).
fof(c_0_451,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_452,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_453,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_454,plain,
! [X3] :
( element(esk86_1(X3),powerset(X3))
& empty(esk86_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_278])]) ).
fof(c_0_455,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_456,plain,
! [X2] :
( ( relation(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) )
& ( function(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) )
& ( one_to_one(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_280])])]) ).
fof(c_0_457,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk26_1(X5),X5)
| X5 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_281])])])])]) ).
fof(c_0_458,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_282])])]) ).
fof(c_0_459,plain,
! [X2] : succ(X2) = set_union2(X2,singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_460,plain,
! [X2] :
( ( ~ empty(succ(X2))
| ~ ordinal(X2) )
& ( epsilon_transitive(succ(X2))
| ~ ordinal(X2) )
& ( epsilon_connected(succ(X2))
| ~ ordinal(X2) )
& ( ordinal(succ(X2))
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_284])])]) ).
fof(c_0_461,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_462,plain,
! [X3] : element(esk77_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_286])]) ).
fof(c_0_463,plain,
! [X2,X3] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) )
& ( ~ epsilon_transitive(X3)
| ~ epsilon_connected(X3)
| ordinal(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_287])])])])]) ).
fof(c_0_464,plain,
! [X2] :
( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_288])]) ).
fof(c_0_465,plain,
! [X2] :
( ~ relation(X2)
| relation_inverse(relation_inverse(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_289])]) ).
fof(c_0_466,plain,
! [X2] :
( ( empty(relation_rng(X2))
| ~ empty(X2) )
& ( relation(relation_rng(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_290])])]) ).
fof(c_0_467,plain,
! [X2] :
( ( empty(relation_dom(X2))
| ~ empty(X2) )
& ( relation(relation_dom(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_291])])]) ).
fof(c_0_468,plain,
! [X2] :
( ( epsilon_transitive(union(X2))
| ~ ordinal(X2) )
& ( epsilon_connected(union(X2))
| ~ ordinal(X2) )
& ( ordinal(union(X2))
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_292])])]) ).
fof(c_0_469,plain,
! [X2] :
( ( empty(relation_inverse(X2))
| ~ empty(X2) )
& ( relation(relation_inverse(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_293])])]) ).
fof(c_0_470,plain,
! [X2] :
( ~ relation(X2)
| relation(relation_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_294])]) ).
fof(c_0_471,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_472,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_473,plain,
! [X2] : ~ empty(succ(X2)),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_474,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_298])])])]) ).
fof(c_0_475,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_476,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_300]) ).
fof(c_0_477,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_478,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_302]) ).
fof(c_0_479,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_303]) ).
fof(c_0_480,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_481,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_305]) ).
fof(c_0_482,plain,
! [X2,X3] :
( ( ~ being_limit_ordinal(X2)
| X2 = union(X2) )
& ( X3 != union(X3)
| being_limit_ordinal(X3) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_306])])])]) ).
fof(c_0_483,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ empty(X2) )
& ( epsilon_connected(X2)
| ~ empty(X2) )
& ( ordinal(X2)
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_307])])]) ).
fof(c_0_484,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_308])]) ).
fof(c_0_485,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_309])])]) ).
fof(c_0_486,plain,
! [X2] :
( ~ empty(X2)
| function(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_310])]) ).
fof(c_0_487,plain,
! [X2,X3] :
( relation(identity_relation(X2))
& function(identity_relation(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_311])])]) ).
fof(c_0_488,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_312]) ).
fof(c_0_489,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_313])]) ).
fof(c_0_490,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[c_0_314]) ).
fof(c_0_491,plain,
( ~ empty(esk89_0)
& epsilon_transitive(esk89_0)
& epsilon_connected(esk89_0)
& ordinal(esk89_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_315])]) ).
fof(c_0_492,plain,
~ empty(esk87_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_316])]) ).
fof(c_0_493,plain,
( ~ empty(esk85_0)
& relation(esk85_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_317])]) ).
fof(c_0_494,plain,
( relation(esk91_0)
& relation_empty_yielding(esk91_0)
& function(esk91_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_318])]) ).
fof(c_0_495,plain,
( relation(esk90_0)
& relation_empty_yielding(esk90_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_319])]) ).
fof(c_0_496,plain,
( relation(esk88_0)
& function(esk88_0)
& one_to_one(esk88_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_320])]) ).
fof(c_0_497,plain,
( relation(esk84_0)
& function(esk84_0)
& one_to_one(esk84_0)
& empty(esk84_0)
& epsilon_transitive(esk84_0)
& epsilon_connected(esk84_0)
& ordinal(esk84_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_321])]) ).
fof(c_0_498,plain,
( relation(esk83_0)
& empty(esk83_0)
& function(esk83_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_322])]) ).
fof(c_0_499,plain,
empty(esk82_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_323])]) ).
fof(c_0_500,plain,
( empty(esk80_0)
& relation(esk80_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_324])]) ).
fof(c_0_501,plain,
( epsilon_transitive(esk79_0)
& epsilon_connected(esk79_0)
& ordinal(esk79_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_325])]) ).
fof(c_0_502,plain,
( relation(esk78_0)
& function(esk78_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_326])]) ).
fof(c_0_503,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_327 ).
fof(c_0_504,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
c_0_328 ).
fof(c_0_505,axiom,
empty(empty_set),
c_0_329 ).
fof(c_0_506,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_330 ).
fof(c_0_507,axiom,
$true,
c_0_331 ).
fof(c_0_508,axiom,
$true,
c_0_332 ).
fof(c_0_509,axiom,
$true,
c_0_333 ).
fof(c_0_510,axiom,
$true,
c_0_334 ).
fof(c_0_511,axiom,
$true,
c_0_335 ).
fof(c_0_512,axiom,
$true,
c_0_336 ).
fof(c_0_513,axiom,
$true,
c_0_337 ).
fof(c_0_514,axiom,
$true,
c_0_338 ).
fof(c_0_515,axiom,
$true,
c_0_339 ).
fof(c_0_516,axiom,
$true,
c_0_340 ).
fof(c_0_517,axiom,
$true,
c_0_341 ).
fof(c_0_518,axiom,
$true,
c_0_342 ).
fof(c_0_519,axiom,
$true,
c_0_343 ).
fof(c_0_520,axiom,
$true,
c_0_344 ).
fof(c_0_521,axiom,
$true,
c_0_345 ).
fof(c_0_522,axiom,
$true,
c_0_346 ).
fof(c_0_523,axiom,
$true,
c_0_347 ).
fof(c_0_524,axiom,
$true,
c_0_348 ).
fof(c_0_525,axiom,
$true,
c_0_349 ).
fof(c_0_526,axiom,
$true,
c_0_350 ).
fof(c_0_527,axiom,
$true,
c_0_351 ).
cnf(c_0_528,plain,
( in(ordered_pair(X4,esk69_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_529,plain,
( in(ordered_pair(esk69_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_530,plain,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X1)
| ~ in(esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_531,plain,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ in(esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_532,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk71_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk70_3(X1,X2,X3),esk71_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_533,plain,
( X1 = unordered_triple(X2,X3,X4)
| esk17_4(X2,X3,X4,X1) = X4
| esk17_4(X2,X3,X4,X1) = X3
| esk17_4(X2,X3,X4,X1) = X2
| in(esk17_4(X2,X3,X4,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_534,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_535,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_536,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X4 ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_537,plain,
( in(ordered_pair(X4,esk14_4(X1,X3,X2,X4)),X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_538,plain,
( in(ordered_pair(esk11_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_539,plain,
( X4 = ordered_pair(esk35_4(X2,X3,X1,X4),esk36_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_540,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk70_3(X1,X2,X3),esk71_3(X1,X2,X3)),X3)
| in(ordered_pair(esk70_3(X1,X2,X3),esk72_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_541,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk70_3(X1,X2,X3),esk71_3(X1,X2,X3)),X3)
| in(ordered_pair(esk72_3(X1,X2,X3),esk71_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_542,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X2)
| in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_543,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_544,plain,
( X2 = relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(X1,esk10_3(X1,X3,X2)),X3)
| ~ in(esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(esk10_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_545,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk76_3(X2,X1,X3)),X1)
| ~ in(esk76_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_546,plain,
( X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(esk15_3(X1,X3,X2),X4),X1)
| ~ in(esk15_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_547,plain,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk12_3(X1,X3,X2)),X1)
| ~ in(esk12_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_548,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X2)
| in(esk9_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_549,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_550,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk15_3(X1,X3,X2),X2)
| in(ordered_pair(esk15_3(X1,X3,X2),esk16_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_551,plain,
( X2 = relation_image(X1,X3)
| in(esk12_3(X1,X3,X2),X2)
| in(ordered_pair(esk13_3(X1,X3,X2),esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_552,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk47_3(X2,X3,X1),X3)
| ~ in(esk47_3(X2,X3,X1),X2)
| ~ in(esk47_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_553,plain,
( in(esk5_4(X1,X3,X2,X4),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_554,plain,
( X4 = apply(X1,esk5_4(X1,X3,X2,X4))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_555,plain,
( in(esk5_4(X1,X3,X2,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_556,plain,
( in(esk14_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_557,plain,
( in(esk11_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_558,plain,
( in(esk35_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_559,plain,
( in(esk36_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_560,plain,
( X1 = set_difference(X2,X3)
| in(esk56_3(X2,X3,X1),X3)
| ~ in(esk56_3(X2,X3,X1),X2)
| ~ in(esk56_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_561,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk76_3(X2,X1,X3)),X1)
| in(esk76_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_562,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk66_2(X1,X2),esk65_2(X1,X2)),X1)
| ~ in(ordered_pair(esk65_2(X1,X2),esk66_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_563,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X2)
| ~ in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_564,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk37_3(X2,X3,X1),X1)
| esk37_3(X2,X3,X1) = ordered_pair(esk38_3(X2,X3,X1),esk39_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_565,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk10_3(X1,X3,X2),X2)
| in(apply(X1,esk10_3(X1,X3,X2)),X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_566,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk34_3(X2,X3,X1),X1)
| ~ in(esk34_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_567,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk34_3(X2,X3,X1),X1)
| ~ in(esk34_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_568,plain,
( X2 = relation_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(esk6_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_569,plain,
( X1 = set_union2(X2,X3)
| in(esk34_3(X2,X3,X1),X3)
| in(esk34_3(X2,X3,X1),X2)
| in(esk34_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_570,plain,
( X1 = cartesian_product2(X2,X3)
| esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk37_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_571,plain,
( X1 = identity_relation(X2)
| ~ relation(X1)
| esk1_2(X2,X1) != esk2_2(X2,X1)
| ~ in(esk1_2(X2,X1),X2)
| ~ in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_572,plain,
( X1 = set_difference(X2,X3)
| in(esk56_3(X2,X3,X1),X1)
| ~ in(esk56_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_573,plain,
( X2 = relation_image(X1,X3)
| in(esk6_3(X1,X3,X2),X2)
| esk6_3(X1,X3,X2) = apply(X1,esk7_3(X1,X3,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_574,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk45_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_575,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk66_2(X1,X2),esk65_2(X1,X2)),X1)
| in(ordered_pair(esk65_2(X1,X2),esk66_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_576,plain,
( X1 = X2
| in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X2)
| in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_577,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk31_3(X2,X3,X1),X1)
| esk31_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_578,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk31_3(X2,X3,X1),X1)
| esk31_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_579,plain,
( in(ordered_pair(esk60_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_580,plain,
( in(ordered_pair(X3,esk48_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_581,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk10_3(X1,X3,X2),X2)
| in(esk10_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_582,plain,
( X2 = relation_image(X1,X3)
| in(esk6_3(X1,X3,X2),X2)
| in(esk7_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_583,plain,
( X2 = relation_image(X1,X3)
| in(esk6_3(X1,X3,X2),X2)
| in(esk7_3(X1,X3,X2),X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_584,plain,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X3,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_585,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk15_3(X1,X3,X2),X2)
| in(esk16_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_586,plain,
( X2 = relation_image(X1,X3)
| in(esk12_3(X1,X3,X2),X2)
| in(esk13_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_587,plain,
( X1 = set_difference(X2,X3)
| in(esk56_3(X2,X3,X1),X1)
| in(esk56_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_588,plain,
( X1 = set_intersection2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk47_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_589,plain,
( X1 = set_intersection2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk47_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_590,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk37_3(X2,X3,X1),X1)
| in(esk38_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_591,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk37_3(X2,X3,X1),X1)
| in(esk39_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_592,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_593,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk73_2(X1,X2),esk75_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_594,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk63_2(X1,X2),esk64_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_595,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk64_2(X1,X2),esk63_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_596,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk21_2(X1,X2),esk21_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_597,plain,
( X1 = unordered_pair(X2,X3)
| esk31_3(X2,X3,X1) = X3
| esk31_3(X2,X3,X1) = X2
| in(esk31_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_598,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk76_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_599,plain,
( in(X4,X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_600,plain,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_601,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk61_2(X1,X2)),X1)
| ~ in(esk61_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_602,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk49_2(X1,X2),X3),X1)
| ~ in(esk49_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_603,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk22_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_604,plain,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_605,plain,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_606,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk62_2(X1,X2),esk61_2(X1,X2)),X1)
| in(esk61_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_607,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk49_2(X1,X2),esk50_2(X1,X2)),X1)
| in(esk49_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_608,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_609,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_610,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk46_2(X1,X2))
| ~ in(X3,esk46_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_611,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| esk1_2(X2,X1) = esk2_2(X2,X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_612,plain,
( X3 = empty_set
| in(esk45_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_613,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk23_2(X1,X2),X2)
| ~ in(esk23_2(X1,X2),esk24_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_614,plain,
( subset(X1,X2)
| in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_615,plain,
( in(esk57_3(X1,X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_616,plain,
( X3 = apply(X1,esk57_3(X1,X2,X3))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_617,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk73_2(X1,X2),esk74_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_618,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk74_2(X1,X2),esk75_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_619,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk51_2(X1,X2),esk52_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_620,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk52_2(X1,X2),esk51_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_621,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_622,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_623,plain,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| esk58_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(esk58_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_624,plain,
( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X1)
| X3 = X2
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_625,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk54_2(X2,X1),X3)
| ~ in(esk54_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_626,plain,
( in(X3,esk53_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_627,plain,
( in(esk53_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_628,plain,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_629,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk22_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_630,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_631,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_632,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_633,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk32_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_634,plain,
( well_orders(X1,X2)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_635,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_636,plain,
( X2 = X3
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_637,plain,
( X1 = powerset(X2)
| ~ subset(esk27_2(X2,X1),X2)
| ~ in(esk27_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_638,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_639,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_640,plain,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| X4 != apply(X1,X5)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_641,plain,
( X1 = X2
| ~ in(esk92_2(X1,X2),X2)
| ~ in(esk92_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_642,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_643,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_644,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_645,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_646,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_647,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk33_1(X1))
| ~ in(X2,esk33_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_648,plain,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_649,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_650,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_651,plain,
( X2 = relation_rng(X1)
| in(esk58_2(X1,X2),X2)
| esk58_2(X1,X2) = apply(X1,esk59_2(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_652,plain,
( X1 = union(X2)
| in(esk54_2(X2,X1),X1)
| in(esk54_2(X2,X1),esk55_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_653,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_654,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk24_2(X1,X2),X1)
| ~ in(esk23_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_655,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk23_2(X1,X2),X3)
| in(esk23_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_656,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_657,plain,
( ~ in(X1,X2)
| ~ in(X3,esk93_2(X1,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_658,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_659,plain,
( X2 = relation_rng(X1)
| in(esk58_2(X1,X2),X2)
| in(esk59_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_660,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_661,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_662,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_663,plain,
( in(apply(X1,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_664,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_665,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_666,plain,
( X1 = ordered_pair(esk18_2(X2,X1),esk19_2(X2,X1))
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_667,plain,
( in(X3,esk95_2(X2,X1))
| ~ in(X1,esk94_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_668,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_669,plain,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_670,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_671,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_672,plain,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_673,plain,
( X1 = singleton(X2)
| esk25_2(X2,X1) != X2
| ~ in(esk25_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_674,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_675,plain,
( X2 = empty_set
| in(esk32_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_676,plain,
( X1 = union(X2)
| in(esk54_2(X2,X1),X1)
| in(esk55_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_677,plain,
( X1 = powerset(X2)
| subset(esk27_2(X2,X1),X2)
| in(esk27_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_678,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_679,plain,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_680,plain,
( X1 = X2
| in(esk92_2(X1,X2),X2)
| in(esk92_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_681,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_682,plain,
( in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_683,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_684,plain,
( in(esk95_2(X2,X1),esk94_1(X2))
| ~ in(X1,esk94_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_685,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_686,plain,
( subset(X1,X2)
| ~ in(esk44_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_687,plain,
( in(X1,esk94_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk94_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_688,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_689,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_690,plain,
( in(X1,esk94_1(X2))
| are_equipotent(X1,esk94_1(X2))
| ~ subset(X1,esk94_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_691,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_692,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_693,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_694,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_695,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_696,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_697,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_698,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| esk63_2(X1,X2) != esk64_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_699,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| esk51_2(X1,X2) != esk52_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_700,plain,
( in(esk93_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_701,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_702,plain,
( is_transitive_in(X1,X2)
| in(esk73_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_703,plain,
( is_transitive_in(X1,X2)
| in(esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_704,plain,
( is_transitive_in(X1,X2)
| in(esk75_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_705,plain,
( is_connected_in(X1,X2)
| in(esk63_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_706,plain,
( is_connected_in(X1,X2)
| in(esk64_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_707,plain,
( is_antisymmetric_in(X1,X2)
| in(esk51_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_708,plain,
( is_antisymmetric_in(X1,X2)
| in(esk52_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_709,plain,
( is_well_founded_in(X1,X2)
| subset(esk46_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_710,plain,
( is_reflexive_in(X1,X2)
| in(esk21_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_711,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_712,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_713,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_714,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_715,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_716,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_717,plain,
( X1 = singleton(X2)
| esk25_2(X2,X1) = X2
| in(esk25_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_718,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_719,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_720,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_721,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_722,plain,
( one_to_one(X1)
| apply(X1,esk67_1(X1)) = apply(X1,esk68_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_723,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_724,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_725,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_726,plain,
( subset(X1,X2)
| in(esk44_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_727,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_728,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_729,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_730,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_731,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_732,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_733,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_734,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_735,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_736,plain,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_737,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_738,plain,
( epsilon_connected(X1)
| ~ in(esk40_1(X1),esk41_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_739,plain,
( epsilon_connected(X1)
| ~ in(esk41_1(X1),esk40_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_740,plain,
( one_to_one(X1)
| in(esk67_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_741,plain,
( one_to_one(X1)
| in(esk68_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_742,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_743,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_744,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_745,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_746,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_747,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_748,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_749,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_750,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_751,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_752,plain,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_753,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_754,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_755,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_756,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_757,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_758,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_759,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_760,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_761,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_762,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_763,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_764,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_765,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk46_2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_766,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_767,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_768,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_769,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_770,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_771,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_772,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_773,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_774,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_775,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_776,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_777,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_778,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_779,plain,
( well_founded_relation(X1)
| subset(esk33_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_780,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_781,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_782,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_783,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_784,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_785,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_786,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_787,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_788,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_789,plain,
( epsilon_transitive(X1)
| ~ subset(esk28_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_790,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_791,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_792,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_793,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_794,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_795,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_796,plain,
( relation(X1)
| esk20_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_797,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_798,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_799,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk67_1(X1) != esk68_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_800,plain,
( empty(X1)
| element(esk81_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_801,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_802,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_803,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_804,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_805,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_806,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_807,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_808,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_809,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_810,plain,
element(esk86_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_811,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_812,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_813,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_814,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_815,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_816,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_817,plain,
( epsilon_connected(X1)
| in(esk40_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_818,plain,
( epsilon_connected(X1)
| in(esk41_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_819,plain,
( epsilon_transitive(X1)
| in(esk28_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_820,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_821,plain,
( relation(X1)
| in(esk20_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_822,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_823,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_824,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_825,plain,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_826,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_827,plain,
( X1 = empty_set
| in(esk26_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_828,plain,
( empty(X1)
| ~ empty(esk81_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_829,plain,
in(X1,esk94_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_830,plain,
element(esk77_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_831,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_832,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_833,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_834,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_835,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_836,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_837,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk33_1(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_838,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_839,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_840,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_841,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_842,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_843,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_844,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_845,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_846,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_847,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_848,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_849,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_850,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_851,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_852,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_853,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_854,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_855,plain,
( epsilon_connected(X1)
| esk40_1(X1) != esk41_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_856,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_857,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_858,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_859,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_860,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_861,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_862,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_863,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_864,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_865,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_866,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_867,plain,
( being_limit_ordinal(X1)
| X1 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_868,plain,
( X1 = union(X1)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_869,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_870,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_871,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_872,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_873,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_874,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_875,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_876,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_877,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_878,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_879,plain,
empty(esk86_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_880,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_881,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_882,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_883,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_884,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_885,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_886,plain,
~ empty(esk89_0),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_887,plain,
~ empty(esk87_0),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_888,plain,
~ empty(esk85_0),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_889,plain,
relation(esk91_0),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_890,plain,
relation_empty_yielding(esk91_0),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_891,plain,
function(esk91_0),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_892,plain,
relation(esk90_0),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_893,plain,
relation_empty_yielding(esk90_0),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_894,plain,
epsilon_transitive(esk89_0),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_895,plain,
epsilon_connected(esk89_0),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_896,plain,
ordinal(esk89_0),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_897,plain,
relation(esk88_0),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_898,plain,
function(esk88_0),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_899,plain,
one_to_one(esk88_0),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_900,plain,
relation(esk85_0),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_901,plain,
relation(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_902,plain,
function(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_903,plain,
one_to_one(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_904,plain,
empty(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_905,plain,
epsilon_transitive(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_906,plain,
epsilon_connected(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_907,plain,
ordinal(esk84_0),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_908,plain,
relation(esk83_0),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_909,plain,
empty(esk83_0),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_910,plain,
function(esk83_0),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_911,plain,
empty(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_912,plain,
empty(esk80_0),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_913,plain,
relation(esk80_0),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_914,plain,
epsilon_transitive(esk79_0),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_915,plain,
epsilon_connected(esk79_0),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_916,plain,
ordinal(esk79_0),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_917,plain,
relation(esk78_0),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_918,plain,
function(esk78_0),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_919,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_920,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_921,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_922,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_923,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_924,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_925,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_926,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_927,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_928,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_929,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_930,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_931,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_932,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_933,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_934,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_935,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_936,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_510]) ).
cnf(c_0_937,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_938,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_512]) ).
cnf(c_0_939,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_940,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_941,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_942,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_943,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_944,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_518]) ).
cnf(c_0_945,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_946,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_947,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_521]) ).
cnf(c_0_948,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_522]) ).
cnf(c_0_949,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_950,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_951,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_952,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_953,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_954,plain,
( in(ordered_pair(X4,esk69_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
c_0_528,
[final] ).
cnf(c_0_955,plain,
( in(ordered_pair(esk69_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
c_0_529,
[final] ).
cnf(c_0_956,plain,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X1)
| ~ in(esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X2) ),
c_0_530,
[final] ).
cnf(c_0_957,plain,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ in(esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2) ),
c_0_531,
[final] ).
cnf(c_0_958,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk71_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk70_3(X1,X2,X3),esk71_3(X1,X2,X3)),X3) ),
c_0_532,
[final] ).
cnf(c_0_959,plain,
( X1 = unordered_triple(X2,X3,X4)
| esk17_4(X2,X3,X4,X1) = X4
| esk17_4(X2,X3,X4,X1) = X3
| esk17_4(X2,X3,X4,X1) = X2
| in(esk17_4(X2,X3,X4,X1),X1) ),
c_0_533,
[final] ).
cnf(c_0_960,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X2 ),
c_0_534,
[final] ).
cnf(c_0_961,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X3 ),
c_0_535,
[final] ).
cnf(c_0_962,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X4 ),
c_0_536,
[final] ).
cnf(c_0_963,plain,
( in(ordered_pair(X4,esk14_4(X1,X3,X2,X4)),X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_537,
[final] ).
cnf(c_0_964,plain,
( in(ordered_pair(esk11_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_538,
[final] ).
cnf(c_0_965,plain,
( ordered_pair(esk35_4(X2,X3,X1,X4),esk36_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_539,
[final] ).
cnf(c_0_966,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk70_3(X1,X2,X3),esk71_3(X1,X2,X3)),X3)
| in(ordered_pair(esk70_3(X1,X2,X3),esk72_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_540,
[final] ).
cnf(c_0_967,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk70_3(X1,X2,X3),esk71_3(X1,X2,X3)),X3)
| in(ordered_pair(esk72_3(X1,X2,X3),esk71_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_541,
[final] ).
cnf(c_0_968,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X2)
| in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_542,
[final] ).
cnf(c_0_969,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_543,
[final] ).
cnf(c_0_970,plain,
( X2 = relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(X1,esk10_3(X1,X3,X2)),X3)
| ~ in(esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(esk10_3(X1,X3,X2),X2) ),
c_0_544,
[final] ).
cnf(c_0_971,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk76_3(X2,X1,X3)),X1)
| ~ in(esk76_3(X2,X1,X3),X3) ),
c_0_545,
[final] ).
cnf(c_0_972,plain,
( X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(esk15_3(X1,X3,X2),X4),X1)
| ~ in(esk15_3(X1,X3,X2),X2) ),
c_0_546,
[final] ).
cnf(c_0_973,plain,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk12_3(X1,X3,X2)),X1)
| ~ in(esk12_3(X1,X3,X2),X2) ),
c_0_547,
[final] ).
cnf(c_0_974,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk8_3(X3,X1,X2),esk9_3(X3,X1,X2)),X2)
| in(esk9_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_548,
[final] ).
cnf(c_0_975,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_549,
[final] ).
cnf(c_0_976,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk15_3(X1,X3,X2),X2)
| in(ordered_pair(esk15_3(X1,X3,X2),esk16_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
c_0_550,
[final] ).
cnf(c_0_977,plain,
( X2 = relation_image(X1,X3)
| in(esk12_3(X1,X3,X2),X2)
| in(ordered_pair(esk13_3(X1,X3,X2),esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
c_0_551,
[final] ).
cnf(c_0_978,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk47_3(X2,X3,X1),X3)
| ~ in(esk47_3(X2,X3,X1),X2)
| ~ in(esk47_3(X2,X3,X1),X1) ),
c_0_552,
[final] ).
cnf(c_0_979,plain,
( in(esk5_4(X1,X3,X2,X4),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_553,
[final] ).
cnf(c_0_980,plain,
( apply(X1,esk5_4(X1,X3,X2,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_554,
[final] ).
cnf(c_0_981,plain,
( in(esk5_4(X1,X3,X2,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_555,
[final] ).
cnf(c_0_982,plain,
( in(esk14_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_556,
[final] ).
cnf(c_0_983,plain,
( in(esk11_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_557,
[final] ).
cnf(c_0_984,plain,
( in(esk35_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_558,
[final] ).
cnf(c_0_985,plain,
( in(esk36_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_559,
[final] ).
cnf(c_0_986,plain,
( X1 = set_difference(X2,X3)
| in(esk56_3(X2,X3,X1),X3)
| ~ in(esk56_3(X2,X3,X1),X2)
| ~ in(esk56_3(X2,X3,X1),X1) ),
c_0_560,
[final] ).
cnf(c_0_987,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk76_3(X2,X1,X3)),X1)
| in(esk76_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_561,
[final] ).
cnf(c_0_988,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk66_2(X1,X2),esk65_2(X1,X2)),X1)
| ~ in(ordered_pair(esk65_2(X1,X2),esk66_2(X1,X2)),X2) ),
c_0_562,
[final] ).
cnf(c_0_989,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X2)
| ~ in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X1) ),
c_0_563,
[final] ).
cnf(c_0_990,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk37_3(X2,X3,X1),X1)
| ordered_pair(esk38_3(X2,X3,X1),esk39_3(X2,X3,X1)) = esk37_3(X2,X3,X1) ),
c_0_564,
[final] ).
cnf(c_0_991,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk10_3(X1,X3,X2),X2)
| in(apply(X1,esk10_3(X1,X3,X2)),X3)
| ~ function(X1)
| ~ relation(X1) ),
c_0_565,
[final] ).
cnf(c_0_992,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk34_3(X2,X3,X1),X1)
| ~ in(esk34_3(X2,X3,X1),X2) ),
c_0_566,
[final] ).
cnf(c_0_993,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk34_3(X2,X3,X1),X1)
| ~ in(esk34_3(X2,X3,X1),X3) ),
c_0_567,
[final] ).
cnf(c_0_994,plain,
( X2 = relation_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(esk6_3(X1,X3,X2),X2) ),
c_0_568,
[final] ).
cnf(c_0_995,plain,
( X1 = set_union2(X2,X3)
| in(esk34_3(X2,X3,X1),X3)
| in(esk34_3(X2,X3,X1),X2)
| in(esk34_3(X2,X3,X1),X1) ),
c_0_569,
[final] ).
cnf(c_0_996,plain,
( X1 = cartesian_product2(X2,X3)
| esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk37_3(X2,X3,X1),X1) ),
c_0_570,
[final] ).
cnf(c_0_997,plain,
( X1 = identity_relation(X2)
| ~ relation(X1)
| esk2_2(X2,X1) != esk1_2(X2,X1)
| ~ in(esk1_2(X2,X1),X2)
| ~ in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1) ),
c_0_571,
[final] ).
cnf(c_0_998,plain,
( X1 = set_difference(X2,X3)
| in(esk56_3(X2,X3,X1),X1)
| ~ in(esk56_3(X2,X3,X1),X3) ),
c_0_572,
[final] ).
cnf(c_0_999,plain,
( X2 = relation_image(X1,X3)
| in(esk6_3(X1,X3,X2),X2)
| apply(X1,esk7_3(X1,X3,X2)) = esk6_3(X1,X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_573,
[final] ).
cnf(c_0_1000,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk45_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
c_0_574,
[final] ).
cnf(c_0_1001,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk66_2(X1,X2),esk65_2(X1,X2)),X1)
| in(ordered_pair(esk65_2(X1,X2),esk66_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_575,
[final] ).
cnf(c_0_1002,plain,
( X1 = X2
| in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X2)
| in(ordered_pair(esk29_2(X1,X2),esk30_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_576,
[final] ).
cnf(c_0_1003,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk31_3(X2,X3,X1),X1)
| esk31_3(X2,X3,X1) != X2 ),
c_0_577,
[final] ).
cnf(c_0_1004,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk31_3(X2,X3,X1),X1)
| esk31_3(X2,X3,X1) != X3 ),
c_0_578,
[final] ).
cnf(c_0_1005,plain,
( in(ordered_pair(esk60_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_579,
[final] ).
cnf(c_0_1006,plain,
( in(ordered_pair(X3,esk48_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
c_0_580,
[final] ).
cnf(c_0_1007,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk10_3(X1,X3,X2),X2)
| in(esk10_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_581,
[final] ).
cnf(c_0_1008,plain,
( X2 = relation_image(X1,X3)
| in(esk6_3(X1,X3,X2),X2)
| in(esk7_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_582,
[final] ).
cnf(c_0_1009,plain,
( X2 = relation_image(X1,X3)
| in(esk6_3(X1,X3,X2),X2)
| in(esk7_3(X1,X3,X2),X3)
| ~ function(X1)
| ~ relation(X1) ),
c_0_583,
[final] ).
cnf(c_0_1010,plain,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X3,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
c_0_584,
[final] ).
cnf(c_0_1011,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk15_3(X1,X3,X2),X2)
| in(esk16_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_585,
[final] ).
cnf(c_0_1012,plain,
( X2 = relation_image(X1,X3)
| in(esk12_3(X1,X3,X2),X2)
| in(esk13_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_586,
[final] ).
cnf(c_0_1013,plain,
( X1 = set_difference(X2,X3)
| in(esk56_3(X2,X3,X1),X1)
| in(esk56_3(X2,X3,X1),X2) ),
c_0_587,
[final] ).
cnf(c_0_1014,plain,
( X1 = set_intersection2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk47_3(X2,X3,X1),X2) ),
c_0_588,
[final] ).
cnf(c_0_1015,plain,
( X1 = set_intersection2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk47_3(X2,X3,X1),X3) ),
c_0_589,
[final] ).
cnf(c_0_1016,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk37_3(X2,X3,X1),X1)
| in(esk38_3(X2,X3,X1),X2) ),
c_0_590,
[final] ).
cnf(c_0_1017,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk37_3(X2,X3,X1),X1)
| in(esk39_3(X2,X3,X1),X3) ),
c_0_591,
[final] ).
cnf(c_0_1018,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X2) ),
c_0_592,
[final] ).
cnf(c_0_1019,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk73_2(X1,X2),esk75_2(X1,X2)),X1) ),
c_0_593,
[final] ).
cnf(c_0_1020,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk63_2(X1,X2),esk64_2(X1,X2)),X1) ),
c_0_594,
[final] ).
cnf(c_0_1021,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk64_2(X1,X2),esk63_2(X1,X2)),X1) ),
c_0_595,
[final] ).
cnf(c_0_1022,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk21_2(X1,X2),esk21_2(X1,X2)),X1) ),
c_0_596,
[final] ).
cnf(c_0_1023,plain,
( X1 = unordered_pair(X2,X3)
| esk31_3(X2,X3,X1) = X3
| esk31_3(X2,X3,X1) = X2
| in(esk31_3(X2,X3,X1),X1) ),
c_0_597,
[final] ).
cnf(c_0_1024,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk76_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_598,
[final] ).
cnf(c_0_1025,plain,
( in(X4,X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
c_0_599,
[final] ).
cnf(c_0_1026,plain,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
c_0_600,
[final] ).
cnf(c_0_1027,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk61_2(X1,X2)),X1)
| ~ in(esk61_2(X1,X2),X2) ),
c_0_601,
[final] ).
cnf(c_0_1028,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk49_2(X1,X2),X3),X1)
| ~ in(esk49_2(X1,X2),X2) ),
c_0_602,
[final] ).
cnf(c_0_1029,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk22_3(X1,X2,X3)) ),
c_0_603,
[final] ).
cnf(c_0_1030,plain,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
c_0_604,
[final] ).
cnf(c_0_1031,plain,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
c_0_605,
[final] ).
cnf(c_0_1032,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk62_2(X1,X2),esk61_2(X1,X2)),X1)
| in(esk61_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_606,
[final] ).
cnf(c_0_1033,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk49_2(X1,X2),esk50_2(X1,X2)),X1)
| in(esk49_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_607,
[final] ).
cnf(c_0_1034,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
c_0_608,
[final] ).
cnf(c_0_1035,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_609,
[final] ).
cnf(c_0_1036,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk46_2(X1,X2))
| ~ in(X3,esk46_2(X1,X2)) ),
c_0_610,
[final] ).
cnf(c_0_1037,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| esk2_2(X2,X1) = esk1_2(X2,X1)
| ~ relation(X1) ),
c_0_611,
[final] ).
cnf(c_0_1038,plain,
( X3 = empty_set
| in(esk45_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
c_0_612,
[final] ).
cnf(c_0_1039,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk23_2(X1,X2),X2)
| ~ in(esk23_2(X1,X2),esk24_2(X1,X2)) ),
c_0_613,
[final] ).
cnf(c_0_1040,plain,
( subset(X1,X2)
| in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_614,
[final] ).
cnf(c_0_1041,plain,
( in(esk57_3(X1,X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_615,
[final] ).
cnf(c_0_1042,plain,
( apply(X1,esk57_3(X1,X2,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_616,
[final] ).
cnf(c_0_1043,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk73_2(X1,X2),esk74_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_617,
[final] ).
cnf(c_0_1044,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk74_2(X1,X2),esk75_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_618,
[final] ).
cnf(c_0_1045,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk51_2(X1,X2),esk52_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_619,
[final] ).
cnf(c_0_1046,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk52_2(X1,X2),esk51_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_620,
[final] ).
cnf(c_0_1047,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
c_0_621,
[final] ).
cnf(c_0_1048,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
c_0_622,
[final] ).
cnf(c_0_1049,plain,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| esk58_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(esk58_2(X1,X2),X2) ),
c_0_623,
[final] ).
cnf(c_0_1050,plain,
( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X1)
| X3 = X2
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
c_0_624,
[final] ).
cnf(c_0_1051,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk54_2(X2,X1),X3)
| ~ in(esk54_2(X2,X1),X1) ),
c_0_625,
[final] ).
cnf(c_0_1052,plain,
( in(X3,esk53_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_626,
[final] ).
cnf(c_0_1053,plain,
( in(esk53_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_627,
[final] ).
cnf(c_0_1054,plain,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
c_0_628,
[final] ).
cnf(c_0_1055,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk22_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
c_0_629,
[final] ).
cnf(c_0_1056,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_630,
[final] ).
cnf(c_0_1057,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_631,
[final] ).
cnf(c_0_1058,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
c_0_632,
[final] ).
cnf(c_0_1059,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk32_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
c_0_633,
[final] ).
cnf(c_0_1060,plain,
( well_orders(X1,X2)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
c_0_634,
[final] ).
cnf(c_0_1061,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_635,
[final] ).
cnf(c_0_1062,plain,
( X2 = X3
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
c_0_636,
[final] ).
cnf(c_0_1063,plain,
( X1 = powerset(X2)
| ~ subset(esk27_2(X2,X1),X2)
| ~ in(esk27_2(X2,X1),X1) ),
c_0_637,
[final] ).
cnf(c_0_1064,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_638,
[final] ).
cnf(c_0_1065,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
c_0_639,
[final] ).
cnf(c_0_1066,plain,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| X4 != apply(X1,X5)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
c_0_640,
[final] ).
cnf(c_0_1067,plain,
( X1 = X2
| ~ in(esk92_2(X1,X2),X2)
| ~ in(esk92_2(X1,X2),X1) ),
c_0_641,
[final] ).
cnf(c_0_1068,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
c_0_642,
[final] ).
cnf(c_0_1069,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_643,
[final] ).
cnf(c_0_1070,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_644,
[final] ).
cnf(c_0_1071,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_645,
[final] ).
cnf(c_0_1072,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
c_0_646,
[final] ).
cnf(c_0_1073,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk33_1(X1))
| ~ in(X2,esk33_1(X1)) ),
c_0_647,
[final] ).
cnf(c_0_1074,plain,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
c_0_648,
[final] ).
cnf(c_0_1075,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_649,
[final] ).
cnf(c_0_1076,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_650,
[final] ).
cnf(c_0_1077,plain,
( X2 = relation_rng(X1)
| in(esk58_2(X1,X2),X2)
| apply(X1,esk59_2(X1,X2)) = esk58_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_651,
[final] ).
cnf(c_0_1078,plain,
( X1 = union(X2)
| in(esk54_2(X2,X1),X1)
| in(esk54_2(X2,X1),esk55_2(X2,X1)) ),
c_0_652,
[final] ).
cnf(c_0_1079,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
c_0_653,
[final] ).
cnf(c_0_1080,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk24_2(X1,X2),X1)
| ~ in(esk23_2(X1,X2),X2) ),
c_0_654,
[final] ).
cnf(c_0_1081,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk23_2(X1,X2),X3)
| in(esk23_2(X1,X2),X2)
| ~ in(X3,X1) ),
c_0_655,
[final] ).
cnf(c_0_1082,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_656,
[final] ).
cnf(c_0_1083,plain,
( ~ in(X1,X2)
| ~ in(X3,esk93_2(X1,X2))
| ~ in(X3,X2) ),
c_0_657,
[final] ).
cnf(c_0_1084,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_658,
[final] ).
cnf(c_0_1085,plain,
( X2 = relation_rng(X1)
| in(esk58_2(X1,X2),X2)
| in(esk59_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_659,
[final] ).
cnf(c_0_1086,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
c_0_660,
[final] ).
cnf(c_0_1087,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
c_0_661,
[final] ).
cnf(c_0_1088,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
c_0_662,
[final] ).
cnf(c_0_1089,plain,
( in(apply(X1,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_663,
[final] ).
cnf(c_0_1090,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_664,
[final] ).
cnf(c_0_1091,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_665,
[final] ).
cnf(c_0_1092,plain,
( ordered_pair(esk18_2(X2,X1),esk19_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
c_0_666,
[final] ).
cnf(c_0_1093,plain,
( in(X3,esk95_2(X2,X1))
| ~ in(X1,esk94_1(X2))
| ~ subset(X3,X1) ),
c_0_667,
[final] ).
cnf(c_0_1094,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_668,
[final] ).
cnf(c_0_1095,plain,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_669,
[final] ).
cnf(c_0_1096,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_670,
[final] ).
cnf(c_0_1097,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_671,
[final] ).
cnf(c_0_1098,plain,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
c_0_672,
[final] ).
cnf(c_0_1099,plain,
( X1 = singleton(X2)
| esk25_2(X2,X1) != X2
| ~ in(esk25_2(X2,X1),X1) ),
c_0_673,
[final] ).
cnf(c_0_1100,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
c_0_674,
[final] ).
cnf(c_0_1101,plain,
( X2 = empty_set
| in(esk32_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
c_0_675,
[final] ).
cnf(c_0_1102,plain,
( X1 = union(X2)
| in(esk54_2(X2,X1),X1)
| in(esk55_2(X2,X1),X2) ),
c_0_676,
[final] ).
cnf(c_0_1103,plain,
( X1 = powerset(X2)
| subset(esk27_2(X2,X1),X2)
| in(esk27_2(X2,X1),X1) ),
c_0_677,
[final] ).
cnf(c_0_1104,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_678,
[final] ).
cnf(c_0_1105,plain,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
c_0_679,
[final] ).
cnf(c_0_1106,plain,
( X1 = X2
| in(esk92_2(X1,X2),X2)
| in(esk92_2(X1,X2),X1) ),
c_0_680,
[final] ).
cnf(c_0_1107,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
c_0_681,
[final] ).
cnf(c_0_1108,plain,
( in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_682,
[final] ).
cnf(c_0_1109,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_683,
[final] ).
cnf(c_0_1110,plain,
( in(esk95_2(X2,X1),esk94_1(X2))
| ~ in(X1,esk94_1(X2)) ),
c_0_684,
[final] ).
cnf(c_0_1111,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_685,
[final] ).
cnf(c_0_1112,plain,
( subset(X1,X2)
| ~ in(esk44_2(X1,X2),X2) ),
c_0_686,
[final] ).
cnf(c_0_1113,plain,
( in(X1,esk94_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk94_1(X2)) ),
c_0_687,
[final] ).
cnf(c_0_1114,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_688,
[final] ).
cnf(c_0_1115,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_689,
[final] ).
cnf(c_0_1116,plain,
( in(X1,esk94_1(X2))
| are_equipotent(X1,esk94_1(X2))
| ~ subset(X1,esk94_1(X2)) ),
c_0_690,
[final] ).
cnf(c_0_1117,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
c_0_691,
[final] ).
cnf(c_0_1118,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
c_0_692,
[final] ).
cnf(c_0_1119,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_693,
[final] ).
cnf(c_0_1120,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_694,
[final] ).
cnf(c_0_1121,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
c_0_695,
[final] ).
cnf(c_0_1122,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_696,
[final] ).
cnf(c_0_1123,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_697,
[final] ).
cnf(c_0_1124,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| esk63_2(X1,X2) != esk64_2(X1,X2) ),
c_0_698,
[final] ).
cnf(c_0_1125,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| esk52_2(X1,X2) != esk51_2(X1,X2) ),
c_0_699,
[final] ).
cnf(c_0_1126,plain,
( in(esk93_2(X1,X2),X2)
| ~ in(X1,X2) ),
c_0_700,
[final] ).
cnf(c_0_1127,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_701,
[final] ).
cnf(c_0_1128,plain,
( is_transitive_in(X1,X2)
| in(esk73_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_702,
[final] ).
cnf(c_0_1129,plain,
( is_transitive_in(X1,X2)
| in(esk74_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_703,
[final] ).
cnf(c_0_1130,plain,
( is_transitive_in(X1,X2)
| in(esk75_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_704,
[final] ).
cnf(c_0_1131,plain,
( is_connected_in(X1,X2)
| in(esk63_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_705,
[final] ).
cnf(c_0_1132,plain,
( is_connected_in(X1,X2)
| in(esk64_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_706,
[final] ).
cnf(c_0_1133,plain,
( is_antisymmetric_in(X1,X2)
| in(esk51_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_707,
[final] ).
cnf(c_0_1134,plain,
( is_antisymmetric_in(X1,X2)
| in(esk52_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_708,
[final] ).
cnf(c_0_1135,plain,
( is_well_founded_in(X1,X2)
| subset(esk46_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_709,
[final] ).
cnf(c_0_1136,plain,
( is_reflexive_in(X1,X2)
| in(esk21_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_710,
[final] ).
cnf(c_0_1137,plain,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_711,
[final] ).
cnf(c_0_1138,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_712,
[final] ).
cnf(c_0_1139,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_713,
[final] ).
cnf(c_0_1140,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_714,
[final] ).
cnf(c_0_1141,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_715,
[final] ).
cnf(c_0_1142,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_716,
[final] ).
cnf(c_0_1143,plain,
( X1 = singleton(X2)
| esk25_2(X2,X1) = X2
| in(esk25_2(X2,X1),X1) ),
c_0_717,
[final] ).
cnf(c_0_1144,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
c_0_718,
[final] ).
cnf(c_0_1145,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
c_0_719,
[final] ).
cnf(c_0_1146,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_720,
[final] ).
cnf(c_0_1147,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_721,
[final] ).
cnf(c_0_1148,plain,
( one_to_one(X1)
| apply(X1,esk68_1(X1)) = apply(X1,esk67_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_722,
[final] ).
cnf(c_0_1149,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_723,
[final] ).
cnf(c_0_1150,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_724,
[final] ).
cnf(c_0_1151,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
c_0_725,
[final] ).
cnf(c_0_1152,plain,
( subset(X1,X2)
| in(esk44_2(X1,X2),X1) ),
c_0_726,
[final] ).
cnf(c_0_1153,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
c_0_727,
[final] ).
cnf(c_0_1154,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_728,
[final] ).
cnf(c_0_1155,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_729,
[final] ).
cnf(c_0_1156,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
c_0_730,
[final] ).
cnf(c_0_1157,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
c_0_731,
[final] ).
cnf(c_0_1158,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_732,
[final] ).
cnf(c_0_1159,plain,
~ empty(unordered_pair(X1,X2)),
c_0_733,
[final] ).
cnf(c_0_1160,plain,
~ empty(ordered_pair(X1,X2)),
c_0_734,
[final] ).
cnf(c_0_1161,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_735,
[final] ).
cnf(c_0_1162,plain,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
c_0_736,
[final] ).
cnf(c_0_1163,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
c_0_737,
[final] ).
cnf(c_0_1164,plain,
( epsilon_connected(X1)
| ~ in(esk40_1(X1),esk41_1(X1)) ),
c_0_738,
[final] ).
cnf(c_0_1165,plain,
( epsilon_connected(X1)
| ~ in(esk41_1(X1),esk40_1(X1)) ),
c_0_739,
[final] ).
cnf(c_0_1166,plain,
( one_to_one(X1)
| in(esk67_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_740,
[final] ).
cnf(c_0_1167,plain,
( one_to_one(X1)
| in(esk68_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_741,
[final] ).
cnf(c_0_1168,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_742,
[final] ).
cnf(c_0_1169,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_743,
[final] ).
cnf(c_0_1170,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_744,
[final] ).
cnf(c_0_1171,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_745,
[final] ).
cnf(c_0_1172,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_746,
[final] ).
cnf(c_0_1173,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_747,
[final] ).
cnf(c_0_1174,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_748,
[final] ).
cnf(c_0_1175,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_749,
[final] ).
cnf(c_0_1176,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_750,
[final] ).
cnf(c_0_1177,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_751,
[final] ).
cnf(c_0_1178,plain,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_752,
[final] ).
cnf(c_0_1179,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_753,
[final] ).
cnf(c_0_1180,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_754,
[final] ).
cnf(c_0_1181,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_755,
[final] ).
cnf(c_0_1182,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_756,
[final] ).
cnf(c_0_1183,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_757,
[final] ).
cnf(c_0_1184,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_758,
[final] ).
cnf(c_0_1185,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_759,
[final] ).
cnf(c_0_1186,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_760,
[final] ).
cnf(c_0_1187,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_761,
[final] ).
cnf(c_0_1188,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_762,
[final] ).
cnf(c_0_1189,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_763,
[final] ).
cnf(c_0_1190,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_764,
[final] ).
cnf(c_0_1191,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk46_2(X1,X2) != empty_set ),
c_0_765,
[final] ).
cnf(c_0_1192,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
c_0_766,
[final] ).
cnf(c_0_1193,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
c_0_767,
[final] ).
cnf(c_0_1194,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
c_0_768,
[final] ).
cnf(c_0_1195,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
c_0_769,
[final] ).
cnf(c_0_1196,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
c_0_770,
[final] ).
cnf(c_0_1197,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
c_0_771,
[final] ).
cnf(c_0_1198,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
c_0_772,
[final] ).
cnf(c_0_1199,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_773,
[final] ).
cnf(c_0_1200,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_774,
[final] ).
cnf(c_0_1201,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
c_0_775,
[final] ).
cnf(c_0_1202,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_776,
[final] ).
cnf(c_0_1203,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_777,
[final] ).
cnf(c_0_1204,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_778,
[final] ).
cnf(c_0_1205,plain,
( well_founded_relation(X1)
| subset(esk33_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_779,
[final] ).
cnf(c_0_1206,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
c_0_780,
[final] ).
cnf(c_0_1207,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
c_0_781,
[final] ).
cnf(c_0_1208,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
c_0_782,
[final] ).
cnf(c_0_1209,plain,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
c_0_783,
[final] ).
cnf(c_0_1210,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
c_0_784,
[final] ).
cnf(c_0_1211,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_785,
[final] ).
cnf(c_0_1212,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_786,
[final] ).
cnf(c_0_1213,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_787,
[final] ).
cnf(c_0_1214,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_788,
[final] ).
cnf(c_0_1215,plain,
( epsilon_transitive(X1)
| ~ subset(esk28_1(X1),X1) ),
c_0_789,
[final] ).
cnf(c_0_1216,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
c_0_790,
[final] ).
cnf(c_0_1217,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
c_0_791,
[final] ).
cnf(c_0_1218,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
c_0_792,
[final] ).
cnf(c_0_1219,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
c_0_793,
[final] ).
cnf(c_0_1220,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_794,
[final] ).
cnf(c_0_1221,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_795,
[final] ).
cnf(c_0_1222,plain,
( relation(X1)
| esk20_1(X1) != ordered_pair(X2,X3) ),
c_0_796,
[final] ).
cnf(c_0_1223,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_797,
[final] ).
cnf(c_0_1224,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_798,
[final] ).
cnf(c_0_1225,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk68_1(X1) != esk67_1(X1) ),
c_0_799,
[final] ).
cnf(c_0_1226,plain,
( empty(X1)
| element(esk81_1(X1),powerset(X1)) ),
c_0_800,
[final] ).
cnf(c_0_1227,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_801,
[final] ).
cnf(c_0_1228,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_802,
[final] ).
cnf(c_0_1229,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
c_0_803,
[final] ).
cnf(c_0_1230,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_804,
[final] ).
cnf(c_0_1231,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
c_0_805,
[final] ).
cnf(c_0_1232,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
c_0_806,
[final] ).
cnf(c_0_1233,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_807,
[final] ).
cnf(c_0_1234,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_808,
[final] ).
cnf(c_0_1235,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_809,
[final] ).
cnf(c_0_1236,plain,
element(esk86_1(X1),powerset(X1)),
c_0_810,
[final] ).
cnf(c_0_1237,plain,
element(cast_to_subset(X1),powerset(X1)),
c_0_811,
[final] ).
cnf(c_0_1238,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_812,
[final] ).
cnf(c_0_1239,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_813,
[final] ).
cnf(c_0_1240,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_814,
[final] ).
cnf(c_0_1241,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_815,
[final] ).
cnf(c_0_1242,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_816,
[final] ).
cnf(c_0_1243,plain,
( epsilon_connected(X1)
| in(esk40_1(X1),X1) ),
c_0_817,
[final] ).
cnf(c_0_1244,plain,
( epsilon_connected(X1)
| in(esk41_1(X1),X1) ),
c_0_818,
[final] ).
cnf(c_0_1245,plain,
( epsilon_transitive(X1)
| in(esk28_1(X1),X1) ),
c_0_819,
[final] ).
cnf(c_0_1246,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_820,
[final] ).
cnf(c_0_1247,plain,
( relation(X1)
| in(esk20_1(X1),X1) ),
c_0_821,
[final] ).
cnf(c_0_1248,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_822,
[final] ).
cnf(c_0_1249,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_823,
[final] ).
cnf(c_0_1250,plain,
set_union2(X1,singleton(X1)) = succ(X1),
c_0_824,
[final] ).
cnf(c_0_1251,plain,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
c_0_825,
[final] ).
cnf(c_0_1252,plain,
~ proper_subset(X1,X1),
c_0_826,
[final] ).
cnf(c_0_1253,plain,
( X1 = empty_set
| in(esk26_1(X1),X1) ),
c_0_827,
[final] ).
cnf(c_0_1254,plain,
( empty(X1)
| ~ empty(esk81_1(X1)) ),
c_0_828,
[final] ).
cnf(c_0_1255,plain,
in(X1,esk94_1(X1)),
c_0_829,
[final] ).
cnf(c_0_1256,plain,
element(esk77_1(X1),X1),
c_0_830,
[final] ).
cnf(c_0_1257,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_831,
[final] ).
cnf(c_0_1258,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_832,
[final] ).
cnf(c_0_1259,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_833,
[final] ).
cnf(c_0_1260,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_834,
[final] ).
cnf(c_0_1261,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_835,
[final] ).
cnf(c_0_1262,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_836,
[final] ).
cnf(c_0_1263,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk33_1(X1) != empty_set ),
c_0_837,
[final] ).
cnf(c_0_1264,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_838,
[final] ).
cnf(c_0_1265,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
c_0_839,
[final] ).
cnf(c_0_1266,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_840,
[final] ).
cnf(c_0_1267,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_841,
[final] ).
cnf(c_0_1268,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
c_0_842,
[final] ).
cnf(c_0_1269,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
c_0_843,
[final] ).
cnf(c_0_1270,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
c_0_844,
[final] ).
cnf(c_0_1271,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
c_0_845,
[final] ).
cnf(c_0_1272,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
c_0_846,
[final] ).
cnf(c_0_1273,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
c_0_847,
[final] ).
cnf(c_0_1274,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
c_0_848,
[final] ).
cnf(c_0_1275,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
c_0_849,
[final] ).
cnf(c_0_1276,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
c_0_850,
[final] ).
cnf(c_0_1277,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
c_0_851,
[final] ).
cnf(c_0_1278,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
c_0_852,
[final] ).
cnf(c_0_1279,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
c_0_853,
[final] ).
cnf(c_0_1280,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
c_0_854,
[final] ).
cnf(c_0_1281,plain,
( epsilon_connected(X1)
| esk40_1(X1) != esk41_1(X1) ),
c_0_855,
[final] ).
cnf(c_0_1282,plain,
~ empty(singleton(X1)),
c_0_856,
[final] ).
cnf(c_0_1283,plain,
~ empty(powerset(X1)),
c_0_857,
[final] ).
cnf(c_0_1284,plain,
~ empty(succ(X1)),
c_0_858,
[final] ).
cnf(c_0_1285,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_859,
[final] ).
cnf(c_0_1286,plain,
set_intersection2(X1,X1) = X1,
c_0_860,
[final] ).
cnf(c_0_1287,plain,
set_union2(X1,X1) = X1,
c_0_861,
[final] ).
cnf(c_0_1288,plain,
subset(X1,X1),
c_0_862,
[final] ).
cnf(c_0_1289,plain,
set_difference(X1,empty_set) = X1,
c_0_863,
[final] ).
cnf(c_0_1290,plain,
set_union2(X1,empty_set) = X1,
c_0_864,
[final] ).
cnf(c_0_1291,plain,
set_difference(empty_set,X1) = empty_set,
c_0_865,
[final] ).
cnf(c_0_1292,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_866,
[final] ).
cnf(c_0_1293,plain,
( being_limit_ordinal(X1)
| union(X1) != X1 ),
c_0_867,
[final] ).
cnf(c_0_1294,plain,
( union(X1) = X1
| ~ being_limit_ordinal(X1) ),
c_0_868,
[final] ).
cnf(c_0_1295,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
c_0_869,
[final] ).
cnf(c_0_1296,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_870,
[final] ).
cnf(c_0_1297,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_871,
[final] ).
cnf(c_0_1298,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
c_0_872,
[final] ).
cnf(c_0_1299,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
c_0_873,
[final] ).
cnf(c_0_1300,plain,
( ordinal(X1)
| ~ empty(X1) ),
c_0_874,
[final] ).
cnf(c_0_1301,plain,
( relation(X1)
| ~ empty(X1) ),
c_0_875,
[final] ).
cnf(c_0_1302,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_876,
[final] ).
cnf(c_0_1303,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_877,
[final] ).
cnf(c_0_1304,plain,
( function(X1)
| ~ empty(X1) ),
c_0_878,
[final] ).
cnf(c_0_1305,plain,
empty(esk86_1(X1)),
c_0_879,
[final] ).
cnf(c_0_1306,plain,
relation(identity_relation(X1)),
c_0_880,
[final] ).
cnf(c_0_1307,plain,
function(identity_relation(X1)),
c_0_881,
[final] ).
cnf(c_0_1308,plain,
relation(identity_relation(X1)),
c_0_882,
[final] ).
cnf(c_0_1309,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
c_0_883,
[final] ).
cnf(c_0_1310,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_884,
[final] ).
cnf(c_0_1311,plain,
cast_to_subset(X1) = X1,
c_0_885,
[final] ).
cnf(c_0_1312,plain,
~ empty(esk89_0),
c_0_886,
[final] ).
cnf(c_0_1313,plain,
~ empty(esk87_0),
c_0_887,
[final] ).
cnf(c_0_1314,plain,
~ empty(esk85_0),
c_0_888,
[final] ).
cnf(c_0_1315,plain,
relation(esk91_0),
c_0_889,
[final] ).
cnf(c_0_1316,plain,
relation_empty_yielding(esk91_0),
c_0_890,
[final] ).
cnf(c_0_1317,plain,
function(esk91_0),
c_0_891,
[final] ).
cnf(c_0_1318,plain,
relation(esk90_0),
c_0_892,
[final] ).
cnf(c_0_1319,plain,
relation_empty_yielding(esk90_0),
c_0_893,
[final] ).
cnf(c_0_1320,plain,
epsilon_transitive(esk89_0),
c_0_894,
[final] ).
cnf(c_0_1321,plain,
epsilon_connected(esk89_0),
c_0_895,
[final] ).
cnf(c_0_1322,plain,
ordinal(esk89_0),
c_0_896,
[final] ).
cnf(c_0_1323,plain,
relation(esk88_0),
c_0_897,
[final] ).
cnf(c_0_1324,plain,
function(esk88_0),
c_0_898,
[final] ).
cnf(c_0_1325,plain,
one_to_one(esk88_0),
c_0_899,
[final] ).
cnf(c_0_1326,plain,
relation(esk85_0),
c_0_900,
[final] ).
cnf(c_0_1327,plain,
relation(esk84_0),
c_0_901,
[final] ).
cnf(c_0_1328,plain,
function(esk84_0),
c_0_902,
[final] ).
cnf(c_0_1329,plain,
one_to_one(esk84_0),
c_0_903,
[final] ).
cnf(c_0_1330,plain,
empty(esk84_0),
c_0_904,
[final] ).
cnf(c_0_1331,plain,
epsilon_transitive(esk84_0),
c_0_905,
[final] ).
cnf(c_0_1332,plain,
epsilon_connected(esk84_0),
c_0_906,
[final] ).
cnf(c_0_1333,plain,
ordinal(esk84_0),
c_0_907,
[final] ).
cnf(c_0_1334,plain,
relation(esk83_0),
c_0_908,
[final] ).
cnf(c_0_1335,plain,
empty(esk83_0),
c_0_909,
[final] ).
cnf(c_0_1336,plain,
function(esk83_0),
c_0_910,
[final] ).
cnf(c_0_1337,plain,
empty(esk82_0),
c_0_911,
[final] ).
cnf(c_0_1338,plain,
empty(esk80_0),
c_0_912,
[final] ).
cnf(c_0_1339,plain,
relation(esk80_0),
c_0_913,
[final] ).
cnf(c_0_1340,plain,
epsilon_transitive(esk79_0),
c_0_914,
[final] ).
cnf(c_0_1341,plain,
epsilon_connected(esk79_0),
c_0_915,
[final] ).
cnf(c_0_1342,plain,
ordinal(esk79_0),
c_0_916,
[final] ).
cnf(c_0_1343,plain,
relation(esk78_0),
c_0_917,
[final] ).
cnf(c_0_1344,plain,
function(esk78_0),
c_0_918,
[final] ).
cnf(c_0_1345,plain,
empty(empty_set),
c_0_919,
[final] ).
cnf(c_0_1346,plain,
relation(empty_set),
c_0_920,
[final] ).
cnf(c_0_1347,plain,
relation(empty_set),
c_0_921,
[final] ).
cnf(c_0_1348,plain,
relation_empty_yielding(empty_set),
c_0_922,
[final] ).
cnf(c_0_1349,plain,
function(empty_set),
c_0_923,
[final] ).
cnf(c_0_1350,plain,
one_to_one(empty_set),
c_0_924,
[final] ).
cnf(c_0_1351,plain,
empty(empty_set),
c_0_925,
[final] ).
cnf(c_0_1352,plain,
epsilon_transitive(empty_set),
c_0_926,
[final] ).
cnf(c_0_1353,plain,
epsilon_connected(empty_set),
c_0_927,
[final] ).
cnf(c_0_1354,plain,
ordinal(empty_set),
c_0_928,
[final] ).
cnf(c_0_1355,plain,
empty(empty_set),
c_0_929,
[final] ).
cnf(c_0_1356,plain,
empty(empty_set),
c_0_930,
[final] ).
cnf(c_0_1357,plain,
relation(empty_set),
c_0_931,
[final] ).
cnf(c_0_1358,plain,
relation_empty_yielding(empty_set),
c_0_932,
[final] ).
cnf(c_0_1359,plain,
$true,
c_0_933,
[final] ).
cnf(c_0_1360,plain,
$true,
c_0_934,
[final] ).
cnf(c_0_1361,plain,
$true,
c_0_935,
[final] ).
cnf(c_0_1362,plain,
$true,
c_0_936,
[final] ).
cnf(c_0_1363,plain,
$true,
c_0_937,
[final] ).
cnf(c_0_1364,plain,
$true,
c_0_938,
[final] ).
cnf(c_0_1365,plain,
$true,
c_0_939,
[final] ).
cnf(c_0_1366,plain,
$true,
c_0_940,
[final] ).
cnf(c_0_1367,plain,
$true,
c_0_941,
[final] ).
cnf(c_0_1368,plain,
$true,
c_0_942,
[final] ).
cnf(c_0_1369,plain,
$true,
c_0_943,
[final] ).
cnf(c_0_1370,plain,
$true,
c_0_944,
[final] ).
cnf(c_0_1371,plain,
$true,
c_0_945,
[final] ).
cnf(c_0_1372,plain,
$true,
c_0_946,
[final] ).
cnf(c_0_1373,plain,
$true,
c_0_947,
[final] ).
cnf(c_0_1374,plain,
$true,
c_0_948,
[final] ).
cnf(c_0_1375,plain,
$true,
c_0_949,
[final] ).
cnf(c_0_1376,plain,
$true,
c_0_950,
[final] ).
cnf(c_0_1377,plain,
$true,
c_0_951,
[final] ).
cnf(c_0_1378,plain,
$true,
c_0_952,
[final] ).
cnf(c_0_1379,plain,
$true,
c_0_953,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_954_0,axiom,
( in(ordered_pair(X4,sk1_esk69_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_954_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk69_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_954_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk69_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_954_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk69_5(X1,X2,X3,X4,X5)),X1)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_954_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk69_5(X1,X2,X3,X4,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_954_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk69_5(X1,X2,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_955_0,axiom,
( in(ordered_pair(sk1_esk69_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_955_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk69_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_955_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk69_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_955_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk69_5(X1,X2,X3,X4,X5),X5),X2)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_955_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk69_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_955_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk69_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_956_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ in(sk1_esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_956_1,axiom,
( ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ in(sk1_esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_956_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ in(sk1_esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_956_3,axiom,
( ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(sk1_esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_956_4,axiom,
( ~ in(sk1_esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_956_5,axiom,
( ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| ~ in(sk1_esk9_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_957_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_957_1,axiom,
( ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_957_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_957_3,axiom,
( ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_957_4,axiom,
( ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_957_5,axiom,
( ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_958_0,axiom,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_958_1,axiom,
( ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_958_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_958_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_958_4,axiom,
( ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_958_5,axiom,
( ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_958_6,axiom,
( ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(sk1_esk70_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk71_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_958]) ).
cnf(c_0_959_0,axiom,
( X1 = unordered_triple(X2,X3,X4)
| sk1_esk17_4(X2,X3,X4,X1) = X4
| sk1_esk17_4(X2,X3,X4,X1) = X3
| sk1_esk17_4(X2,X3,X4,X1) = X2
| in(sk1_esk17_4(X2,X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_959]) ).
cnf(c_0_959_1,axiom,
( sk1_esk17_4(X2,X3,X4,X1) = X4
| X1 = unordered_triple(X2,X3,X4)
| sk1_esk17_4(X2,X3,X4,X1) = X3
| sk1_esk17_4(X2,X3,X4,X1) = X2
| in(sk1_esk17_4(X2,X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_959]) ).
cnf(c_0_959_2,axiom,
( sk1_esk17_4(X2,X3,X4,X1) = X3
| sk1_esk17_4(X2,X3,X4,X1) = X4
| X1 = unordered_triple(X2,X3,X4)
| sk1_esk17_4(X2,X3,X4,X1) = X2
| in(sk1_esk17_4(X2,X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_959]) ).
cnf(c_0_959_3,axiom,
( sk1_esk17_4(X2,X3,X4,X1) = X2
| sk1_esk17_4(X2,X3,X4,X1) = X3
| sk1_esk17_4(X2,X3,X4,X1) = X4
| X1 = unordered_triple(X2,X3,X4)
| in(sk1_esk17_4(X2,X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_959]) ).
cnf(c_0_959_4,axiom,
( in(sk1_esk17_4(X2,X3,X4,X1),X1)
| sk1_esk17_4(X2,X3,X4,X1) = X2
| sk1_esk17_4(X2,X3,X4,X1) = X3
| sk1_esk17_4(X2,X3,X4,X1) = X4
| X1 = unordered_triple(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_959]) ).
cnf(c_0_960_0,axiom,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| sk1_esk17_4(X2,X3,X4,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_960]) ).
cnf(c_0_960_1,axiom,
( ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| X1 = unordered_triple(X2,X3,X4)
| sk1_esk17_4(X2,X3,X4,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_960]) ).
cnf(c_0_960_2,axiom,
( sk1_esk17_4(X2,X3,X4,X1) != X2
| ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| X1 = unordered_triple(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_960]) ).
cnf(c_0_961_0,axiom,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| sk1_esk17_4(X2,X3,X4,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_961]) ).
cnf(c_0_961_1,axiom,
( ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| X1 = unordered_triple(X2,X3,X4)
| sk1_esk17_4(X2,X3,X4,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_961]) ).
cnf(c_0_961_2,axiom,
( sk1_esk17_4(X2,X3,X4,X1) != X3
| ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| X1 = unordered_triple(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_961]) ).
cnf(c_0_962_0,axiom,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| sk1_esk17_4(X2,X3,X4,X1) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_962]) ).
cnf(c_0_962_1,axiom,
( ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| X1 = unordered_triple(X2,X3,X4)
| sk1_esk17_4(X2,X3,X4,X1) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_962]) ).
cnf(c_0_962_2,axiom,
( sk1_esk17_4(X2,X3,X4,X1) != X4
| ~ in(sk1_esk17_4(X2,X3,X4,X1),X1)
| X1 = unordered_triple(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_962]) ).
cnf(c_0_963_0,axiom,
( in(ordered_pair(X4,sk1_esk14_4(X1,X3,X2,X4)),X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_963]) ).
cnf(c_0_963_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk14_4(X1,X3,X2,X4)),X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_963]) ).
cnf(c_0_963_2,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk14_4(X1,X3,X2,X4)),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_963]) ).
cnf(c_0_963_3,axiom,
( ~ in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk14_4(X1,X3,X2,X4)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_963]) ).
cnf(c_0_964_0,axiom,
( in(ordered_pair(sk1_esk11_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_964]) ).
cnf(c_0_964_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk11_4(X1,X3,X2,X4),X4),X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_964]) ).
cnf(c_0_964_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(sk1_esk11_4(X1,X3,X2,X4),X4),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_964]) ).
cnf(c_0_964_3,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(sk1_esk11_4(X1,X3,X2,X4),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_964]) ).
cnf(c_0_965_0,axiom,
( ordered_pair(sk1_esk35_4(X2,X3,X1,X4),sk1_esk36_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_965]) ).
cnf(c_0_965_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk35_4(X2,X3,X1,X4),sk1_esk36_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_965]) ).
cnf(c_0_965_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk35_4(X2,X3,X1,X4),sk1_esk36_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_965]) ).
cnf(c_0_966_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk72_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_966]) ).
cnf(c_0_966_1,axiom,
( in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk72_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_966]) ).
cnf(c_0_966_2,axiom,
( in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk72_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_966]) ).
cnf(c_0_966_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk72_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_966]) ).
cnf(c_0_966_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk72_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_966]) ).
cnf(c_0_966_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk72_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_966]) ).
cnf(c_0_967_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk72_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_967]) ).
cnf(c_0_967_1,axiom,
( in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk72_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_967]) ).
cnf(c_0_967_2,axiom,
( in(ordered_pair(sk1_esk72_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_967]) ).
cnf(c_0_967_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk72_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_967]) ).
cnf(c_0_967_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk72_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_967]) ).
cnf(c_0_967_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk72_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk70_3(X1,X2,X3),sk1_esk71_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_967]) ).
cnf(c_0_968_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_968]) ).
cnf(c_0_968_1,axiom,
( in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_968]) ).
cnf(c_0_968_2,axiom,
( in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_968]) ).
cnf(c_0_968_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_968]) ).
cnf(c_0_968_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_968]) ).
cnf(c_0_969_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_969_1,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_969_2,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_969_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_969_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_970_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(sk1_esk10_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_970_1,axiom,
( ~ function(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(sk1_esk10_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_970_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(sk1_esk10_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_970_3,axiom,
( ~ in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(sk1_esk10_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_970_4,axiom,
( ~ in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(sk1_esk10_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_970_5,axiom,
( ~ in(sk1_esk10_3(X1,X3,X2),X2)
| ~ in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_971_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| ~ in(sk1_esk76_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_971_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| ~ in(sk1_esk76_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_971_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| ~ in(sk1_esk76_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_971_3,axiom,
( ~ in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(sk1_esk76_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_971_4,axiom,
( ~ in(sk1_esk76_3(X2,X1,X3),X3)
| ~ in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_972_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(sk1_esk15_3(X1,X3,X2),X4),X1)
| ~ in(sk1_esk15_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_972_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(X4,X3)
| ~ in(ordered_pair(sk1_esk15_3(X1,X3,X2),X4),X1)
| ~ in(sk1_esk15_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_972_2,axiom,
( ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(ordered_pair(sk1_esk15_3(X1,X3,X2),X4),X1)
| ~ in(sk1_esk15_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_972_3,axiom,
( ~ in(ordered_pair(sk1_esk15_3(X1,X3,X2),X4),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(sk1_esk15_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_972_4,axiom,
( ~ in(sk1_esk15_3(X1,X3,X2),X2)
| ~ in(ordered_pair(sk1_esk15_3(X1,X3,X2),X4),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_973_0,axiom,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,sk1_esk12_3(X1,X3,X2)),X1)
| ~ in(sk1_esk12_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_973_1,axiom,
( ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,sk1_esk12_3(X1,X3,X2)),X1)
| ~ in(sk1_esk12_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_973_2,axiom,
( ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(ordered_pair(X4,sk1_esk12_3(X1,X3,X2)),X1)
| ~ in(sk1_esk12_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_973_3,axiom,
( ~ in(ordered_pair(X4,sk1_esk12_3(X1,X3,X2)),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(sk1_esk12_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_973_4,axiom,
( ~ in(sk1_esk12_3(X1,X3,X2),X2)
| ~ in(ordered_pair(X4,sk1_esk12_3(X1,X3,X2)),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_974_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| in(sk1_esk9_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
cnf(c_0_974_1,axiom,
( in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| in(sk1_esk9_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
cnf(c_0_974_2,axiom,
( in(sk1_esk9_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
cnf(c_0_974_3,axiom,
( ~ relation(X1)
| in(sk1_esk9_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
cnf(c_0_974_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk9_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk8_3(X3,X1,X2),sk1_esk9_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
cnf(c_0_975_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| in(sk1_esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_975]) ).
cnf(c_0_975_1,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| in(sk1_esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_975]) ).
cnf(c_0_975_2,axiom,
( in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_975]) ).
cnf(c_0_975_3,axiom,
( ~ relation(X1)
| in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_975]) ).
cnf(c_0_975_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_975]) ).
cnf(c_0_976_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| in(sk1_esk15_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk15_3(X1,X3,X2),sk1_esk16_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_976]) ).
cnf(c_0_976_1,axiom,
( in(sk1_esk15_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| in(ordered_pair(sk1_esk15_3(X1,X3,X2),sk1_esk16_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_976]) ).
cnf(c_0_976_2,axiom,
( in(ordered_pair(sk1_esk15_3(X1,X3,X2),sk1_esk16_3(X1,X3,X2)),X1)
| in(sk1_esk15_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_976]) ).
cnf(c_0_976_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk15_3(X1,X3,X2),sk1_esk16_3(X1,X3,X2)),X1)
| in(sk1_esk15_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_976]) ).
cnf(c_0_977_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk12_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk13_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_977]) ).
cnf(c_0_977_1,axiom,
( in(sk1_esk12_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(ordered_pair(sk1_esk13_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_977]) ).
cnf(c_0_977_2,axiom,
( in(ordered_pair(sk1_esk13_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| in(sk1_esk12_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_977]) ).
cnf(c_0_977_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk13_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| in(sk1_esk12_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_977]) ).
cnf(c_0_978_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk47_3(X2,X3,X1),X3)
| ~ in(sk1_esk47_3(X2,X3,X1),X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_978]) ).
cnf(c_0_978_1,axiom,
( ~ in(sk1_esk47_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk47_3(X2,X3,X1),X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_978]) ).
cnf(c_0_978_2,axiom,
( ~ in(sk1_esk47_3(X2,X3,X1),X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_978]) ).
cnf(c_0_978_3,axiom,
( ~ in(sk1_esk47_3(X2,X3,X1),X1)
| ~ in(sk1_esk47_3(X2,X3,X1),X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_978]) ).
cnf(c_0_979_0,axiom,
( in(sk1_esk5_4(X1,X3,X2,X4),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_979]) ).
cnf(c_0_979_1,axiom,
( ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),relation_dom(X1))
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_979]) ).
cnf(c_0_979_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),relation_dom(X1))
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_979]) ).
cnf(c_0_979_3,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),relation_dom(X1))
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_979]) ).
cnf(c_0_979_4,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_979]) ).
cnf(c_0_980_0,axiom,
( apply(X1,sk1_esk5_4(X1,X3,X2,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_980]) ).
cnf(c_0_980_1,axiom,
( ~ function(X1)
| apply(X1,sk1_esk5_4(X1,X3,X2,X4)) = X4
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_980]) ).
cnf(c_0_980_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk5_4(X1,X3,X2,X4)) = X4
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_980]) ).
cnf(c_0_980_3,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk5_4(X1,X3,X2,X4)) = X4
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_980]) ).
cnf(c_0_980_4,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk5_4(X1,X3,X2,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_980]) ).
cnf(c_0_981_0,axiom,
( in(sk1_esk5_4(X1,X3,X2,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_981]) ).
cnf(c_0_981_1,axiom,
( ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_981]) ).
cnf(c_0_981_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),X3)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_981]) ).
cnf(c_0_981_3,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_981]) ).
cnf(c_0_981_4,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk5_4(X1,X3,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_981]) ).
cnf(c_0_982_0,axiom,
( in(sk1_esk14_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_982]) ).
cnf(c_0_982_1,axiom,
( ~ relation(X1)
| in(sk1_esk14_4(X1,X3,X2,X4),X3)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_982]) ).
cnf(c_0_982_2,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk14_4(X1,X3,X2,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_982]) ).
cnf(c_0_982_3,axiom,
( ~ in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk14_4(X1,X3,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_982]) ).
cnf(c_0_983_0,axiom,
( in(sk1_esk11_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_983]) ).
cnf(c_0_983_1,axiom,
( ~ relation(X1)
| in(sk1_esk11_4(X1,X3,X2,X4),X3)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_983]) ).
cnf(c_0_983_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk11_4(X1,X3,X2,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_983]) ).
cnf(c_0_983_3,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk11_4(X1,X3,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_983]) ).
cnf(c_0_984_0,axiom,
( in(sk1_esk35_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_984]) ).
cnf(c_0_984_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk35_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_984]) ).
cnf(c_0_984_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk35_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_984]) ).
cnf(c_0_985_0,axiom,
( in(sk1_esk36_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_985]) ).
cnf(c_0_985_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk36_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_985]) ).
cnf(c_0_985_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk36_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_985]) ).
cnf(c_0_986_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk56_3(X2,X3,X1),X3)
| ~ in(sk1_esk56_3(X2,X3,X1),X2)
| ~ in(sk1_esk56_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_986]) ).
cnf(c_0_986_1,axiom,
( in(sk1_esk56_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk56_3(X2,X3,X1),X2)
| ~ in(sk1_esk56_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_986]) ).
cnf(c_0_986_2,axiom,
( ~ in(sk1_esk56_3(X2,X3,X1),X2)
| in(sk1_esk56_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk56_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_986]) ).
cnf(c_0_986_3,axiom,
( ~ in(sk1_esk56_3(X2,X3,X1),X1)
| ~ in(sk1_esk56_3(X2,X3,X1),X2)
| in(sk1_esk56_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_986]) ).
cnf(c_0_987_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| in(sk1_esk76_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_987]) ).
cnf(c_0_987_1,axiom,
( in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| in(sk1_esk76_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_987]) ).
cnf(c_0_987_2,axiom,
( in(sk1_esk76_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_987]) ).
cnf(c_0_987_3,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk76_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_987]) ).
cnf(c_0_987_4,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk76_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk76_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_987]) ).
cnf(c_0_988_0,axiom,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_988]) ).
cnf(c_0_988_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_988]) ).
cnf(c_0_988_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_988]) ).
cnf(c_0_988_3,axiom,
( ~ in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_988]) ).
cnf(c_0_988_4,axiom,
( ~ in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_988]) ).
cnf(c_0_989_0,axiom,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_989]) ).
cnf(c_0_989_1,axiom,
( ~ relation(X1)
| X1 = X2
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_989]) ).
cnf(c_0_989_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_989]) ).
cnf(c_0_989_3,axiom,
( ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_989]) ).
cnf(c_0_989_4,axiom,
( ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_989]) ).
cnf(c_0_990_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk37_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk38_3(X2,X3,X1),sk1_esk39_3(X2,X3,X1)) = sk1_esk37_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_990]) ).
cnf(c_0_990_1,axiom,
( in(sk1_esk37_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk38_3(X2,X3,X1),sk1_esk39_3(X2,X3,X1)) = sk1_esk37_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_990]) ).
cnf(c_0_990_2,axiom,
( ordered_pair(sk1_esk38_3(X2,X3,X1),sk1_esk39_3(X2,X3,X1)) = sk1_esk37_3(X2,X3,X1)
| in(sk1_esk37_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_990]) ).
cnf(c_0_991_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| in(sk1_esk10_3(X1,X3,X2),X2)
| in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_991]) ).
cnf(c_0_991_1,axiom,
( in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_991]) ).
cnf(c_0_991_2,axiom,
( in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_991]) ).
cnf(c_0_991_3,axiom,
( ~ function(X1)
| in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_991]) ).
cnf(c_0_991_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(apply(X1,sk1_esk10_3(X1,X3,X2)),X3)
| in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_991]) ).
cnf(c_0_992_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X1)
| ~ in(sk1_esk34_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_992]) ).
cnf(c_0_992_1,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_992]) ).
cnf(c_0_992_2,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X2)
| ~ in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_992]) ).
cnf(c_0_993_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X1)
| ~ in(sk1_esk34_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_993]) ).
cnf(c_0_993_1,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_993]) ).
cnf(c_0_993_2,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_993]) ).
cnf(c_0_994_0,axiom,
( X2 = relation_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(sk1_esk6_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_994_1,axiom,
( ~ function(X1)
| X2 = relation_image(X1,X3)
| ~ relation(X1)
| sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(sk1_esk6_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_994_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = relation_image(X1,X3)
| sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(sk1_esk6_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_994_3,axiom,
( sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_image(X1,X3)
| ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(sk1_esk6_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_994_4,axiom,
( ~ in(X4,X3)
| sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_image(X1,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(sk1_esk6_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_994_5,axiom,
( ~ in(X4,relation_dom(X1))
| ~ in(X4,X3)
| sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_image(X1,X3)
| ~ in(sk1_esk6_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_994_6,axiom,
( ~ in(sk1_esk6_3(X1,X3,X2),X2)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,X3)
| sk1_esk6_3(X1,X3,X2) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_994]) ).
cnf(c_0_995_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X3)
| in(sk1_esk34_3(X2,X3,X1),X2)
| in(sk1_esk34_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_995]) ).
cnf(c_0_995_1,axiom,
( in(sk1_esk34_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X2)
| in(sk1_esk34_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_995]) ).
cnf(c_0_995_2,axiom,
( in(sk1_esk34_3(X2,X3,X1),X2)
| in(sk1_esk34_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_995]) ).
cnf(c_0_995_3,axiom,
( in(sk1_esk34_3(X2,X3,X1),X1)
| in(sk1_esk34_3(X2,X3,X1),X2)
| in(sk1_esk34_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_995]) ).
cnf(c_0_996_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk37_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_996]) ).
cnf(c_0_996_1,axiom,
( sk1_esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk37_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_996]) ).
cnf(c_0_996_2,axiom,
( ~ in(X5,X3)
| sk1_esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk37_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_996]) ).
cnf(c_0_996_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk37_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_996]) ).
cnf(c_0_996_4,axiom,
( ~ in(sk1_esk37_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk37_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_996]) ).
cnf(c_0_997_0,axiom,
( X1 = identity_relation(X2)
| ~ relation(X1)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_997]) ).
cnf(c_0_997_1,axiom,
( ~ relation(X1)
| X1 = identity_relation(X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_997]) ).
cnf(c_0_997_2,axiom,
( sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_997]) ).
cnf(c_0_997_3,axiom,
( ~ in(sk1_esk1_2(X2,X1),X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_997]) ).
cnf(c_0_997_4,axiom,
( ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_997]) ).
cnf(c_0_998_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk56_3(X2,X3,X1),X1)
| ~ in(sk1_esk56_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_998]) ).
cnf(c_0_998_1,axiom,
( in(sk1_esk56_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk56_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_998]) ).
cnf(c_0_998_2,axiom,
( ~ in(sk1_esk56_3(X2,X3,X1),X3)
| in(sk1_esk56_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_998]) ).
cnf(c_0_999_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk6_3(X1,X3,X2),X2)
| apply(X1,sk1_esk7_3(X1,X3,X2)) = sk1_esk6_3(X1,X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_999]) ).
cnf(c_0_999_1,axiom,
( in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| apply(X1,sk1_esk7_3(X1,X3,X2)) = sk1_esk6_3(X1,X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_999]) ).
cnf(c_0_999_2,axiom,
( apply(X1,sk1_esk7_3(X1,X3,X2)) = sk1_esk6_3(X1,X3,X2)
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_999]) ).
cnf(c_0_999_3,axiom,
( ~ function(X1)
| apply(X1,sk1_esk7_3(X1,X3,X2)) = sk1_esk6_3(X1,X3,X2)
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_999]) ).
cnf(c_0_999_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk7_3(X1,X3,X2)) = sk1_esk6_3(X1,X3,X2)
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_999]) ).
cnf(c_0_1000_0,axiom,
( X3 = empty_set
| disjoint(fiber(X1,sk1_esk45_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1000]) ).
cnf(c_0_1000_1,axiom,
( disjoint(fiber(X1,sk1_esk45_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1000]) ).
cnf(c_0_1000_2,axiom,
( ~ relation(X1)
| disjoint(fiber(X1,sk1_esk45_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1000]) ).
cnf(c_0_1000_3,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk45_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1000]) ).
cnf(c_0_1000_4,axiom,
( ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk45_3(X1,X2,X3)),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1000]) ).
cnf(c_0_1001_0,axiom,
( X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1001]) ).
cnf(c_0_1001_1,axiom,
( in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1001]) ).
cnf(c_0_1001_2,axiom,
( in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1001]) ).
cnf(c_0_1001_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1001]) ).
cnf(c_0_1001_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk65_2(X1,X2),sk1_esk66_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk66_2(X1,X2),sk1_esk65_2(X1,X2)),X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1001]) ).
cnf(c_0_1002_0,axiom,
( X1 = X2
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1002]) ).
cnf(c_0_1002_1,axiom,
( in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| X1 = X2
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1002]) ).
cnf(c_0_1002_2,axiom,
( in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1002]) ).
cnf(c_0_1002_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1002]) ).
cnf(c_0_1002_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1002]) ).
cnf(c_0_1003_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk31_3(X2,X3,X1),X1)
| sk1_esk31_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1003]) ).
cnf(c_0_1003_1,axiom,
( ~ in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk31_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1003]) ).
cnf(c_0_1003_2,axiom,
( sk1_esk31_3(X2,X3,X1) != X2
| ~ in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1003]) ).
cnf(c_0_1004_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk31_3(X2,X3,X1),X1)
| sk1_esk31_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1004]) ).
cnf(c_0_1004_1,axiom,
( ~ in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk31_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1004]) ).
cnf(c_0_1004_2,axiom,
( sk1_esk31_3(X2,X3,X1) != X3
| ~ in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1004]) ).
cnf(c_0_1005_0,axiom,
( in(ordered_pair(sk1_esk60_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1005]) ).
cnf(c_0_1005_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk60_3(X1,X2,X3),X3),X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1005]) ).
cnf(c_0_1005_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk60_3(X1,X2,X3),X3),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1005]) ).
cnf(c_0_1005_3,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk60_3(X1,X2,X3),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1005]) ).
cnf(c_0_1006_0,axiom,
( in(ordered_pair(X3,sk1_esk48_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1006]) ).
cnf(c_0_1006_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,sk1_esk48_3(X1,X2,X3)),X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1006]) ).
cnf(c_0_1006_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk48_3(X1,X2,X3)),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1006]) ).
cnf(c_0_1006_3,axiom,
( ~ in(X3,X2)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk48_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1006]) ).
cnf(c_0_1007_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| in(sk1_esk10_3(X1,X3,X2),X2)
| in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1007]) ).
cnf(c_0_1007_1,axiom,
( in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1007]) ).
cnf(c_0_1007_2,axiom,
( in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1007]) ).
cnf(c_0_1007_3,axiom,
( ~ function(X1)
| in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1007]) ).
cnf(c_0_1007_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk10_3(X1,X3,X2),relation_dom(X1))
| in(sk1_esk10_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1007]) ).
cnf(c_0_1008_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk6_3(X1,X3,X2),X2)
| in(sk1_esk7_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1008]) ).
cnf(c_0_1008_1,axiom,
( in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(sk1_esk7_3(X1,X3,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1008]) ).
cnf(c_0_1008_2,axiom,
( in(sk1_esk7_3(X1,X3,X2),relation_dom(X1))
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1008]) ).
cnf(c_0_1008_3,axiom,
( ~ function(X1)
| in(sk1_esk7_3(X1,X3,X2),relation_dom(X1))
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1008]) ).
cnf(c_0_1008_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk7_3(X1,X3,X2),relation_dom(X1))
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1008]) ).
cnf(c_0_1009_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk6_3(X1,X3,X2),X2)
| in(sk1_esk7_3(X1,X3,X2),X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1009]) ).
cnf(c_0_1009_1,axiom,
( in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(sk1_esk7_3(X1,X3,X2),X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1009]) ).
cnf(c_0_1009_2,axiom,
( in(sk1_esk7_3(X1,X3,X2),X3)
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1009]) ).
cnf(c_0_1009_3,axiom,
( ~ function(X1)
| in(sk1_esk7_3(X1,X3,X2),X3)
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1009]) ).
cnf(c_0_1009_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk7_3(X1,X3,X2),X3)
| in(sk1_esk6_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1009]) ).
cnf(c_0_1010_0,axiom,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X3,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X3,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_2,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X3,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_3,axiom,
( ~ in(ordered_pair(X2,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X3,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_4,axiom,
( ~ in(X3,X5)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_5,axiom,
( ~ in(X4,X5)
| ~ in(X3,X5)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X2,X5)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_6,axiom,
( ~ in(X2,X5)
| ~ in(X4,X5)
| ~ in(X3,X5)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| in(ordered_pair(X2,X3),X1)
| ~ is_transitive_in(X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1010_7,axiom,
( ~ is_transitive_in(X1,X5)
| ~ in(X2,X5)
| ~ in(X4,X5)
| ~ in(X3,X5)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1010]) ).
cnf(c_0_1011_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| in(sk1_esk15_3(X1,X3,X2),X2)
| in(sk1_esk16_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1011]) ).
cnf(c_0_1011_1,axiom,
( in(sk1_esk15_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| in(sk1_esk16_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1011]) ).
cnf(c_0_1011_2,axiom,
( in(sk1_esk16_3(X1,X3,X2),X3)
| in(sk1_esk15_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1011]) ).
cnf(c_0_1011_3,axiom,
( ~ relation(X1)
| in(sk1_esk16_3(X1,X3,X2),X3)
| in(sk1_esk15_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1011]) ).
cnf(c_0_1012_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk12_3(X1,X3,X2),X2)
| in(sk1_esk13_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1012]) ).
cnf(c_0_1012_1,axiom,
( in(sk1_esk12_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(sk1_esk13_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1012]) ).
cnf(c_0_1012_2,axiom,
( in(sk1_esk13_3(X1,X3,X2),X3)
| in(sk1_esk12_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1012]) ).
cnf(c_0_1012_3,axiom,
( ~ relation(X1)
| in(sk1_esk13_3(X1,X3,X2),X3)
| in(sk1_esk12_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1012]) ).
cnf(c_0_1013_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk56_3(X2,X3,X1),X1)
| in(sk1_esk56_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1013]) ).
cnf(c_0_1013_1,axiom,
( in(sk1_esk56_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk56_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1013]) ).
cnf(c_0_1013_2,axiom,
( in(sk1_esk56_3(X2,X3,X1),X2)
| in(sk1_esk56_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1013]) ).
cnf(c_0_1014_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| in(sk1_esk47_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1014]) ).
cnf(c_0_1014_1,axiom,
( in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1014]) ).
cnf(c_0_1014_2,axiom,
( in(sk1_esk47_3(X2,X3,X1),X2)
| in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1014]) ).
cnf(c_0_1015_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| in(sk1_esk47_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1015]) ).
cnf(c_0_1015_1,axiom,
( in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1015]) ).
cnf(c_0_1015_2,axiom,
( in(sk1_esk47_3(X2,X3,X1),X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1015]) ).
cnf(c_0_1016_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk37_3(X2,X3,X1),X1)
| in(sk1_esk38_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1016]) ).
cnf(c_0_1016_1,axiom,
( in(sk1_esk37_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk38_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1016]) ).
cnf(c_0_1016_2,axiom,
( in(sk1_esk38_3(X2,X3,X1),X2)
| in(sk1_esk37_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1016]) ).
cnf(c_0_1017_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk37_3(X2,X3,X1),X1)
| in(sk1_esk39_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1017]) ).
cnf(c_0_1017_1,axiom,
( in(sk1_esk37_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk39_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1017]) ).
cnf(c_0_1017_2,axiom,
( in(sk1_esk39_3(X2,X3,X1),X3)
| in(sk1_esk37_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1017]) ).
cnf(c_0_1018_0,axiom,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1018]) ).
cnf(c_0_1018_1,axiom,
( ~ relation(X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1018]) ).
cnf(c_0_1018_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1018]) ).
cnf(c_0_1018_3,axiom,
( ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1018]) ).
cnf(c_0_1019_0,axiom,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk75_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1019]) ).
cnf(c_0_1019_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,X2)
| ~ in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk75_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1019]) ).
cnf(c_0_1019_2,axiom,
( ~ in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk75_2(X1,X2)),X1)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1019]) ).
cnf(c_0_1020_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk63_2(X1,X2),sk1_esk64_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1020]) ).
cnf(c_0_1020_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ in(ordered_pair(sk1_esk63_2(X1,X2),sk1_esk64_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1020]) ).
cnf(c_0_1020_2,axiom,
( ~ in(ordered_pair(sk1_esk63_2(X1,X2),sk1_esk64_2(X1,X2)),X1)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1020]) ).
cnf(c_0_1021_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk64_2(X1,X2),sk1_esk63_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1021]) ).
cnf(c_0_1021_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ in(ordered_pair(sk1_esk64_2(X1,X2),sk1_esk63_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1021]) ).
cnf(c_0_1021_2,axiom,
( ~ in(ordered_pair(sk1_esk64_2(X1,X2),sk1_esk63_2(X1,X2)),X1)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1021]) ).
cnf(c_0_1022_0,axiom,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk21_2(X1,X2),sk1_esk21_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1022]) ).
cnf(c_0_1022_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,X2)
| ~ in(ordered_pair(sk1_esk21_2(X1,X2),sk1_esk21_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1022]) ).
cnf(c_0_1022_2,axiom,
( ~ in(ordered_pair(sk1_esk21_2(X1,X2),sk1_esk21_2(X1,X2)),X1)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1022]) ).
cnf(c_0_1023_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk31_3(X2,X3,X1) = X3
| sk1_esk31_3(X2,X3,X1) = X2
| in(sk1_esk31_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1023]) ).
cnf(c_0_1023_1,axiom,
( sk1_esk31_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk31_3(X2,X3,X1) = X2
| in(sk1_esk31_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1023]) ).
cnf(c_0_1023_2,axiom,
( sk1_esk31_3(X2,X3,X1) = X2
| sk1_esk31_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk31_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1023]) ).
cnf(c_0_1023_3,axiom,
( in(sk1_esk31_3(X2,X3,X1),X1)
| sk1_esk31_3(X2,X3,X1) = X2
| sk1_esk31_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1023]) ).
cnf(c_0_1024_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| element(sk1_esk76_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1024]) ).
cnf(c_0_1024_1,axiom,
( element(sk1_esk76_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1024]) ).
cnf(c_0_1024_2,axiom,
( ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk76_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1024]) ).
cnf(c_0_1024_3,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk76_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1024]) ).
cnf(c_0_1025_0,axiom,
( in(X4,X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1025]) ).
cnf(c_0_1025_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1025]) ).
cnf(c_0_1025_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1025]) ).
cnf(c_0_1025_3,axiom,
( X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1025]) ).
cnf(c_0_1025_4,axiom,
( ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1025]) ).
cnf(c_0_1025_5,axiom,
( ~ in(subset_complement(X2,X4),X1)
| ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1025]) ).
cnf(c_0_1026_0,axiom,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1026]) ).
cnf(c_0_1026_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1026]) ).
cnf(c_0_1026_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1026]) ).
cnf(c_0_1026_3,axiom,
( X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1026]) ).
cnf(c_0_1026_4,axiom,
( ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1026]) ).
cnf(c_0_1026_5,axiom,
( ~ in(X4,X3)
| ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1026]) ).
cnf(c_0_1027_0,axiom,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sk1_esk61_2(X1,X2)),X1)
| ~ in(sk1_esk61_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1027]) ).
cnf(c_0_1027_1,axiom,
( ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(ordered_pair(X3,sk1_esk61_2(X1,X2)),X1)
| ~ in(sk1_esk61_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1027]) ).
cnf(c_0_1027_2,axiom,
( ~ in(ordered_pair(X3,sk1_esk61_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk61_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1027]) ).
cnf(c_0_1027_3,axiom,
( ~ in(sk1_esk61_2(X1,X2),X2)
| ~ in(ordered_pair(X3,sk1_esk61_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1027]) ).
cnf(c_0_1028_0,axiom,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk49_2(X1,X2),X3),X1)
| ~ in(sk1_esk49_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1028]) ).
cnf(c_0_1028_1,axiom,
( ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(ordered_pair(sk1_esk49_2(X1,X2),X3),X1)
| ~ in(sk1_esk49_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1028]) ).
cnf(c_0_1028_2,axiom,
( ~ in(ordered_pair(sk1_esk49_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(sk1_esk49_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1028]) ).
cnf(c_0_1028_3,axiom,
( ~ in(sk1_esk49_2(X1,X2),X2)
| ~ in(ordered_pair(sk1_esk49_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1028]) ).
cnf(c_0_1029_0,axiom,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk22_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1029]) ).
cnf(c_0_1029_1,axiom,
( in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk22_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1029]) ).
cnf(c_0_1029_2,axiom,
( X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set
| ~ in(X3,sk1_esk22_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1029]) ).
cnf(c_0_1029_3,axiom,
( ~ in(X3,sk1_esk22_3(X1,X2,X3))
| X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1029]) ).
cnf(c_0_1030_0,axiom,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1030_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1030_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1030_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1030_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1030_5,axiom,
( ~ in(ordered_pair(X6,X5),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1030_6,axiom,
( ~ in(ordered_pair(X4,X6),X1)
| ~ in(ordered_pair(X6,X5),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1030]) ).
cnf(c_0_1031_0,axiom,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1031_1,axiom,
( ~ relation(X1)
| X2 = X3
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1031_2,axiom,
( ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1)
| X2 = X3
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1031_3,axiom,
( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1)
| X2 = X3
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1031_4,axiom,
( ~ in(X3,X4)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1)
| X2 = X3
| ~ in(X2,X4)
| ~ is_antisymmetric_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1031_5,axiom,
( ~ in(X2,X4)
| ~ in(X3,X4)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1)
| X2 = X3
| ~ is_antisymmetric_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1031_6,axiom,
( ~ is_antisymmetric_in(X1,X4)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1031]) ).
cnf(c_0_1032_0,axiom,
( X2 = relation_rng(X1)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| in(sk1_esk61_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1032]) ).
cnf(c_0_1032_1,axiom,
( in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| in(sk1_esk61_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1032]) ).
cnf(c_0_1032_2,axiom,
( in(sk1_esk61_2(X1,X2),X2)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1032]) ).
cnf(c_0_1032_3,axiom,
( ~ relation(X1)
| in(sk1_esk61_2(X1,X2),X2)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1032]) ).
cnf(c_0_1033_0,axiom,
( X2 = relation_dom(X1)
| in(ordered_pair(sk1_esk49_2(X1,X2),sk1_esk50_2(X1,X2)),X1)
| in(sk1_esk49_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1033]) ).
cnf(c_0_1033_1,axiom,
( in(ordered_pair(sk1_esk49_2(X1,X2),sk1_esk50_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| in(sk1_esk49_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1033]) ).
cnf(c_0_1033_2,axiom,
( in(sk1_esk49_2(X1,X2),X2)
| in(ordered_pair(sk1_esk49_2(X1,X2),sk1_esk50_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1033]) ).
cnf(c_0_1033_3,axiom,
( ~ relation(X1)
| in(sk1_esk49_2(X1,X2),X2)
| in(ordered_pair(sk1_esk49_2(X1,X2),sk1_esk50_2(X1,X2)),X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1033]) ).
cnf(c_0_1034_0,axiom,
( X1 = identity_relation(X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| in(sk1_esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1034]) ).
cnf(c_0_1034_1,axiom,
( in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| in(sk1_esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1034]) ).
cnf(c_0_1034_2,axiom,
( in(sk1_esk1_2(X2,X1),X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1034]) ).
cnf(c_0_1034_3,axiom,
( ~ relation(X1)
| in(sk1_esk1_2(X2,X1),X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1034]) ).
cnf(c_0_1035_0,axiom,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1035]) ).
cnf(c_0_1035_1,axiom,
( ~ element(X3,powerset(X1))
| element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1035]) ).
cnf(c_0_1035_2,axiom,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| element(subset_difference(X1,X2,X3),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1035]) ).
cnf(c_0_1036_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),sk1_esk46_2(X1,X2))
| ~ in(X3,sk1_esk46_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1036]) ).
cnf(c_0_1036_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ disjoint(fiber(X1,X3),sk1_esk46_2(X1,X2))
| ~ in(X3,sk1_esk46_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1036]) ).
cnf(c_0_1036_2,axiom,
( ~ disjoint(fiber(X1,X3),sk1_esk46_2(X1,X2))
| ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ in(X3,sk1_esk46_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1036]) ).
cnf(c_0_1036_3,axiom,
( ~ in(X3,sk1_esk46_2(X1,X2))
| ~ disjoint(fiber(X1,X3),sk1_esk46_2(X1,X2))
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1036]) ).
cnf(c_0_1037_0,axiom,
( X1 = identity_relation(X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1037]) ).
cnf(c_0_1037_1,axiom,
( in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1037]) ).
cnf(c_0_1037_2,axiom,
( sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1037]) ).
cnf(c_0_1037_3,axiom,
( ~ relation(X1)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1037]) ).
cnf(c_0_1038_0,axiom,
( X3 = empty_set
| in(sk1_esk45_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1038]) ).
cnf(c_0_1038_1,axiom,
( in(sk1_esk45_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1038]) ).
cnf(c_0_1038_2,axiom,
( ~ relation(X1)
| in(sk1_esk45_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1038]) ).
cnf(c_0_1038_3,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| in(sk1_esk45_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1038]) ).
cnf(c_0_1038_4,axiom,
( ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| in(sk1_esk45_3(X1,X2,X3),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1038]) ).
cnf(c_0_1039_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(sk1_esk23_2(X1,X2),X2)
| ~ in(sk1_esk23_2(X1,X2),sk1_esk24_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1039]) ).
cnf(c_0_1039_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk23_2(X1,X2),X2)
| ~ in(sk1_esk23_2(X1,X2),sk1_esk24_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1039]) ).
cnf(c_0_1039_2,axiom,
( ~ in(sk1_esk23_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk23_2(X1,X2),sk1_esk24_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1039]) ).
cnf(c_0_1039_3,axiom,
( ~ in(sk1_esk23_2(X1,X2),sk1_esk24_2(X1,X2))
| ~ in(sk1_esk23_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1039]) ).
cnf(c_0_1040_0,axiom,
( subset(X1,X2)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1040]) ).
cnf(c_0_1040_1,axiom,
( in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1040]) ).
cnf(c_0_1040_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1040]) ).
cnf(c_0_1040_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1040]) ).
cnf(c_0_1041_0,axiom,
( in(sk1_esk57_3(X1,X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1041]) ).
cnf(c_0_1041_1,axiom,
( ~ function(X1)
| in(sk1_esk57_3(X1,X2,X3),relation_dom(X1))
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1041]) ).
cnf(c_0_1041_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk57_3(X1,X2,X3),relation_dom(X1))
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1041]) ).
cnf(c_0_1041_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk57_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1041]) ).
cnf(c_0_1041_4,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk57_3(X1,X2,X3),relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1041]) ).
cnf(c_0_1042_0,axiom,
( apply(X1,sk1_esk57_3(X1,X2,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1042]) ).
cnf(c_0_1042_1,axiom,
( ~ function(X1)
| apply(X1,sk1_esk57_3(X1,X2,X3)) = X3
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1042]) ).
cnf(c_0_1042_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk57_3(X1,X2,X3)) = X3
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1042]) ).
cnf(c_0_1042_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk57_3(X1,X2,X3)) = X3
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1042]) ).
cnf(c_0_1042_4,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk57_3(X1,X2,X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1042]) ).
cnf(c_0_1043_0,axiom,
( is_transitive_in(X1,X2)
| in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1043]) ).
cnf(c_0_1043_1,axiom,
( in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1043]) ).
cnf(c_0_1043_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1043]) ).
cnf(c_0_1044_0,axiom,
( is_transitive_in(X1,X2)
| in(ordered_pair(sk1_esk74_2(X1,X2),sk1_esk75_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1044]) ).
cnf(c_0_1044_1,axiom,
( in(ordered_pair(sk1_esk74_2(X1,X2),sk1_esk75_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1044]) ).
cnf(c_0_1044_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk74_2(X1,X2),sk1_esk75_2(X1,X2)),X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1044]) ).
cnf(c_0_1045_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(sk1_esk51_2(X1,X2),sk1_esk52_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1045]) ).
cnf(c_0_1045_1,axiom,
( in(ordered_pair(sk1_esk51_2(X1,X2),sk1_esk52_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1045]) ).
cnf(c_0_1045_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk51_2(X1,X2),sk1_esk52_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1045]) ).
cnf(c_0_1046_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk51_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1046]) ).
cnf(c_0_1046_1,axiom,
( in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk51_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1046]) ).
cnf(c_0_1046_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk51_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1046]) ).
cnf(c_0_1047_0,axiom,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1047]) ).
cnf(c_0_1047_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1047]) ).
cnf(c_0_1047_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1047]) ).
cnf(c_0_1047_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1047]) ).
cnf(c_0_1047_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1047]) ).
cnf(c_0_1047_5,axiom,
( ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1047]) ).
cnf(c_0_1048_0,axiom,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1048]) ).
cnf(c_0_1048_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1048]) ).
cnf(c_0_1048_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1048]) ).
cnf(c_0_1048_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1048]) ).
cnf(c_0_1048_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1048]) ).
cnf(c_0_1048_5,axiom,
( ~ in(X4,X3)
| ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1048]) ).
cnf(c_0_1049_0,axiom,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk58_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk58_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1049]) ).
cnf(c_0_1049_1,axiom,
( ~ function(X1)
| X2 = relation_rng(X1)
| ~ relation(X1)
| sk1_esk58_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk58_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1049]) ).
cnf(c_0_1049_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| sk1_esk58_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk58_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1049]) ).
cnf(c_0_1049_3,axiom,
( sk1_esk58_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk58_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1049]) ).
cnf(c_0_1049_4,axiom,
( ~ in(X3,relation_dom(X1))
| sk1_esk58_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk58_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1049]) ).
cnf(c_0_1049_5,axiom,
( ~ in(sk1_esk58_2(X1,X2),X2)
| ~ in(X3,relation_dom(X1))
| sk1_esk58_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1049]) ).
cnf(c_0_1050_0,axiom,
( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X1)
| X3 = X2
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1050_1,axiom,
( in(ordered_pair(X3,X2),X1)
| in(ordered_pair(X2,X3),X1)
| X3 = X2
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1050_2,axiom,
( X3 = X2
| in(ordered_pair(X3,X2),X1)
| in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1050_3,axiom,
( ~ relation(X1)
| X3 = X2
| in(ordered_pair(X3,X2),X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1050_4,axiom,
( ~ in(X2,X4)
| ~ relation(X1)
| X3 = X2
| in(ordered_pair(X3,X2),X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X3,X4)
| ~ is_connected_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1050_5,axiom,
( ~ in(X3,X4)
| ~ in(X2,X4)
| ~ relation(X1)
| X3 = X2
| in(ordered_pair(X3,X2),X1)
| in(ordered_pair(X2,X3),X1)
| ~ is_connected_in(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1050_6,axiom,
( ~ is_connected_in(X1,X4)
| ~ in(X3,X4)
| ~ in(X2,X4)
| ~ relation(X1)
| X3 = X2
| in(ordered_pair(X3,X2),X1)
| in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1050]) ).
cnf(c_0_1051_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk54_2(X2,X1),X3)
| ~ in(sk1_esk54_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1051]) ).
cnf(c_0_1051_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk54_2(X2,X1),X3)
| ~ in(sk1_esk54_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1051]) ).
cnf(c_0_1051_2,axiom,
( ~ in(sk1_esk54_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk54_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1051]) ).
cnf(c_0_1051_3,axiom,
( ~ in(sk1_esk54_2(X2,X1),X1)
| ~ in(sk1_esk54_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1051]) ).
cnf(c_0_1052_0,axiom,
( in(X3,sk1_esk53_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1052]) ).
cnf(c_0_1052_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk53_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1052]) ).
cnf(c_0_1052_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk53_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1052]) ).
cnf(c_0_1053_0,axiom,
( in(sk1_esk53_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1053]) ).
cnf(c_0_1053_1,axiom,
( X1 != union(X2)
| in(sk1_esk53_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1053]) ).
cnf(c_0_1053_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk53_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1053]) ).
cnf(c_0_1054_0,axiom,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1054]) ).
cnf(c_0_1054_1,axiom,
( ~ function(X1)
| in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1054]) ).
cnf(c_0_1054_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1054]) ).
cnf(c_0_1054_3,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1054]) ).
cnf(c_0_1054_4,axiom,
( ~ in(apply(X1,X4),X3)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1054]) ).
cnf(c_0_1054_5,axiom,
( ~ in(X4,relation_dom(X1))
| ~ in(apply(X1,X4),X3)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1054]) ).
cnf(c_0_1055_0,axiom,
( X1 = empty_set
| in(X3,X2)
| in(sk1_esk22_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1055]) ).
cnf(c_0_1055_1,axiom,
( in(X3,X2)
| X1 = empty_set
| in(sk1_esk22_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1055]) ).
cnf(c_0_1055_2,axiom,
( in(sk1_esk22_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1055]) ).
cnf(c_0_1055_3,axiom,
( X2 != set_meet(X1)
| in(sk1_esk22_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1055]) ).
cnf(c_0_1056_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1056]) ).
cnf(c_0_1056_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1056]) ).
cnf(c_0_1056_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1056]) ).
cnf(c_0_1056_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1056]) ).
cnf(c_0_1056_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1056]) ).
cnf(c_0_1057_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1057]) ).
cnf(c_0_1057_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1057]) ).
cnf(c_0_1057_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1057]) ).
cnf(c_0_1057_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1057]) ).
cnf(c_0_1057_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1057]) ).
cnf(c_0_1058_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1058]) ).
cnf(c_0_1058_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1058]) ).
cnf(c_0_1058_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1058]) ).
cnf(c_0_1058_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1058]) ).
cnf(c_0_1058_4,axiom,
( ~ subset(X1,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1058]) ).
cnf(c_0_1059_0,axiom,
( X2 = empty_set
| disjoint(fiber(X1,sk1_esk32_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1059]) ).
cnf(c_0_1059_1,axiom,
( disjoint(fiber(X1,sk1_esk32_2(X1,X2)),X2)
| X2 = empty_set
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1059]) ).
cnf(c_0_1059_2,axiom,
( ~ relation(X1)
| disjoint(fiber(X1,sk1_esk32_2(X1,X2)),X2)
| X2 = empty_set
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1059]) ).
cnf(c_0_1059_3,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk32_2(X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1059]) ).
cnf(c_0_1059_4,axiom,
( ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk32_2(X1,X2)),X2)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1059]) ).
cnf(c_0_1060_0,axiom,
( well_orders(X1,X2)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1060_1,axiom,
( ~ relation(X1)
| well_orders(X1,X2)
| ~ is_well_founded_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1060_2,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| well_orders(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1060_3,axiom,
( ~ is_connected_in(X1,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| well_orders(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1060_4,axiom,
( ~ is_antisymmetric_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| well_orders(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1060_5,axiom,
( ~ is_transitive_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| well_orders(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1060_6,axiom,
( ~ is_reflexive_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1060]) ).
cnf(c_0_1061_0,axiom,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1061]) ).
cnf(c_0_1061_1,axiom,
( ~ element(X3,powerset(X1))
| subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1061]) ).
cnf(c_0_1061_2,axiom,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1061]) ).
cnf(c_0_1062_0,axiom,
( X2 = X3
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1062_1,axiom,
( ~ function(X1)
| X2 = X3
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1062_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = X3
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1062_3,axiom,
( apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1062_4,axiom,
( ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1062_5,axiom,
( ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1062_6,axiom,
( ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1062]) ).
cnf(c_0_1063_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk27_2(X2,X1),X2)
| ~ in(sk1_esk27_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1063]) ).
cnf(c_0_1063_1,axiom,
( ~ subset(sk1_esk27_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk27_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1063]) ).
cnf(c_0_1063_2,axiom,
( ~ in(sk1_esk27_2(X2,X1),X1)
| ~ subset(sk1_esk27_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1063]) ).
cnf(c_0_1064_0,axiom,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1064]) ).
cnf(c_0_1064_1,axiom,
( ~ relation(X1)
| in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1064]) ).
cnf(c_0_1064_2,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1064]) ).
cnf(c_0_1064_3,axiom,
( ~ in(X5,X3)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1064]) ).
cnf(c_0_1064_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1064]) ).
cnf(c_0_1065_0,axiom,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1065]) ).
cnf(c_0_1065_1,axiom,
( ~ relation(X1)
| in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1065]) ).
cnf(c_0_1065_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1065]) ).
cnf(c_0_1065_3,axiom,
( ~ in(X5,X3)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1065]) ).
cnf(c_0_1065_4,axiom,
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(X5,X3)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1065]) ).
cnf(c_0_1066_0,axiom,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| X4 != apply(X1,X5)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1066_1,axiom,
( ~ function(X1)
| in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| X4 != apply(X1,X5)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1066_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| X2 != relation_image(X1,X3)
| X4 != apply(X1,X5)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1066_3,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| X4 != apply(X1,X5)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1066_4,axiom,
( X4 != apply(X1,X5)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| ~ in(X5,X3)
| ~ in(X5,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1066_5,axiom,
( ~ in(X5,X3)
| X4 != apply(X1,X5)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2)
| ~ in(X5,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1066_6,axiom,
( ~ in(X5,relation_dom(X1))
| ~ in(X5,X3)
| X4 != apply(X1,X5)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1066]) ).
cnf(c_0_1067_0,axiom,
( X1 = X2
| ~ in(sk1_esk92_2(X1,X2),X2)
| ~ in(sk1_esk92_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1067]) ).
cnf(c_0_1067_1,axiom,
( ~ in(sk1_esk92_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk92_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1067]) ).
cnf(c_0_1067_2,axiom,
( ~ in(sk1_esk92_2(X1,X2),X1)
| ~ in(sk1_esk92_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1067]) ).
cnf(c_0_1068_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1068]) ).
cnf(c_0_1068_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1068]) ).
cnf(c_0_1068_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1068]) ).
cnf(c_0_1068_3,axiom,
( X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1068]) ).
cnf(c_0_1068_4,axiom,
( ~ in(ordered_pair(X4,X3),X2)
| X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1068]) ).
cnf(c_0_1069_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1069]) ).
cnf(c_0_1069_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1069]) ).
cnf(c_0_1069_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1069]) ).
cnf(c_0_1069_3,axiom,
( X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1069]) ).
cnf(c_0_1069_4,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1069]) ).
cnf(c_0_1070_0,axiom,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1070]) ).
cnf(c_0_1070_1,axiom,
( ~ function(X1)
| X3 = apply(X1,X2)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1070]) ).
cnf(c_0_1070_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1070]) ).
cnf(c_0_1070_3,axiom,
( ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1070]) ).
cnf(c_0_1070_4,axiom,
( ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1070]) ).
cnf(c_0_1071_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1071]) ).
cnf(c_0_1071_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1071]) ).
cnf(c_0_1071_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1071]) ).
cnf(c_0_1071_3,axiom,
( X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1071]) ).
cnf(c_0_1071_4,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1071]) ).
cnf(c_0_1072_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1072]) ).
cnf(c_0_1072_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1072]) ).
cnf(c_0_1072_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1072]) ).
cnf(c_0_1072_3,axiom,
( X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1072]) ).
cnf(c_0_1072_4,axiom,
( ~ in(ordered_pair(X3,X4),X2)
| X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1072]) ).
cnf(c_0_1073_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),sk1_esk33_1(X1))
| ~ in(X2,sk1_esk33_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1073]) ).
cnf(c_0_1073_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ disjoint(fiber(X1,X2),sk1_esk33_1(X1))
| ~ in(X2,sk1_esk33_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1073]) ).
cnf(c_0_1073_2,axiom,
( ~ disjoint(fiber(X1,X2),sk1_esk33_1(X1))
| ~ relation(X1)
| well_founded_relation(X1)
| ~ in(X2,sk1_esk33_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1073]) ).
cnf(c_0_1073_3,axiom,
( ~ in(X2,sk1_esk33_1(X1))
| ~ disjoint(fiber(X1,X2),sk1_esk33_1(X1))
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1073]) ).
cnf(c_0_1074_0,axiom,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1074]) ).
cnf(c_0_1074_1,axiom,
( X5 = X3
| X5 = X4
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1074]) ).
cnf(c_0_1074_2,axiom,
( X5 = X2
| X5 = X3
| X5 = X4
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1074]) ).
cnf(c_0_1074_3,axiom,
( X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1074]) ).
cnf(c_0_1074_4,axiom,
( ~ in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1074]) ).
cnf(c_0_1075_0,axiom,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1075]) ).
cnf(c_0_1075_1,axiom,
( ~ relation(X1)
| in(X5,X3)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1075]) ).
cnf(c_0_1075_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X5,X3)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1075]) ).
cnf(c_0_1075_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1075]) ).
cnf(c_0_1075_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1075]) ).
cnf(c_0_1076_0,axiom,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1076]) ).
cnf(c_0_1076_1,axiom,
( ~ relation(X1)
| in(X4,X3)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1076]) ).
cnf(c_0_1076_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X4,X3)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1076]) ).
cnf(c_0_1076_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1076]) ).
cnf(c_0_1076_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1076]) ).
cnf(c_0_1077_0,axiom,
( X2 = relation_rng(X1)
| in(sk1_esk58_2(X1,X2),X2)
| apply(X1,sk1_esk59_2(X1,X2)) = sk1_esk58_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1077]) ).
cnf(c_0_1077_1,axiom,
( in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1)
| apply(X1,sk1_esk59_2(X1,X2)) = sk1_esk58_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1077]) ).
cnf(c_0_1077_2,axiom,
( apply(X1,sk1_esk59_2(X1,X2)) = sk1_esk58_2(X1,X2)
| in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1077]) ).
cnf(c_0_1077_3,axiom,
( ~ function(X1)
| apply(X1,sk1_esk59_2(X1,X2)) = sk1_esk58_2(X1,X2)
| in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1077]) ).
cnf(c_0_1077_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk59_2(X1,X2)) = sk1_esk58_2(X1,X2)
| in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1077]) ).
cnf(c_0_1078_0,axiom,
( X1 = union(X2)
| in(sk1_esk54_2(X2,X1),X1)
| in(sk1_esk54_2(X2,X1),sk1_esk55_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1078]) ).
cnf(c_0_1078_1,axiom,
( in(sk1_esk54_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk54_2(X2,X1),sk1_esk55_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1078]) ).
cnf(c_0_1078_2,axiom,
( in(sk1_esk54_2(X2,X1),sk1_esk55_2(X2,X1))
| in(sk1_esk54_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1078]) ).
cnf(c_0_1079_0,axiom,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1079]) ).
cnf(c_0_1079_1,axiom,
( ~ function(X1)
| in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1079]) ).
cnf(c_0_1079_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1079]) ).
cnf(c_0_1079_3,axiom,
( ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X3),X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1079]) ).
cnf(c_0_1079_4,axiom,
( X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1079]) ).
cnf(c_0_1080_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk24_2(X1,X2),X1)
| ~ in(sk1_esk23_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1080]) ).
cnf(c_0_1080_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk24_2(X1,X2),X1)
| ~ in(sk1_esk23_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1080]) ).
cnf(c_0_1080_2,axiom,
( in(sk1_esk24_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk23_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1080]) ).
cnf(c_0_1080_3,axiom,
( ~ in(sk1_esk23_2(X1,X2),X2)
| in(sk1_esk24_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1080]) ).
cnf(c_0_1081_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk23_2(X1,X2),X3)
| in(sk1_esk23_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1081]) ).
cnf(c_0_1081_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk23_2(X1,X2),X3)
| in(sk1_esk23_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1081]) ).
cnf(c_0_1081_2,axiom,
( in(sk1_esk23_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk23_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1081]) ).
cnf(c_0_1081_3,axiom,
( in(sk1_esk23_2(X1,X2),X2)
| in(sk1_esk23_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1081]) ).
cnf(c_0_1081_4,axiom,
( ~ in(X3,X1)
| in(sk1_esk23_2(X1,X2),X2)
| in(sk1_esk23_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1081]) ).
cnf(c_0_1082_0,axiom,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1082]) ).
cnf(c_0_1082_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1082]) ).
cnf(c_0_1083_0,axiom,
( ~ in(X1,X2)
| ~ in(X3,sk1_esk93_2(X1,X2))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1083]) ).
cnf(c_0_1083_1,axiom,
( ~ in(X3,sk1_esk93_2(X1,X2))
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1083]) ).
cnf(c_0_1083_2,axiom,
( ~ in(X3,X2)
| ~ in(X3,sk1_esk93_2(X1,X2))
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1083]) ).
cnf(c_0_1084_0,axiom,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1084]) ).
cnf(c_0_1084_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1084]) ).
cnf(c_0_1084_2,axiom,
( X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1084]) ).
cnf(c_0_1084_3,axiom,
( ~ in(X6,X3)
| X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1084]) ).
cnf(c_0_1084_4,axiom,
( ~ in(X5,X2)
| ~ in(X6,X3)
| X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1084]) ).
cnf(c_0_1085_0,axiom,
( X2 = relation_rng(X1)
| in(sk1_esk58_2(X1,X2),X2)
| in(sk1_esk59_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1085]) ).
cnf(c_0_1085_1,axiom,
( in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1)
| in(sk1_esk59_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1085]) ).
cnf(c_0_1085_2,axiom,
( in(sk1_esk59_2(X1,X2),relation_dom(X1))
| in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1085]) ).
cnf(c_0_1085_3,axiom,
( ~ function(X1)
| in(sk1_esk59_2(X1,X2),relation_dom(X1))
| in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1085]) ).
cnf(c_0_1085_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk59_2(X1,X2),relation_dom(X1))
| in(sk1_esk58_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1085]) ).
cnf(c_0_1086_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1086]) ).
cnf(c_0_1086_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1086]) ).
cnf(c_0_1086_2,axiom,
( X5 != X2
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1086]) ).
cnf(c_0_1087_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1087]) ).
cnf(c_0_1087_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1087]) ).
cnf(c_0_1087_2,axiom,
( X5 != X3
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1087]) ).
cnf(c_0_1088_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_1088]) ).
cnf(c_0_1088_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_1088]) ).
cnf(c_0_1088_2,axiom,
( X5 != X4
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1088]) ).
cnf(c_0_1089_0,axiom,
( in(apply(X1,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1089]) ).
cnf(c_0_1089_1,axiom,
( ~ function(X1)
| in(apply(X1,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1089]) ).
cnf(c_0_1089_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(apply(X1,X4),X3)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1089]) ).
cnf(c_0_1089_3,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(apply(X1,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1089]) ).
cnf(c_0_1089_4,axiom,
( ~ in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(apply(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1089]) ).
cnf(c_0_1090_0,axiom,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1090]) ).
cnf(c_0_1090_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1090]) ).
cnf(c_0_1091_0,axiom,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1091]) ).
cnf(c_0_1091_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(union_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1091]) ).
cnf(c_0_1092_0,axiom,
( ordered_pair(sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1092]) ).
cnf(c_0_1092_1,axiom,
( ~ in(X1,X2)
| ordered_pair(sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) = X1
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1092]) ).
cnf(c_0_1092_2,axiom,
( ~ relation(X2)
| ~ in(X1,X2)
| ordered_pair(sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1092]) ).
cnf(c_0_1093_0,axiom,
( in(X3,sk1_esk95_2(X2,X1))
| ~ in(X1,sk1_esk94_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1093]) ).
cnf(c_0_1093_1,axiom,
( ~ in(X1,sk1_esk94_1(X2))
| in(X3,sk1_esk95_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1093]) ).
cnf(c_0_1093_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk94_1(X2))
| in(X3,sk1_esk95_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1093]) ).
cnf(c_0_1094_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1094]) ).
cnf(c_0_1094_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1094]) ).
cnf(c_0_1094_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1094]) ).
cnf(c_0_1094_3,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1094]) ).
cnf(c_0_1095_0,axiom,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1095]) ).
cnf(c_0_1095_1,axiom,
( ~ function(X1)
| in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1095]) ).
cnf(c_0_1095_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1095]) ).
cnf(c_0_1095_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(X3,X2)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1095]) ).
cnf(c_0_1095_4,axiom,
( X3 != apply(X1,X4)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(X3,X2)
| ~ in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1095]) ).
cnf(c_0_1095_5,axiom,
( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1095]) ).
cnf(c_0_1096_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1096]) ).
cnf(c_0_1096_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1096]) ).
cnf(c_0_1096_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1096]) ).
cnf(c_0_1096_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1096]) ).
cnf(c_0_1097_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1097]) ).
cnf(c_0_1097_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1097]) ).
cnf(c_0_1097_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1097]) ).
cnf(c_0_1097_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1097]) ).
cnf(c_0_1098_0,axiom,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1098]) ).
cnf(c_0_1098_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X2,X2),X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1098]) ).
cnf(c_0_1098_2,axiom,
( ~ in(X2,X3)
| ~ relation(X1)
| in(ordered_pair(X2,X2),X1)
| ~ is_reflexive_in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1098]) ).
cnf(c_0_1098_3,axiom,
( ~ is_reflexive_in(X1,X3)
| ~ in(X2,X3)
| ~ relation(X1)
| in(ordered_pair(X2,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1098]) ).
cnf(c_0_1099_0,axiom,
( X1 = singleton(X2)
| sk1_esk25_2(X2,X1) != X2
| ~ in(sk1_esk25_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1099]) ).
cnf(c_0_1099_1,axiom,
( sk1_esk25_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk25_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1099]) ).
cnf(c_0_1099_2,axiom,
( ~ in(sk1_esk25_2(X2,X1),X1)
| sk1_esk25_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1099]) ).
cnf(c_0_1100_0,axiom,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1100]) ).
cnf(c_0_1100_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1100]) ).
cnf(c_0_1101_0,axiom,
( X2 = empty_set
| in(sk1_esk32_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1101_1,axiom,
( in(sk1_esk32_2(X1,X2),X2)
| X2 = empty_set
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1101_2,axiom,
( ~ relation(X1)
| in(sk1_esk32_2(X1,X2),X2)
| X2 = empty_set
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1101_3,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| in(sk1_esk32_2(X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1101_4,axiom,
( ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1)
| in(sk1_esk32_2(X1,X2),X2)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1102_0,axiom,
( X1 = union(X2)
| in(sk1_esk54_2(X2,X1),X1)
| in(sk1_esk55_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1102_1,axiom,
( in(sk1_esk54_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk55_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1102_2,axiom,
( in(sk1_esk55_2(X2,X1),X2)
| in(sk1_esk54_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1103_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk27_2(X2,X1),X2)
| in(sk1_esk27_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1103]) ).
cnf(c_0_1103_1,axiom,
( subset(sk1_esk27_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk27_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1103]) ).
cnf(c_0_1103_2,axiom,
( in(sk1_esk27_2(X2,X1),X1)
| subset(sk1_esk27_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1103]) ).
cnf(c_0_1104_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1104_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1104_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1104_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1105_0,axiom,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_1,axiom,
( X2 = X1
| in(X1,X2)
| in(X2,X1)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_2,axiom,
( in(X2,X1)
| X2 = X1
| in(X1,X2)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_3,axiom,
( ~ in(X1,X3)
| in(X2,X1)
| X2 = X1
| in(X1,X2)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_4,axiom,
( ~ in(X2,X3)
| ~ in(X1,X3)
| in(X2,X1)
| X2 = X1
| in(X1,X2)
| ~ epsilon_connected(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_5,axiom,
( ~ epsilon_connected(X3)
| ~ in(X2,X3)
| ~ in(X1,X3)
| in(X2,X1)
| X2 = X1
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1106_0,axiom,
( X1 = X2
| in(sk1_esk92_2(X1,X2),X2)
| in(sk1_esk92_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1106]) ).
cnf(c_0_1106_1,axiom,
( in(sk1_esk92_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk92_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1106]) ).
cnf(c_0_1106_2,axiom,
( in(sk1_esk92_2(X1,X2),X1)
| in(sk1_esk92_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1106]) ).
cnf(c_0_1107_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1107_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1107_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1107_3,axiom,
( X3 != X4
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1107_4,axiom,
( ~ in(X3,X2)
| X3 != X4
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1108_0,axiom,
( in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1108_1,axiom,
( ~ function(X1)
| in(X4,relation_dom(X1))
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1108_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,relation_dom(X1))
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1108_3,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,relation_dom(X1))
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1108_4,axiom,
( ~ in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| in(X4,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1109_0,axiom,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1109_1,axiom,
( ~ relation(X1)
| X3 = X4
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1109_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1109_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1110_0,axiom,
( in(sk1_esk95_2(X2,X1),sk1_esk94_1(X2))
| ~ in(X1,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1110]) ).
cnf(c_0_1110_1,axiom,
( ~ in(X1,sk1_esk94_1(X2))
| in(sk1_esk95_2(X2,X1),sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1110]) ).
cnf(c_0_1111_0,axiom,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1111]) ).
cnf(c_0_1111_1,axiom,
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1111]) ).
cnf(c_0_1112_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk44_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1112]) ).
cnf(c_0_1112_1,axiom,
( ~ in(sk1_esk44_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1112]) ).
cnf(c_0_1113_0,axiom,
( in(X1,sk1_esk94_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1113]) ).
cnf(c_0_1113_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk94_1(X2))
| ~ in(X3,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1113]) ).
cnf(c_0_1113_2,axiom,
( ~ in(X3,sk1_esk94_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1113]) ).
cnf(c_0_1114_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1114_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1114_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1114_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1115_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1115_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1115_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1115_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1116_0,axiom,
( in(X1,sk1_esk94_1(X2))
| are_equipotent(X1,sk1_esk94_1(X2))
| ~ subset(X1,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1116]) ).
cnf(c_0_1116_1,axiom,
( are_equipotent(X1,sk1_esk94_1(X2))
| in(X1,sk1_esk94_1(X2))
| ~ subset(X1,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1116]) ).
cnf(c_0_1116_2,axiom,
( ~ subset(X1,sk1_esk94_1(X2))
| are_equipotent(X1,sk1_esk94_1(X2))
| in(X1,sk1_esk94_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1116]) ).
cnf(c_0_1117_0,axiom,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1117]) ).
cnf(c_0_1117_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1117]) ).
cnf(c_0_1118_0,axiom,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1118_1,axiom,
( in(X3,X4)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1118_2,axiom,
( X2 != set_meet(X1)
| in(X3,X4)
| X1 = empty_set
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1118_3,axiom,
( ~ in(X4,X1)
| X2 != set_meet(X1)
| in(X3,X4)
| X1 = empty_set
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1118_4,axiom,
( ~ in(X3,X2)
| ~ in(X4,X1)
| X2 != set_meet(X1)
| in(X3,X4)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1119_0,axiom,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1119]) ).
cnf(c_0_1119_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| meet_of_subsets(X1,X2) = set_meet(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1119]) ).
cnf(c_0_1120_0,axiom,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1120]) ).
cnf(c_0_1120_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| union_of_subsets(X1,X2) = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1120]) ).
cnf(c_0_1121_0,axiom,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1121]) ).
cnf(c_0_1121_1,axiom,
( ~ element(X3,powerset(X2))
| element(X1,X2)
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1121]) ).
cnf(c_0_1121_2,axiom,
( ~ in(X1,X3)
| ~ element(X3,powerset(X2))
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1121]) ).
cnf(c_0_1122_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1122]) ).
cnf(c_0_1122_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1122]) ).
cnf(c_0_1122_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1122]) ).
cnf(c_0_1123_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1123]) ).
cnf(c_0_1123_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1123]) ).
cnf(c_0_1123_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1123]) ).
cnf(c_0_1123_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1123]) ).
cnf(c_0_1124_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| sk1_esk63_2(X1,X2) != sk1_esk64_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1124]) ).
cnf(c_0_1124_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| sk1_esk63_2(X1,X2) != sk1_esk64_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1124]) ).
cnf(c_0_1124_2,axiom,
( sk1_esk63_2(X1,X2) != sk1_esk64_2(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1124]) ).
cnf(c_0_1125_0,axiom,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| sk1_esk52_2(X1,X2) != sk1_esk51_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1125]) ).
cnf(c_0_1125_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,X2)
| sk1_esk52_2(X1,X2) != sk1_esk51_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1125]) ).
cnf(c_0_1125_2,axiom,
( sk1_esk52_2(X1,X2) != sk1_esk51_2(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1125]) ).
cnf(c_0_1126_0,axiom,
( in(sk1_esk93_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1126]) ).
cnf(c_0_1126_1,axiom,
( ~ in(X1,X2)
| in(sk1_esk93_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1126]) ).
cnf(c_0_1127_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1127_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1127_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1128_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk73_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1128]) ).
cnf(c_0_1128_1,axiom,
( in(sk1_esk73_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1128]) ).
cnf(c_0_1128_2,axiom,
( ~ relation(X1)
| in(sk1_esk73_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1128]) ).
cnf(c_0_1129_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1129]) ).
cnf(c_0_1129_1,axiom,
( in(sk1_esk74_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1129]) ).
cnf(c_0_1129_2,axiom,
( ~ relation(X1)
| in(sk1_esk74_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1129]) ).
cnf(c_0_1130_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk75_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1130_1,axiom,
( in(sk1_esk75_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1130_2,axiom,
( ~ relation(X1)
| in(sk1_esk75_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1131_0,axiom,
( is_connected_in(X1,X2)
| in(sk1_esk63_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1131_1,axiom,
( in(sk1_esk63_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1131_2,axiom,
( ~ relation(X1)
| in(sk1_esk63_2(X1,X2),X2)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1132_0,axiom,
( is_connected_in(X1,X2)
| in(sk1_esk64_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1132]) ).
cnf(c_0_1132_1,axiom,
( in(sk1_esk64_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1132]) ).
cnf(c_0_1132_2,axiom,
( ~ relation(X1)
| in(sk1_esk64_2(X1,X2),X2)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1132]) ).
cnf(c_0_1133_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(sk1_esk51_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1133]) ).
cnf(c_0_1133_1,axiom,
( in(sk1_esk51_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1133]) ).
cnf(c_0_1133_2,axiom,
( ~ relation(X1)
| in(sk1_esk51_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1133]) ).
cnf(c_0_1134_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(sk1_esk52_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1134]) ).
cnf(c_0_1134_1,axiom,
( in(sk1_esk52_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1134]) ).
cnf(c_0_1134_2,axiom,
( ~ relation(X1)
| in(sk1_esk52_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1134]) ).
cnf(c_0_1135_0,axiom,
( is_well_founded_in(X1,X2)
| subset(sk1_esk46_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1135]) ).
cnf(c_0_1135_1,axiom,
( subset(sk1_esk46_2(X1,X2),X2)
| is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1135]) ).
cnf(c_0_1135_2,axiom,
( ~ relation(X1)
| subset(sk1_esk46_2(X1,X2),X2)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1135]) ).
cnf(c_0_1136_0,axiom,
( is_reflexive_in(X1,X2)
| in(sk1_esk21_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1136]) ).
cnf(c_0_1136_1,axiom,
( in(sk1_esk21_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1136]) ).
cnf(c_0_1136_2,axiom,
( ~ relation(X1)
| in(sk1_esk21_2(X1,X2),X2)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1136]) ).
cnf(c_0_1137_0,axiom,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1137]) ).
cnf(c_0_1137_1,axiom,
( ~ relation(X1)
| set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1137]) ).
cnf(c_0_1138_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1138]) ).
cnf(c_0_1138_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1138]) ).
cnf(c_0_1138_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1138]) ).
cnf(c_0_1139_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1139]) ).
cnf(c_0_1139_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1139]) ).
cnf(c_0_1139_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1139]) ).
cnf(c_0_1140_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1140]) ).
cnf(c_0_1140_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1140]) ).
cnf(c_0_1140_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1140]) ).
cnf(c_0_1141_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1141]) ).
cnf(c_0_1141_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1141]) ).
cnf(c_0_1141_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1141]) ).
cnf(c_0_1142_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1142]) ).
cnf(c_0_1142_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1142]) ).
cnf(c_0_1142_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1142]) ).
cnf(c_0_1143_0,axiom,
( X1 = singleton(X2)
| sk1_esk25_2(X2,X1) = X2
| in(sk1_esk25_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1143]) ).
cnf(c_0_1143_1,axiom,
( sk1_esk25_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk25_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1143]) ).
cnf(c_0_1143_2,axiom,
( in(sk1_esk25_2(X2,X1),X1)
| sk1_esk25_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1143]) ).
cnf(c_0_1144_0,axiom,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1144]) ).
cnf(c_0_1144_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1144]) ).
cnf(c_0_1145_0,axiom,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1145_1,axiom,
( X3 = empty_set
| in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1145_2,axiom,
( ~ function(X1)
| X3 = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1145_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| X3 = empty_set
| in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1145_4,axiom,
( X3 != apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| X3 = empty_set
| in(X2,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1147_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1147]) ).
cnf(c_0_1147_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1147]) ).
cnf(c_0_1147_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1147]) ).
cnf(c_0_1148_0,axiom,
( one_to_one(X1)
| apply(X1,sk1_esk68_1(X1)) = apply(X1,sk1_esk67_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1148_1,axiom,
( apply(X1,sk1_esk68_1(X1)) = apply(X1,sk1_esk67_1(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1148_2,axiom,
( ~ function(X1)
| apply(X1,sk1_esk68_1(X1)) = apply(X1,sk1_esk67_1(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1148_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk68_1(X1)) = apply(X1,sk1_esk67_1(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1149_0,axiom,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_1,axiom,
( ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1150_0,axiom,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1150_1,axiom,
( ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1150_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1150_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1150_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1151_0,axiom,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1151]) ).
cnf(c_0_1151_1,axiom,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1151]) ).
cnf(c_0_1151_2,axiom,
( ~ empty(cartesian_product2(X1,X2))
| empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1151]) ).
cnf(c_0_1152_0,axiom,
( subset(X1,X2)
| in(sk1_esk44_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1152]) ).
cnf(c_0_1152_1,axiom,
( in(sk1_esk44_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1152]) ).
cnf(c_0_1153_0,axiom,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1153_1,axiom,
( X3 = apply(X1,X2)
| in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1153_2,axiom,
( ~ function(X1)
| X3 = apply(X1,X2)
| in(X2,relation_dom(X1))
| ~ relation(X1)
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1153_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| in(X2,relation_dom(X1))
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1153_4,axiom,
( X3 != empty_set
| ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| in(X2,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1154_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1154]) ).
cnf(c_0_1154_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1154]) ).
cnf(c_0_1155_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1155]) ).
cnf(c_0_1155_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1155]) ).
cnf(c_0_1156_0,axiom,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1156]) ).
cnf(c_0_1156_1,axiom,
( ~ ordinal(X1)
| subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1156]) ).
cnf(c_0_1156_2,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| subset(X2,X1)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1156]) ).
cnf(c_0_1156_3,axiom,
( ~ ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1156]) ).
cnf(c_0_1157_0,axiom,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1157]) ).
cnf(c_0_1157_1,axiom,
( ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1157]) ).
cnf(c_0_1157_2,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1157]) ).
cnf(c_0_1157_3,axiom,
( ~ subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1157]) ).
cnf(c_0_1158_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1158]) ).
cnf(c_0_1158_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1158]) ).
cnf(c_0_1158_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1158]) ).
cnf(c_0_1158_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1158]) ).
cnf(c_0_1161_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1161_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1161_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1162_0,axiom,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_1,axiom,
( ~ relation(X1)
| well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_2,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| well_ordering(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_3,axiom,
( ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1)
| well_ordering(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_4,axiom,
( ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1)
| well_ordering(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_5,axiom,
( ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1)
| well_ordering(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_6,axiom,
( ~ reflexive(X1)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1)
| well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1163_0,axiom,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1163_1,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1164_0,axiom,
( epsilon_connected(X1)
| ~ in(sk1_esk40_1(X1),sk1_esk41_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1164_1,axiom,
( ~ in(sk1_esk40_1(X1),sk1_esk41_1(X1))
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1165_0,axiom,
( epsilon_connected(X1)
| ~ in(sk1_esk41_1(X1),sk1_esk40_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1165_1,axiom,
( ~ in(sk1_esk41_1(X1),sk1_esk40_1(X1))
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1166_0,axiom,
( one_to_one(X1)
| in(sk1_esk67_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_1,axiom,
( in(sk1_esk67_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_2,axiom,
( ~ function(X1)
| in(sk1_esk67_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk67_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1167_0,axiom,
( one_to_one(X1)
| in(sk1_esk68_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1167_1,axiom,
( in(sk1_esk68_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1167_2,axiom,
( ~ function(X1)
| in(sk1_esk68_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1167_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk68_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1168_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1168_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1168_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1169_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1169_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1169_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1170_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1170_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1171_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1171]) ).
cnf(c_0_1171_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1171]) ).
cnf(c_0_1172_0,axiom,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1173_0,axiom,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1173_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1173_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1174_0,axiom,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1174_1,axiom,
( ~ function(X1)
| relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1174_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_rng_restriction(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1175_0,axiom,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1175_1,axiom,
( ~ function(X1)
| function(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1175_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_rng_restriction(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1176_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1176_1,axiom,
( ~ function(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1176_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1177_0,axiom,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1177_1,axiom,
( ~ function(X1)
| function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1177_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1178_0,axiom,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1178_1,axiom,
( ~ relation(X2)
| relation(set_difference(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1178_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_difference(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1179_0,axiom,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1179_1,axiom,
( ~ relation(X2)
| relation(set_union2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1179_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1180_0,axiom,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1180_1,axiom,
( ~ relation(X2)
| relation(set_intersection2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1180_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1181_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1181_1,axiom,
( ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1181_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1182_0,axiom,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1182_1,axiom,
( ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1182_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1183_0,axiom,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1183_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1183_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1184_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1184_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1184_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1185_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1185_1,axiom,
( ~ relation(X2)
| relation(relation_composition(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1185_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1186_0,axiom,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1186_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1186_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1187_0,axiom,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1187_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1187_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1188_0,axiom,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1188_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1188_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1189_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1189_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1189_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1190_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1190_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1190_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1191_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| sk1_esk46_2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1191_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| sk1_esk46_2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1191_2,axiom,
( sk1_esk46_2(X1,X2) != empty_set
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1192_0,axiom,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1192_1,axiom,
( ~ in(X1,X2)
| subset(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1192_2,axiom,
( ~ epsilon_transitive(X2)
| ~ in(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1193_0,axiom,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1193_1,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1193_2,axiom,
( ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1194_0,axiom,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1194_1,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1194_2,axiom,
( ~ is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1195_0,axiom,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1195_1,axiom,
( ~ relation(X1)
| connected(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1195_2,axiom,
( ~ is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1196_0,axiom,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1196_1,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1196_2,axiom,
( ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1197_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1197_1,axiom,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1198_0,axiom,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1198_1,axiom,
( ordinal_subset(X2,X1)
| ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1198_2,axiom,
( ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ordinal_subset(X1,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1198_3,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ordinal_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1199_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1199_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1199_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1200_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1200_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1200_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1201_0,axiom,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1201_1,axiom,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1201_2,axiom,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1202_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1202_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1202_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1203_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1203_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1203_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1204_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1204_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1204_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1205_0,axiom,
( well_founded_relation(X1)
| subset(sk1_esk33_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1205_1,axiom,
( subset(sk1_esk33_1(X1),relation_field(X1))
| well_founded_relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1205_2,axiom,
( ~ relation(X1)
| subset(sk1_esk33_1(X1),relation_field(X1))
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1206_0,axiom,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1206]) ).
cnf(c_0_1206_1,axiom,
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1206]) ).
cnf(c_0_1207_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1207]) ).
cnf(c_0_1207_1,axiom,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1207]) ).
cnf(c_0_1208_0,axiom,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1208_1,axiom,
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1209_0,axiom,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1209]) ).
cnf(c_0_1209_1,axiom,
( ~ relation(X1)
| set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1209]) ).
cnf(c_0_1210_0,axiom,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1210_1,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1211_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1211_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1212_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1212_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1213_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1213_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1214_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1214_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1215_0,axiom,
( epsilon_transitive(X1)
| ~ subset(sk1_esk28_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1215_1,axiom,
( ~ subset(sk1_esk28_1(X1),X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1216_0,axiom,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1216_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1216_2,axiom,
( ~ reflexive(X1)
| ~ relation(X1)
| is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1217_0,axiom,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1217_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,relation_field(X1))
| ~ transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1217_2,axiom,
( ~ transitive(X1)
| ~ relation(X1)
| is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1218_0,axiom,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,relation_field(X1))
| ~ connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_2,axiom,
( ~ connected(X1)
| ~ relation(X1)
| is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1219_0,axiom,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1219_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,relation_field(X1))
| ~ antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1219_2,axiom,
( ~ antisymmetric(X1)
| ~ relation(X1)
| is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1220_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1220_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1220_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1221_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1222_0,axiom,
( relation(X1)
| sk1_esk20_1(X1) != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1222_1,axiom,
( sk1_esk20_1(X1) != ordered_pair(X2,X3)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1223_0,axiom,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_1,axiom,
( ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1224_0,axiom,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_1,axiom,
( ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1225_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk68_1(X1) != sk1_esk67_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ relation(X1)
| sk1_esk68_1(X1) != sk1_esk67_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| one_to_one(X1)
| sk1_esk68_1(X1) != sk1_esk67_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_3,axiom,
( sk1_esk68_1(X1) != sk1_esk67_1(X1)
| ~ relation(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1226_0,axiom,
( empty(X1)
| element(sk1_esk81_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1226_1,axiom,
( element(sk1_esk81_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1227_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1227]) ).
cnf(c_0_1227_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1227]) ).
cnf(c_0_1228_0,axiom,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1228_1,axiom,
( ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1228_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1228_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1229_0,axiom,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1229_1,axiom,
( ~ ordinal(X2)
| ordinal_subset(X1,X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1229_2,axiom,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1230_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1230_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1230_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1231_0,axiom,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1231_1,axiom,
( ~ empty(relation_rng(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1231_2,axiom,
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1232_0,axiom,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1232_1,axiom,
( ~ empty(relation_dom(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1232_2,axiom,
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1238_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1238_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1238_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1239_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1239_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1240_0,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1240_1,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1240_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1240_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1241_0,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1241_1,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1241_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1241_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1242_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1242_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1242_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1242_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1243_0,axiom,
( epsilon_connected(X1)
| in(sk1_esk40_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1243_1,axiom,
( in(sk1_esk40_1(X1),X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1244_0,axiom,
( epsilon_connected(X1)
| in(sk1_esk41_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1244]) ).
cnf(c_0_1244_1,axiom,
( in(sk1_esk41_1(X1),X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1244]) ).
cnf(c_0_1245_0,axiom,
( epsilon_transitive(X1)
| in(sk1_esk28_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1245_1,axiom,
( in(sk1_esk28_1(X1),X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1246_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1246_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1247_0,axiom,
( relation(X1)
| in(sk1_esk20_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1247_1,axiom,
( in(sk1_esk20_1(X1),X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1248_0,axiom,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1248_1,axiom,
( ~ function(X1)
| relation(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1248_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1249_0,axiom,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1249_1,axiom,
( ~ function(X1)
| function(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1249_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1251_0,axiom,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1251]) ).
cnf(c_0_1251_1,axiom,
( ~ empty(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1251]) ).
cnf(c_0_1253_0,axiom,
( X1 = empty_set
| in(sk1_esk26_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1253]) ).
cnf(c_0_1253_1,axiom,
( in(sk1_esk26_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1253]) ).
cnf(c_0_1254_0,axiom,
( empty(X1)
| ~ empty(sk1_esk81_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1254]) ).
cnf(c_0_1254_1,axiom,
( ~ empty(sk1_esk81_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1254]) ).
cnf(c_0_1257_0,axiom,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1257_1,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1257_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1258_0,axiom,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1258_1,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1258_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1259_0,axiom,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1259_1,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1259_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1260_0,axiom,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_1,axiom,
( ~ relation(X1)
| connected(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1261_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1262_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_1,axiom,
( ~ epsilon_connected(X1)
| ordinal(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_2,axiom,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1263_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| sk1_esk33_1(X1) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| sk1_esk33_1(X1) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_2,axiom,
( sk1_esk33_1(X1) != empty_set
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1264_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1264_1,axiom,
( ~ epsilon_connected(X1)
| ordinal(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1264_2,axiom,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1265_0,axiom,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1265_1,axiom,
( ~ relation(X1)
| relation_inverse(relation_inverse(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1266_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1266_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1267_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1267]) ).
cnf(c_0_1267_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1267]) ).
cnf(c_0_1268_0,axiom,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1268_1,axiom,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1269_0,axiom,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1269_1,axiom,
( ~ empty(X1)
| relation(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1270_0,axiom,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1270]) ).
cnf(c_0_1270_1,axiom,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1270]) ).
cnf(c_0_1271_0,axiom,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1271_1,axiom,
( ~ empty(X1)
| relation(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1272_0,axiom,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1272_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1273_0,axiom,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1273_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1274_0,axiom,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1274_1,axiom,
( ~ ordinal(X1)
| ordinal(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1275_0,axiom,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1275]) ).
cnf(c_0_1275_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1275]) ).
cnf(c_0_1276_0,axiom,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1276]) ).
cnf(c_0_1276_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1276]) ).
cnf(c_0_1277_0,axiom,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1277]) ).
cnf(c_0_1277_1,axiom,
( ~ ordinal(X1)
| ordinal(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1277]) ).
cnf(c_0_1278_0,axiom,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1278_1,axiom,
( ~ empty(X1)
| empty(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1279_0,axiom,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1279_1,axiom,
( ~ empty(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1280_0,axiom,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1280_1,axiom,
( ~ relation(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1281_0,axiom,
( epsilon_connected(X1)
| sk1_esk40_1(X1) != sk1_esk41_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1281_1,axiom,
( sk1_esk40_1(X1) != sk1_esk41_1(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1285_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1285_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1285_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1293_0,axiom,
( being_limit_ordinal(X1)
| union(X1) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1293_1,axiom,
( union(X1) != X1
| being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1294_0,axiom,
( union(X1) = X1
| ~ being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1294]) ).
cnf(c_0_1294_1,axiom,
( ~ being_limit_ordinal(X1)
| union(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1294]) ).
cnf(c_0_1295_0,axiom,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1295_1,axiom,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1295_2,axiom,
( X2 != set_meet(X1)
| X1 != empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1296_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1296]) ).
cnf(c_0_1296_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1296]) ).
cnf(c_0_1297_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1297]) ).
cnf(c_0_1297_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1297]) ).
cnf(c_0_1298_0,axiom,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1298_1,axiom,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1299_0,axiom,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1299_1,axiom,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1300_0,axiom,
( ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1300]) ).
cnf(c_0_1300_1,axiom,
( ~ empty(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1300]) ).
cnf(c_0_1301_0,axiom,
( relation(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1301_1,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1302_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1302_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1303_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1303_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1304_0,axiom,
( function(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1304_1,axiom,
( ~ empty(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1309_0,axiom,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1309_1,axiom,
( X1 != empty_set
| X2 = set_meet(X1)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1309_2,axiom,
( X2 != empty_set
| X1 != empty_set
| X2 = set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1310_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1310]) ).
cnf(c_0_1310_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1310]) ).
cnf(c_0_1159_0,axiom,
~ empty(unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_1159]) ).
cnf(c_0_1160_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1252_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_1252]) ).
cnf(c_0_1282_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_1282]) ).
cnf(c_0_1283_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_1283]) ).
cnf(c_0_1284_0,axiom,
~ empty(succ(X1)),
inference(literals_permutation,[status(thm)],[c_0_1284]) ).
cnf(c_0_1312_0,axiom,
~ empty(sk1_esk89_0),
inference(literals_permutation,[status(thm)],[c_0_1312]) ).
cnf(c_0_1313_0,axiom,
~ empty(sk1_esk87_0),
inference(literals_permutation,[status(thm)],[c_0_1313]) ).
cnf(c_0_1314_0,axiom,
~ empty(sk1_esk85_0),
inference(literals_permutation,[status(thm)],[c_0_1314]) ).
cnf(c_0_1146_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1146]) ).
cnf(c_0_1233_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1234_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1235_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_1235]) ).
cnf(c_0_1236_0,axiom,
element(sk1_esk86_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1237_0,axiom,
element(cast_to_subset(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1250_0,axiom,
set_union2(X1,singleton(X1)) = succ(X1),
inference(literals_permutation,[status(thm)],[c_0_1250]) ).
cnf(c_0_1255_0,axiom,
in(X1,sk1_esk94_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_1255]) ).
cnf(c_0_1256_0,axiom,
element(sk1_esk77_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_1256]) ).
cnf(c_0_1286_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_1286]) ).
cnf(c_0_1287_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1288_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_1288]) ).
cnf(c_0_1289_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1290_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1291_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_1291]) ).
cnf(c_0_1292_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_1292]) ).
cnf(c_0_1305_0,axiom,
empty(sk1_esk86_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1306_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1307_0,axiom,
function(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1308_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1311_0,axiom,
cast_to_subset(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_1311]) ).
cnf(c_0_1315_0,axiom,
relation(sk1_esk91_0),
inference(literals_permutation,[status(thm)],[c_0_1315]) ).
cnf(c_0_1316_0,axiom,
relation_empty_yielding(sk1_esk91_0),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1317_0,axiom,
function(sk1_esk91_0),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1318_0,axiom,
relation(sk1_esk90_0),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1319_0,axiom,
relation_empty_yielding(sk1_esk90_0),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1320_0,axiom,
epsilon_transitive(sk1_esk89_0),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1321_0,axiom,
epsilon_connected(sk1_esk89_0),
inference(literals_permutation,[status(thm)],[c_0_1321]) ).
cnf(c_0_1322_0,axiom,
ordinal(sk1_esk89_0),
inference(literals_permutation,[status(thm)],[c_0_1322]) ).
cnf(c_0_1323_0,axiom,
relation(sk1_esk88_0),
inference(literals_permutation,[status(thm)],[c_0_1323]) ).
cnf(c_0_1324_0,axiom,
function(sk1_esk88_0),
inference(literals_permutation,[status(thm)],[c_0_1324]) ).
cnf(c_0_1325_0,axiom,
one_to_one(sk1_esk88_0),
inference(literals_permutation,[status(thm)],[c_0_1325]) ).
cnf(c_0_1326_0,axiom,
relation(sk1_esk85_0),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1327_0,axiom,
relation(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1327]) ).
cnf(c_0_1328_0,axiom,
function(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1328]) ).
cnf(c_0_1329_0,axiom,
one_to_one(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1329]) ).
cnf(c_0_1330_0,axiom,
empty(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1330]) ).
cnf(c_0_1331_0,axiom,
epsilon_transitive(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1331]) ).
cnf(c_0_1332_0,axiom,
epsilon_connected(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1332]) ).
cnf(c_0_1333_0,axiom,
ordinal(sk1_esk84_0),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1334_0,axiom,
relation(sk1_esk83_0),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1335_0,axiom,
empty(sk1_esk83_0),
inference(literals_permutation,[status(thm)],[c_0_1335]) ).
cnf(c_0_1336_0,axiom,
function(sk1_esk83_0),
inference(literals_permutation,[status(thm)],[c_0_1336]) ).
cnf(c_0_1337_0,axiom,
empty(sk1_esk82_0),
inference(literals_permutation,[status(thm)],[c_0_1337]) ).
cnf(c_0_1338_0,axiom,
empty(sk1_esk80_0),
inference(literals_permutation,[status(thm)],[c_0_1338]) ).
cnf(c_0_1339_0,axiom,
relation(sk1_esk80_0),
inference(literals_permutation,[status(thm)],[c_0_1339]) ).
cnf(c_0_1340_0,axiom,
epsilon_transitive(sk1_esk79_0),
inference(literals_permutation,[status(thm)],[c_0_1340]) ).
cnf(c_0_1341_0,axiom,
epsilon_connected(sk1_esk79_0),
inference(literals_permutation,[status(thm)],[c_0_1341]) ).
cnf(c_0_1342_0,axiom,
ordinal(sk1_esk79_0),
inference(literals_permutation,[status(thm)],[c_0_1342]) ).
cnf(c_0_1343_0,axiom,
relation(sk1_esk78_0),
inference(literals_permutation,[status(thm)],[c_0_1343]) ).
cnf(c_0_1344_0,axiom,
function(sk1_esk78_0),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1345_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1346_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1346]) ).
cnf(c_0_1347_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1347]) ).
cnf(c_0_1348_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1348]) ).
cnf(c_0_1349_0,axiom,
function(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1349]) ).
cnf(c_0_1350_0,axiom,
one_to_one(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1350]) ).
cnf(c_0_1351_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1351]) ).
cnf(c_0_1352_0,axiom,
epsilon_transitive(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1352]) ).
cnf(c_0_1353_0,axiom,
epsilon_connected(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1354_0,axiom,
ordinal(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1354]) ).
cnf(c_0_1355_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1355]) ).
cnf(c_0_1356_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1356]) ).
cnf(c_0_1357_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1357]) ).
cnf(c_0_1358_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_1358]) ).
cnf(c_0_1359_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1359]) ).
cnf(c_0_1360_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1360]) ).
cnf(c_0_1361_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1361]) ).
cnf(c_0_1362_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1362]) ).
cnf(c_0_1363_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1363]) ).
cnf(c_0_1364_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1364]) ).
cnf(c_0_1365_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1365]) ).
cnf(c_0_1366_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1366]) ).
cnf(c_0_1367_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1368_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1369_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1370_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1370]) ).
cnf(c_0_1371_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1371]) ).
cnf(c_0_1372_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1372]) ).
cnf(c_0_1373_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1373]) ).
cnf(c_0_1374_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1374]) ).
cnf(c_0_1375_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1375]) ).
cnf(c_0_1376_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1376]) ).
cnf(c_0_1377_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1377]) ).
cnf(c_0_1378_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1378]) ).
cnf(c_0_1379_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_1379]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('<stdin>',t68_funct_1) ).
fof(c_0_1_002,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('<stdin>',t54_funct_1) ).
fof(c_0_2_003,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
file('<stdin>',t166_relat_1) ).
fof(c_0_3_004,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
file('<stdin>',t143_relat_1) ).
fof(c_0_4_005,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('<stdin>',t22_funct_1) ).
fof(c_0_5_006,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('<stdin>',t21_funct_1) ).
fof(c_0_6_007,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('<stdin>',t70_funct_1) ).
fof(c_0_7_008,lemma,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X4),X1) )
=> in(ordered_pair(X2,X4),X1) ) ) ),
file('<stdin>',l2_wellord1) ).
fof(c_0_8_009,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('<stdin>',t48_setfam_1) ).
fof(c_0_9_010,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
file('<stdin>',t47_setfam_1) ).
fof(c_0_10_011,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
file('<stdin>',t74_relat_1) ).
fof(c_0_11_012,lemma,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,relation_field(X1))
& in(X3,relation_field(X1))
& X2 != X3
& ~ in(ordered_pair(X2,X3),X1)
& ~ in(ordered_pair(X3,X2),X1) ) ) ),
file('<stdin>',l4_wellord1) ).
fof(c_0_12_013,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
file('<stdin>',l82_funct_1) ).
fof(c_0_13_014,lemma,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
file('<stdin>',l3_wellord1) ).
fof(c_0_14_015,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('<stdin>',t43_subset_1) ).
fof(c_0_15_016,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('<stdin>',t86_relat_1) ).
fof(c_0_16_017,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
file('<stdin>',t115_relat_1) ).
fof(c_0_17_018,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('<stdin>',t23_funct_1) ).
fof(c_0_18_019,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('<stdin>',t16_wellord1) ).
fof(c_0_19_020,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
file('<stdin>',t146_funct_1) ).
fof(c_0_20_021,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('<stdin>',t106_zfmisc_1) ).
fof(c_0_21_022,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('<stdin>',l55_zfmisc_1) ).
fof(c_0_22_023,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('<stdin>',t54_subset_1) ).
fof(c_0_23_024,lemma,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
file('<stdin>',l1_wellord1) ).
fof(c_0_24_025,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('<stdin>',t34_funct_1) ).
fof(c_0_25_026,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('<stdin>',t119_zfmisc_1) ).
fof(c_0_26_027,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('<stdin>',t50_subset_1) ).
fof(c_0_27_028,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('<stdin>',t8_funct_1) ).
fof(c_0_28_029,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('<stdin>',t57_funct_1) ).
fof(c_0_29_030,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
file('<stdin>',t145_funct_1) ).
fof(c_0_30_031,lemma,
! [X1,X2] :
( ordinal(X2)
=> ~ ( subset(X1,X2)
& X1 != empty_set
& ! [X3] :
( ordinal(X3)
=> ~ ( in(X3,X1)
& ! [X4] :
( ordinal(X4)
=> ( in(X4,X1)
=> ordinal_subset(X3,X4) ) ) ) ) ) ),
file('<stdin>',t32_ordinal1) ).
fof(c_0_31_032,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
file('<stdin>',l29_wellord1) ).
fof(c_0_32_033,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
file('<stdin>',t178_relat_1) ).
fof(c_0_33_034,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
file('<stdin>',t45_relat_1) ).
fof(c_0_34_035,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('<stdin>',t44_relat_1) ).
fof(c_0_35_036,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('<stdin>',t72_funct_1) ).
fof(c_0_36_037,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('<stdin>',t30_relat_1) ).
fof(c_0_37_038,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('<stdin>',t20_relat_1) ).
fof(c_0_38_039,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('<stdin>',t47_relat_1) ).
fof(c_0_39_040,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('<stdin>',t46_relat_1) ).
fof(c_0_40_041,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('<stdin>',l3_zfmisc_1) ).
fof(c_0_41_042,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_42_043,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_43_044,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('<stdin>',t118_zfmisc_1) ).
fof(c_0_44_045,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
file('<stdin>',t147_funct_1) ).
fof(c_0_45_046,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
file('<stdin>',t140_relat_1) ).
fof(c_0_46_047,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('<stdin>',t4_xboole_0) ).
fof(c_0_47_048,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_48_049,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_49_050,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_50_051,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('<stdin>',t99_relat_1) ).
fof(c_0_51_052,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('<stdin>',t118_relat_1) ).
fof(c_0_52_053,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('<stdin>',l71_subset_1) ).
fof(c_0_53_054,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('<stdin>',t116_relat_1) ).
fof(c_0_54_055,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('<stdin>',t46_setfam_1) ).
fof(c_0_55_056,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('<stdin>',t136_zfmisc_1) ).
fof(c_0_56_057,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('<stdin>',t56_relat_1) ).
fof(c_0_57_058,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
file('<stdin>',t145_relat_1) ).
fof(c_0_58_059,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('<stdin>',t21_relat_1) ).
fof(c_0_59_060,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_60_061,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('<stdin>',t3_xboole_0) ).
fof(c_0_61_062,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
file('<stdin>',t3_ordinal1) ).
fof(c_0_62_063,lemma,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
file('<stdin>',t41_ordinal1) ).
fof(c_0_63_064,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
file('<stdin>',t160_relat_1) ).
fof(c_0_64_065,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_65_066,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
file('<stdin>',t25_relat_1) ).
fof(c_0_66_067,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
file('<stdin>',t174_relat_1) ).
fof(c_0_67_068,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_rng_restriction(X1,relation_dom_restriction(X2,X1)) ),
file('<stdin>',t18_wellord1) ).
fof(c_0_68_069,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_dom_restriction(relation_rng_restriction(X1,X2),X1) ),
file('<stdin>',t17_wellord1) ).
fof(c_0_69_070,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('<stdin>',t33_ordinal1) ).
fof(c_0_70_071,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_71_072,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_72_073,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
file('<stdin>',t90_relat_1) ).
fof(c_0_73_074,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
file('<stdin>',t119_relat_1) ).
fof(c_0_74_075,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_75_076,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_76_077,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_77_078,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_78_079,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_79_080,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('<stdin>',t31_ordinal1) ).
fof(c_0_80_081,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('<stdin>',t167_relat_1) ).
fof(c_0_81_082,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('<stdin>',t144_relat_1) ).
fof(c_0_82_083,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('<stdin>',t21_ordinal1) ).
fof(c_0_83_084,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('<stdin>',t10_zfmisc_1) ).
fof(c_0_84_085,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('<stdin>',t88_relat_1) ).
fof(c_0_85_086,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('<stdin>',t117_relat_1) ).
fof(c_0_86_087,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_87_088,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_88_089,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('<stdin>',t33_zfmisc_1) ).
fof(c_0_89_090,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('<stdin>',t24_ordinal1) ).
fof(c_0_90_091,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_91_092,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_92_093,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('<stdin>',t8_wellord1) ).
fof(c_0_93_094,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('<stdin>',t5_wellord1) ).
fof(c_0_94_095,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_95_096,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('<stdin>',t35_funct_1) ).
fof(c_0_96_097,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_97_098,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_98_099,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_99_100,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('<stdin>',t94_relat_1) ).
fof(c_0_100_101,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_101_102,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_102_103,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_103_104,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_104_105,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_105_106,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_106_107,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_107_108,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_108_109,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_109_110,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_110_111,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('<stdin>',t55_funct_1) ).
fof(c_0_111_112,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_112_113,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('<stdin>',t23_ordinal1) ).
fof(c_0_113_114,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('<stdin>',t62_funct_1) ).
fof(c_0_114_115,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('<stdin>',t146_relat_1) ).
fof(c_0_115_116,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_116_117,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_117_118,lemma,
! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
file('<stdin>',t42_ordinal1) ).
fof(c_0_118_119,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_119_120,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('<stdin>',t37_relat_1) ).
fof(c_0_120_121,lemma,
! [X1] : in(X1,succ(X1)),
file('<stdin>',t10_ordinal1) ).
fof(c_0_121_122,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('<stdin>',t65_relat_1) ).
fof(c_0_122_123,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_123_124,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('<stdin>',t64_relat_1) ).
fof(c_0_124_125,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_125_126,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_126_127,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('<stdin>',t71_relat_1) ).
fof(c_0_127_128,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_128_129,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_129_130,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('<stdin>',t60_relat_1) ).
fof(c_0_130_131,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
c_0_0 ).
fof(c_0_131_132,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
c_0_1 ).
fof(c_0_132_133,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
c_0_2 ).
fof(c_0_133_134,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
c_0_3 ).
fof(c_0_134_135,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
c_0_4 ).
fof(c_0_135_136,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
c_0_5 ).
fof(c_0_136_137,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
c_0_6 ).
fof(c_0_137_138,lemma,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X4),X1) )
=> in(ordered_pair(X2,X4),X1) ) ) ),
c_0_7 ).
fof(c_0_138_139,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
c_0_8 ).
fof(c_0_139_140,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
c_0_9 ).
fof(c_0_140_141,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
c_0_10 ).
fof(c_0_141_142,lemma,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,relation_field(X1))
& in(X3,relation_field(X1))
& X2 != X3
& ~ in(ordered_pair(X2,X3),X1)
& ~ in(ordered_pair(X3,X2),X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_142_143,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
c_0_12 ).
fof(c_0_143_144,lemma,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
c_0_13 ).
fof(c_0_144_145,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
c_0_14 ).
fof(c_0_145_146,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
c_0_15 ).
fof(c_0_146_147,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
c_0_16 ).
fof(c_0_147_148,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
c_0_17 ).
fof(c_0_148_149,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
c_0_18 ).
fof(c_0_149_150,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
c_0_19 ).
fof(c_0_150_151,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_20 ).
fof(c_0_151_152,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_21 ).
fof(c_0_152_153,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
c_0_22 ).
fof(c_0_153_154,lemma,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
c_0_23 ).
fof(c_0_154_155,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
c_0_24 ).
fof(c_0_155_156,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_25 ).
fof(c_0_156_157,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_157_158,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
c_0_27 ).
fof(c_0_158_159,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
c_0_28 ).
fof(c_0_159_160,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
c_0_29 ).
fof(c_0_160_161,lemma,
! [X1,X2] :
( ordinal(X2)
=> ~ ( subset(X1,X2)
& X1 != empty_set
& ! [X3] :
( ordinal(X3)
=> ~ ( in(X3,X1)
& ! [X4] :
( ordinal(X4)
=> ( in(X4,X1)
=> ordinal_subset(X3,X4) ) ) ) ) ) ),
c_0_30 ).
fof(c_0_161_162,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
inference(assume_negation,[status(cth)],[c_0_31]) ).
fof(c_0_162_163,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
c_0_32 ).
fof(c_0_163_164,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
c_0_33 ).
fof(c_0_164_165,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
c_0_34 ).
fof(c_0_165_166,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
c_0_35 ).
fof(c_0_166_167,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
c_0_36 ).
fof(c_0_167_168,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
c_0_37 ).
fof(c_0_168_169,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
c_0_38 ).
fof(c_0_169_170,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
c_0_39 ).
fof(c_0_170_171,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_40 ).
fof(c_0_171_172,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_41 ).
fof(c_0_172_173,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_42 ).
fof(c_0_173_174,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
c_0_43 ).
fof(c_0_174_175,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
c_0_44 ).
fof(c_0_175_176,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
c_0_45 ).
fof(c_0_176_177,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_177_178,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_47 ).
fof(c_0_178_179,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_48 ).
fof(c_0_179_180,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_49 ).
fof(c_0_180_181,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
c_0_50 ).
fof(c_0_181_182,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
c_0_51 ).
fof(c_0_182_183,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
c_0_52 ).
fof(c_0_183_184,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
c_0_53 ).
fof(c_0_184_185,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
c_0_54 ).
fof(c_0_185_186,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_186_187,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_187_188,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
c_0_57 ).
fof(c_0_188_189,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
c_0_58 ).
fof(c_0_189_190,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_59 ).
fof(c_0_190_191,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_191_192,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
c_0_61 ).
fof(c_0_192_193,lemma,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
c_0_62 ).
fof(c_0_193_194,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
c_0_63 ).
fof(c_0_194_195,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_64 ).
fof(c_0_195_196,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
c_0_65 ).
fof(c_0_196_197,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
c_0_66 ).
fof(c_0_197_198,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_rng_restriction(X1,relation_dom_restriction(X2,X1)) ),
c_0_67 ).
fof(c_0_198_199,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_dom_restriction(relation_rng_restriction(X1,X2),X1) ),
c_0_68 ).
fof(c_0_199_200,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
c_0_69 ).
fof(c_0_200_201,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_70 ).
fof(c_0_201_202,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_71 ).
fof(c_0_202_203,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
c_0_72 ).
fof(c_0_203_204,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
c_0_73 ).
fof(c_0_204_205,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_205_206,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_75 ).
fof(c_0_206_207,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_76 ).
fof(c_0_207_208,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_77 ).
fof(c_0_208_209,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_78 ).
fof(c_0_209_210,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
c_0_79 ).
fof(c_0_210_211,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
c_0_80 ).
fof(c_0_211_212,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
c_0_81 ).
fof(c_0_212_213,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
c_0_82 ).
fof(c_0_213_214,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_83 ).
fof(c_0_214_215,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
c_0_84 ).
fof(c_0_215_216,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
c_0_85 ).
fof(c_0_216_217,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_86 ).
fof(c_0_217_218,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_87 ).
fof(c_0_218_219,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_88 ).
fof(c_0_219_220,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_220_221,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_90 ).
fof(c_0_221_222,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_91 ).
fof(c_0_222_223,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
c_0_92 ).
fof(c_0_223_224,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
c_0_93 ).
fof(c_0_224_225,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_94 ).
fof(c_0_225_226,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
c_0_95 ).
fof(c_0_226_227,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_96 ).
fof(c_0_227_228,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_97 ).
fof(c_0_228_229,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_98 ).
fof(c_0_229_230,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
c_0_99 ).
fof(c_0_230_231,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_100 ).
fof(c_0_231_232,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_101 ).
fof(c_0_232_233,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_102 ).
fof(c_0_233_234,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_103 ).
fof(c_0_234_235,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_104 ).
fof(c_0_235_236,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_105 ).
fof(c_0_236_237,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_106 ).
fof(c_0_237_238,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_107 ).
fof(c_0_238_239,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_108 ).
fof(c_0_239_240,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_109 ).
fof(c_0_240_241,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
c_0_110 ).
fof(c_0_241_242,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_242_243,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
c_0_112 ).
fof(c_0_243_244,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
c_0_113 ).
fof(c_0_244_245,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
c_0_114 ).
fof(c_0_245_246,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_115 ).
fof(c_0_246_247,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_116 ).
fof(c_0_247_248,lemma,
! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_248_249,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_118 ).
fof(c_0_249_250,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
c_0_119 ).
fof(c_0_250_251,lemma,
! [X1] : in(X1,succ(X1)),
c_0_120 ).
fof(c_0_251_252,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
c_0_121 ).
fof(c_0_252_253,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_122 ).
fof(c_0_253_254,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
c_0_123 ).
fof(c_0_254_255,lemma,
! [X1] : subset(empty_set,X1),
c_0_124 ).
fof(c_0_255_256,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_125 ).
fof(c_0_256_257,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
c_0_126 ).
fof(c_0_257_258,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_127 ).
fof(c_0_258_259,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_128 ).
fof(c_0_259_260,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_129 ).
fof(c_0_260_261,lemma,
! [X5,X6,X7,X8] :
( ( relation_dom(X6) = set_intersection2(relation_dom(X7),X5)
| X6 != relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X8,relation_dom(X6))
| apply(X6,X8) = apply(X7,X8)
| X6 != relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk28_3(X5,X6,X7),relation_dom(X6))
| relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
| X6 = relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( apply(X6,esk28_3(X5,X6,X7)) != apply(X7,esk28_3(X5,X6,X7))
| relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
| X6 = relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])])])]) ).
fof(c_0_261_262,lemma,
! [X5,X6,X7,X8,X9,X10] :
( ( relation_dom(X6) = relation_rng(X5)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X8,relation_dom(X5))
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,X8)
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X9,relation_rng(X5))
| ~ in(X10,relation_dom(X5))
| X9 != apply(X5,X10)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X10 = apply(X6,X9)
| ~ in(X10,relation_dom(X5))
| X9 != apply(X5,X10)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk25_2(X5,X6),relation_dom(X5))
| in(esk22_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk24_2(X5,X6) = apply(X5,esk25_2(X5,X6))
| in(esk22_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk24_2(X5,X6),relation_rng(X5))
| esk25_2(X5,X6) != apply(X6,esk24_2(X5,X6))
| in(esk22_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk25_2(X5,X6),relation_dom(X5))
| esk23_2(X5,X6) = apply(X6,esk22_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk24_2(X5,X6) = apply(X5,esk25_2(X5,X6))
| esk23_2(X5,X6) = apply(X6,esk22_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk24_2(X5,X6),relation_rng(X5))
| esk25_2(X5,X6) != apply(X6,esk24_2(X5,X6))
| esk23_2(X5,X6) = apply(X6,esk22_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk25_2(X5,X6),relation_dom(X5))
| ~ in(esk23_2(X5,X6),relation_dom(X5))
| esk22_2(X5,X6) != apply(X5,esk23_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk24_2(X5,X6) = apply(X5,esk25_2(X5,X6))
| ~ in(esk23_2(X5,X6),relation_dom(X5))
| esk22_2(X5,X6) != apply(X5,esk23_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk24_2(X5,X6),relation_rng(X5))
| esk25_2(X5,X6) != apply(X6,esk24_2(X5,X6))
| ~ in(esk23_2(X5,X6),relation_dom(X5))
| esk22_2(X5,X6) != apply(X5,esk23_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])])])])]) ).
fof(c_0_262_263,lemma,
! [X5,X6,X7,X9] :
( ( in(esk14_3(X5,X6,X7),relation_rng(X7))
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(X5,esk14_3(X5,X6,X7)),X7)
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(esk14_3(X5,X6,X7),X6)
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( ~ in(X9,relation_rng(X7))
| ~ in(ordered_pair(X5,X9),X7)
| ~ in(X9,X6)
| in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])])])]) ).
fof(c_0_263_264,lemma,
! [X5,X6,X7,X9] :
( ( in(esk13_3(X5,X6,X7),relation_dom(X7))
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(esk13_3(X5,X6,X7),X5),X7)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(esk13_3(X5,X6,X7),X6)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( ~ in(X9,relation_dom(X7))
| ~ in(ordered_pair(X9,X5),X7)
| ~ in(X9,X6)
| in(X5,relation_image(X7,X6))
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])])])]) ).
fof(c_0_264_265,lemma,
! [X4,X5,X6] :
( ~ relation(X5)
| ~ function(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| apply(relation_composition(X6,X5),X4) = apply(X5,apply(X6,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])]) ).
fof(c_0_265_266,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X6,X4),relation_dom(X5))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])])]) ).
fof(c_0_266_267,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X5,relation_dom(relation_dom_restriction(X6,X4)))
| apply(relation_dom_restriction(X6,X4),X5) = apply(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_136])]) ).
fof(c_0_267_268,lemma,
! [X5,X6,X7,X8] :
( ( ~ transitive(X5)
| ~ in(ordered_pair(X6,X7),X5)
| ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X6,X8),X5)
| ~ relation(X5) )
& ( in(ordered_pair(esk4_1(X5),esk5_1(X5)),X5)
| transitive(X5)
| ~ relation(X5) )
& ( in(ordered_pair(esk5_1(X5),esk6_1(X5)),X5)
| transitive(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk4_1(X5),esk6_1(X5)),X5)
| transitive(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])])])]) ).
fof(c_0_268_269,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| union_of_subsets(X3,complements_of_subsets(X3,X4)) = subset_difference(X3,cast_to_subset(X3),meet_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])]) ).
fof(c_0_269_270,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| subset_difference(X3,cast_to_subset(X3),union_of_subsets(X3,X4)) = meet_of_subsets(X3,complements_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])]) ).
fof(c_0_270_271,lemma,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) )
& ( in(ordered_pair(X5,X6),X8)
| ~ in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) )
& ( ~ in(X5,X7)
| ~ in(ordered_pair(X5,X6),X8)
| in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])])]) ).
fof(c_0_271_272,lemma,
! [X4,X5,X6] :
( ( ~ connected(X4)
| ~ in(X5,relation_field(X4))
| ~ in(X6,relation_field(X4))
| X5 = X6
| in(ordered_pair(X5,X6),X4)
| in(ordered_pair(X6,X5),X4)
| ~ relation(X4) )
& ( in(esk9_1(X4),relation_field(X4))
| connected(X4)
| ~ relation(X4) )
& ( in(esk10_1(X4),relation_field(X4))
| connected(X4)
| ~ relation(X4) )
& ( esk9_1(X4) != esk10_1(X4)
| connected(X4)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk9_1(X4),esk10_1(X4)),X4)
| connected(X4)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk10_1(X4),esk9_1(X4)),X4)
| connected(X4)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_141])])])])])]) ).
fof(c_0_272_273,lemma,
! [X4,X5,X6] :
( ( in(X5,relation_dom(X6))
| ~ in(X5,relation_dom(relation_dom_restriction(X6,X4)))
| ~ relation(X6)
| ~ function(X6) )
& ( in(X5,X4)
| ~ in(X5,relation_dom(relation_dom_restriction(X6,X4)))
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X5,relation_dom(X6))
| ~ in(X5,X4)
| in(X5,relation_dom(relation_dom_restriction(X6,X4)))
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])])]) ).
fof(c_0_273_274,lemma,
! [X4,X5,X6] :
( ( ~ antisymmetric(X4)
| ~ in(ordered_pair(X5,X6),X4)
| ~ in(ordered_pair(X6,X5),X4)
| X5 = X6
| ~ relation(X4) )
& ( in(ordered_pair(esk7_1(X4),esk8_1(X4)),X4)
| antisymmetric(X4)
| ~ relation(X4) )
& ( in(ordered_pair(esk8_1(X4),esk7_1(X4)),X4)
| antisymmetric(X4)
| ~ relation(X4) )
& ( esk7_1(X4) != esk8_1(X4)
| antisymmetric(X4)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])])])]) ).
fof(c_0_274_275,lemma,
! [X4,X5,X6] :
( ( ~ disjoint(X5,X6)
| subset(X5,subset_complement(X4,X6))
| ~ element(X6,powerset(X4))
| ~ element(X5,powerset(X4)) )
& ( ~ subset(X5,subset_complement(X4,X6))
| disjoint(X5,X6)
| ~ element(X6,powerset(X4))
| ~ element(X5,powerset(X4)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])])]) ).
fof(c_0_275_276,lemma,
! [X4,X5,X6] :
( ( in(X4,X5)
| ~ in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) )
& ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) )
& ( ~ in(X4,X5)
| ~ in(X4,relation_dom(X6))
| in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])])]) ).
fof(c_0_276_277,lemma,
! [X4,X5,X6] :
( ( in(X4,X5)
| ~ in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) )
& ( in(X4,relation_rng(X6))
| ~ in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) )
& ( ~ in(X4,X5)
| ~ in(X4,relation_rng(X6))
| in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])])]) ).
fof(c_0_277_278,lemma,
! [X4,X5,X6] :
( ~ relation(X5)
| ~ function(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])])]) ).
fof(c_0_278_279,lemma,
! [X4,X5,X6] :
( ( in(X4,X6)
| ~ in(X4,relation_restriction(X6,X5))
| ~ relation(X6) )
& ( in(X4,cartesian_product2(X5,X5))
| ~ in(X4,relation_restriction(X6,X5))
| ~ relation(X6) )
& ( ~ in(X4,X6)
| ~ in(X4,cartesian_product2(X5,X5))
| in(X4,relation_restriction(X6,X5))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_148])])]) ).
fof(c_0_279_280,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ subset(X3,relation_dom(X4))
| subset(X3,relation_inverse_image(X4,relation_image(X4,X3))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])]) ).
fof(c_0_280_281,lemma,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X9,X11)
| ~ in(X10,X12)
| in(ordered_pair(X9,X10),cartesian_product2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])])])]) ).
fof(c_0_281_282,lemma,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X9,X11)
| ~ in(X10,X12)
| in(ordered_pair(X9,X10),cartesian_product2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])])])])]) ).
fof(c_0_282_283,lemma,
! [X4,X5,X6] :
( ~ element(X6,powerset(X4))
| ~ in(X5,subset_complement(X4,X6))
| ~ in(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])]) ).
fof(c_0_283_284,lemma,
! [X3,X4] :
( ( ~ reflexive(X3)
| ~ in(X4,relation_field(X3))
| in(ordered_pair(X4,X4),X3)
| ~ relation(X3) )
& ( in(esk1_1(X3),relation_field(X3))
| reflexive(X3)
| ~ relation(X3) )
& ( ~ in(ordered_pair(esk1_1(X3),esk1_1(X3)),X3)
| reflexive(X3)
| ~ relation(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])])])]) ).
fof(c_0_284_285,lemma,
! [X4,X5,X6] :
( ( relation_dom(X5) = X4
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X6,X4)
| apply(X5,X6) = X6
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk17_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk17_2(X4,X5)) != esk17_2(X4,X5)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])])])])]) ).
fof(c_0_285_286,lemma,
! [X5,X6,X7,X8] :
( ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])]) ).
fof(c_0_286_287,lemma,
! [X4,X5,X6] :
( X4 = empty_set
| ~ element(X5,powerset(X4))
| ~ element(X6,X4)
| in(X6,X5)
| in(X6,subset_complement(X4,X5)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])]) ).
fof(c_0_287_288,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6)
| ~ function(X6) )
& ( X5 = apply(X6,X4)
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X4,relation_dom(X6))
| X5 != apply(X6,X4)
| in(ordered_pair(X4,X5),X6)
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_157])])]) ).
fof(c_0_288_289,lemma,
! [X3,X4] :
( ( X3 = apply(X4,apply(function_inverse(X4),X3))
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X3 = apply(relation_composition(function_inverse(X4),X4),X3)
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])])]) ).
fof(c_0_289_290,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| subset(relation_image(X4,relation_inverse_image(X4,X3)),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])]) ).
fof(c_0_290_291,lemma,
! [X5,X6,X8] :
( ( ordinal(esk16_2(X5,X6))
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) )
& ( in(esk16_2(X5,X6),X5)
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) )
& ( ~ ordinal(X8)
| ~ in(X8,X5)
| ordinal_subset(esk16_2(X5,X6),X8)
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_160])])])])]) ).
fof(c_0_291_292,negated_conjecture,
( relation(esk3_0)
& ~ subset(relation_dom(relation_rng_restriction(esk2_0,esk3_0)),relation_dom(esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])])]) ).
fof(c_0_292_293,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ subset(X4,X5)
| subset(relation_inverse_image(X6,X4),relation_inverse_image(X6,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])]) ).
fof(c_0_293_294,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| subset(relation_rng(relation_composition(X3,X4)),relation_rng(X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])]) ).
fof(c_0_294_295,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| subset(relation_dom(relation_composition(X3,X4)),relation_dom(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_164])])]) ).
fof(c_0_295_296,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X5,X4)
| apply(relation_dom_restriction(X6,X4),X5) = apply(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])]) ).
fof(c_0_296_297,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_field(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_field(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_166])])]) ).
fof(c_0_297_298,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_167])])]) ).
fof(c_0_298_299,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_168])])]) ).
fof(c_0_299_300,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_169])])]) ).
fof(c_0_300_301,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| in(X6,X4)
| subset(X4,set_difference(X5,singleton(X6))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])])])]) ).
fof(c_0_301_302,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_difference(X4,X6),set_difference(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_171])])])]) ).
fof(c_0_302_303,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_intersection2(X4,X6),set_intersection2(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])])])]) ).
fof(c_0_303_304,lemma,
! [X4,X5,X6,X7] :
( ( subset(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
| ~ subset(X4,X5) )
& ( subset(cartesian_product2(X7,X4),cartesian_product2(X7,X5))
| ~ subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_173])])])])]) ).
fof(c_0_304_305,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| ~ subset(X3,relation_rng(X4))
| relation_image(X4,relation_inverse_image(X4,X3)) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])]) ).
fof(c_0_305_306,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| relation_dom_restriction(relation_rng_restriction(X4,X6),X5) = relation_rng_restriction(X4,relation_dom_restriction(X6,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])]) ).
fof(c_0_306_307,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk21_2(X4,X5),set_intersection2(X4,X5)) )
& ( ~ in(X9,set_intersection2(X7,X8))
| ~ disjoint(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_176])])])])]) ).
fof(c_0_307_308,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])]) ).
fof(c_0_308_309,lemma,
! [X4,X5,X6,X7,X8,X9] :
( ( in(X4,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( in(X5,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( ~ in(X7,X9)
| ~ in(X8,X9)
| subset(unordered_pair(X7,X8),X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])])])])]) ).
fof(c_0_309_310,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,set_intersection2(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_179])]) ).
fof(c_0_310_311,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_dom_restriction(X4,X3)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_180])]) ).
fof(c_0_311_312,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])]) ).
fof(c_0_312_313,lemma,
! [X4,X5] :
( ( in(esk11_2(X4,X5),X4)
| element(X4,powerset(X5)) )
& ( ~ in(esk11_2(X4,X5),X5)
| element(X4,powerset(X5)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_182])])])]) ).
fof(c_0_313_314,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])]) ).
fof(c_0_314_315,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| complements_of_subsets(X3,X4) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])]) ).
fof(c_0_315_316,lemma,
! [X5,X7,X8,X9,X10] :
( in(X5,esk12_1(X5))
& ( ~ in(X7,esk12_1(X5))
| ~ subset(X8,X7)
| in(X8,esk12_1(X5)) )
& ( ~ in(X9,esk12_1(X5))
| in(powerset(X9),esk12_1(X5)) )
& ( ~ subset(X10,esk12_1(X5))
| are_equipotent(X10,esk12_1(X5))
| in(X10,esk12_1(X5)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_185])])])]) ).
fof(c_0_316_317,lemma,
! [X4] :
( ~ relation(X4)
| in(ordered_pair(esk26_1(X4),esk27_1(X4)),X4)
| X4 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])])]) ).
fof(c_0_317_318,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_image(X4,X3) = relation_image(X4,set_intersection2(relation_dom(X4),X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])]) ).
fof(c_0_318_319,lemma,
! [X2] :
( ~ relation(X2)
| subset(X2,cartesian_product2(relation_dom(X2),relation_rng(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])]) ).
fof(c_0_319_320,lemma,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ in(X6,X5)
| in(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])])]) ).
fof(c_0_320_321,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk18_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk18_2(X4,X5),X5)
| disjoint(X4,X5) )
& ( ~ in(X9,X7)
| ~ in(X9,X8)
| ~ disjoint(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])])])])]) ).
fof(c_0_321_322,lemma,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ in(X5,X6)
| ~ in(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_191])])])]) ).
fof(c_0_322_323,lemma,
! [X3,X4] :
( ( ~ being_limit_ordinal(X3)
| ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3)
| ~ ordinal(X3) )
& ( ordinal(esk19_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( in(esk19_1(X3),X3)
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( ~ in(succ(esk19_1(X3)),X3)
| being_limit_ordinal(X3)
| ~ ordinal(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])])])])]) ).
fof(c_0_323_324,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation_rng(relation_composition(X3,X4)) = relation_image(X4,relation_rng(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_193])])]) ).
fof(c_0_324_325,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| X4 = set_union2(X3,set_difference(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_194])]) ).
fof(c_0_325_326,lemma,
! [X3,X4] :
( ( subset(relation_dom(X3),relation_dom(X4))
| ~ subset(X3,X4)
| ~ relation(X4)
| ~ relation(X3) )
& ( subset(relation_rng(X3),relation_rng(X4))
| ~ subset(X3,X4)
| ~ relation(X4)
| ~ relation(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_195])])])]) ).
fof(c_0_326_327,lemma,
! [X3,X4] :
( ~ relation(X4)
| X3 = empty_set
| ~ subset(X3,relation_rng(X4))
| relation_inverse_image(X4,X3) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_196])]) ).
fof(c_0_327_328,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_restriction(X4,X3) = relation_rng_restriction(X3,relation_dom_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])]) ).
fof(c_0_328_329,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_restriction(X4,X3) = relation_dom_restriction(relation_rng_restriction(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])]) ).
fof(c_0_329_330,lemma,
! [X3,X4] :
( ( ~ in(X3,X4)
| ordinal_subset(succ(X3),X4)
| ~ ordinal(X4)
| ~ ordinal(X3) )
& ( ~ ordinal_subset(succ(X3),X4)
| in(X3,X4)
| ~ ordinal(X4)
| ~ ordinal(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_199])])])]) ).
fof(c_0_330_331,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ disjoint(X5,X6)
| disjoint(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])]) ).
fof(c_0_331_332,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])]) ).
fof(c_0_332_333,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_dom(relation_dom_restriction(X4,X3)) = set_intersection2(relation_dom(X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])]) ).
fof(c_0_333_334,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_rng(relation_rng_restriction(X3,X4)) = set_intersection2(relation_rng(X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])]) ).
fof(c_0_334_335,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,singleton(X4)) != X3
| ~ in(X4,X3) )
& ( in(X6,X5)
| set_difference(X5,singleton(X6)) = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])])])]) ).
fof(c_0_335_336,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_205])]) ).
fof(c_0_336_337,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_337_338,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_338_339,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_339_340,lemma,
! [X3] :
( ( in(esk15_1(X3),X3)
| ordinal(X3) )
& ( ~ ordinal(esk15_1(X3))
| ~ subset(esk15_1(X3),X3)
| ordinal(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_209])])])]) ).
fof(c_0_340_341,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_inverse_image(X4,X3),relation_dom(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])]) ).
fof(c_0_341_342,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_image(X4,X3),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])]) ).
fof(c_0_342_343,lemma,
! [X3,X4] :
( ~ epsilon_transitive(X3)
| ~ ordinal(X4)
| ~ proper_subset(X3,X4)
| in(X3,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_212])])]) ).
fof(c_0_343_344,lemma,
! [X5,X6,X7,X8] :
( unordered_pair(X5,X6) != unordered_pair(X7,X8)
| X5 = X7
| X5 = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_213])]) ).
fof(c_0_344_345,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_dom_restriction(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])]) ).
fof(c_0_345_346,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng_restriction(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_215])]) ).
fof(c_0_346_347,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X5,X6)
| subset(singleton(X5),X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_216])])])]) ).
fof(c_0_347_348,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X5,X6)
| subset(singleton(X5),X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_217])])])]) ).
fof(c_0_348_349,lemma,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ordered_pair(X5,X6) != ordered_pair(X7,X8) )
& ( X6 = X8
| ordered_pair(X5,X6) != ordered_pair(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_218])])]) ).
fof(c_0_349_350,lemma,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| in(X3,X4)
| X3 = X4
| in(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_219])])]) ).
fof(c_0_350_351,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_220])]) ).
fof(c_0_351_352,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_221])]) ).
fof(c_0_352_353,lemma,
! [X2] :
( ( ~ well_orders(X2,relation_field(X2))
| well_ordering(X2)
| ~ relation(X2) )
& ( ~ well_ordering(X2)
| well_orders(X2,relation_field(X2))
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_222])])]) ).
fof(c_0_353_354,lemma,
! [X2] :
( ( ~ well_founded_relation(X2)
| is_well_founded_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_well_founded_in(X2,relation_field(X2))
| well_founded_relation(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_223])])]) ).
fof(c_0_354_355,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_224])]) ).
fof(c_0_355_356,lemma,
! [X3,X4] :
( ~ in(X4,X3)
| apply(identity_relation(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_225])]) ).
fof(c_0_356_357,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_226])]) ).
fof(c_0_357_358,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_227])]) ).
fof(c_0_358_359,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_228])]) ).
fof(c_0_359_360,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_dom_restriction(X4,X3) = relation_composition(identity_relation(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_229])]) ).
fof(c_0_360_361,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_361_362,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_362_363,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_363_364,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X5 != empty_set
| subset(X5,singleton(X6)) )
& ( X5 != singleton(X6)
| subset(X5,singleton(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_233])])])])]) ).
fof(c_0_364_365,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X5 != empty_set
| subset(X5,singleton(X6)) )
& ( X5 != singleton(X6)
| subset(X5,singleton(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_234])])])])]) ).
fof(c_0_365_366,lemma,
! [X3,X4,X5,X6] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X5,X6) != X5
| disjoint(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_235])])])]) ).
fof(c_0_366_367,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_236])]) ).
fof(c_0_367_368,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_237])]) ).
fof(c_0_368_369,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_238])])])]) ).
fof(c_0_369_370,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_239])])])]) ).
fof(c_0_370_371,lemma,
! [X2] :
( ( relation_rng(X2) = relation_dom(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) )
& ( relation_dom(X2) = relation_rng(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_240])])]) ).
fof(c_0_371_372,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_241])]) ).
fof(c_0_372_373,lemma,
! [X3,X4] :
( ~ ordinal(X4)
| ~ in(X3,X4)
| ordinal(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_242])]) ).
fof(c_0_373_374,lemma,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| one_to_one(function_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_243])]) ).
fof(c_0_374_375,lemma,
! [X2] :
( ~ relation(X2)
| relation_image(X2,relation_dom(X2)) = relation_rng(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_244])]) ).
fof(c_0_375_376,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_245])]) ).
fof(c_0_376_377,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X4 = X5 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_246])])])]) ).
fof(c_0_377_378,lemma,
! [X3,X5] :
( ( ordinal(esk20_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( X3 = succ(esk20_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( ~ ordinal(X5)
| X3 != succ(X5)
| ~ being_limit_ordinal(X3)
| ~ ordinal(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_247])])])])]) ).
fof(c_0_378_379,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_248])]) ).
fof(c_0_379_380,lemma,
! [X2] :
( ( relation_rng(X2) = relation_dom(relation_inverse(X2))
| ~ relation(X2) )
& ( relation_dom(X2) = relation_rng(relation_inverse(X2))
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_249])])]) ).
fof(c_0_380_381,lemma,
! [X2] : in(X2,succ(X2)),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_381_382,lemma,
! [X2] :
( ( relation_dom(X2) != empty_set
| relation_rng(X2) = empty_set
| ~ relation(X2) )
& ( relation_rng(X2) != empty_set
| relation_dom(X2) = empty_set
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_251])])]) ).
fof(c_0_382_383,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_383_384,lemma,
! [X2] :
( ( relation_dom(X2) != empty_set
| X2 = empty_set
| ~ relation(X2) )
& ( relation_rng(X2) != empty_set
| X2 = empty_set
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_253])])]) ).
fof(c_0_384_385,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_385_386,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_386_387,lemma,
! [X2,X3] :
( relation_dom(identity_relation(X2)) = X2
& relation_rng(identity_relation(X3)) = X3 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_256])])]) ).
fof(c_0_387_388,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_388_389,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_258 ).
fof(c_0_389_390,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_259 ).
cnf(c_0_390_391,lemma,
( X1 = relation_dom_restriction(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3)
| apply(X1,esk28_3(X3,X1,X2)) != apply(X2,esk28_3(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_391_392,lemma,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk22_2(X1,X2) != apply(X1,esk23_2(X1,X2))
| ~ in(esk23_2(X1,X2),relation_dom(X1))
| esk25_2(X1,X2) != apply(X2,esk24_2(X1,X2))
| ~ in(esk24_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_392_393,lemma,
( in(ordered_pair(X2,esk14_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_393_394,lemma,
( in(ordered_pair(esk13_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_394_395,lemma,
( X2 = function_inverse(X1)
| esk23_2(X1,X2) = apply(X2,esk22_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk25_2(X1,X2) != apply(X2,esk24_2(X1,X2))
| ~ in(esk24_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_395_396,lemma,
( X2 = function_inverse(X1)
| esk24_2(X1,X2) = apply(X1,esk25_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk22_2(X1,X2) != apply(X1,esk23_2(X1,X2))
| ~ in(esk23_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_396_397,lemma,
( X2 = function_inverse(X1)
| in(esk22_2(X1,X2),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk25_2(X1,X2) != apply(X2,esk24_2(X1,X2))
| ~ in(esk24_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_397_398,lemma,
( X2 = function_inverse(X1)
| in(esk25_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk22_2(X1,X2) != apply(X1,esk23_2(X1,X2))
| ~ in(esk23_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_398_399,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_399_400,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk28_3(X3,X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_400_401,lemma,
( in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_401_402,lemma,
( in(esk14_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_402_403,lemma,
( in(esk13_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_403_404,lemma,
( in(esk14_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_404_405,lemma,
( in(esk13_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_405_406,lemma,
( in(apply(X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_406_407,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_407_408,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_408_409,lemma,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_409_410,lemma,
( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_410_411,lemma,
( in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_411_412,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_412_413,lemma,
( in(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_413_414,lemma,
( in(X2,relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,X2),X1)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_414_415,lemma,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_415_416,lemma,
( X2 = function_inverse(X1)
| esk23_2(X1,X2) = apply(X2,esk22_2(X1,X2))
| esk24_2(X1,X2) = apply(X1,esk25_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_416_417,lemma,
( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X1)
| X3 = X2
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ in(X3,relation_field(X1))
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_417_418,lemma,
( X2 = function_inverse(X1)
| in(esk22_2(X1,X2),relation_rng(X1))
| esk24_2(X1,X2) = apply(X1,esk25_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_418_419,lemma,
( X2 = function_inverse(X1)
| esk23_2(X1,X2) = apply(X2,esk22_2(X1,X2))
| in(esk25_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_419_420,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_420_421,lemma,
( X2 = function_inverse(X1)
| in(esk22_2(X1,X2),relation_rng(X1))
| in(esk25_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_421_422,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_422_423,lemma,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_423_424,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_424_425,lemma,
( in(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_425_426,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_426_427,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_427_428,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_428_429,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_429_430,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_430_431,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_431_432,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_432_433,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_433_434,lemma,
( in(X2,relation_restriction(X1,X3))
| ~ relation(X1)
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_434_435,lemma,
( subset(X1,relation_inverse_image(X2,relation_image(X2,X1)))
| ~ subset(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_435_436,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_436_437,lemma,
( in(X3,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_437_438,lemma,
( in(X3,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_438_439,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_439_440,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_440_441,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_441_442,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_442_443,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_443_444,lemma,
( X4 = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_444_445,lemma,
( X4 = apply(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_445_446,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk9_1(X1),esk10_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_446_447,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk10_1(X1),esk9_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_447_448,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk4_1(X1),esk6_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_448_449,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk1_1(X1),esk1_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_449_450,lemma,
( apply(X1,X4) = apply(X2,X4)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_450_451,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk17_2(X2,X1)) != esk17_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_451_452,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_452_453,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_453_454,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_454_455,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_455_456,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_456_457,lemma,
( in(X2,cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_457_458,lemma,
( X2 = apply(X1,apply(function_inverse(X1),X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_458_459,lemma,
( X2 = apply(relation_composition(function_inverse(X1),X1),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_459_460,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_460_461,lemma,
( X2 = empty_set
| ordinal_subset(esk16_2(X2,X1),X3)
| ~ ordinal(X1)
| ~ subset(X2,X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_461_462,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(esk2_0,esk3_0)),relation_dom(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_462_463,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_463_464,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_464_465,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_465_466,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_466_467,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_467_468,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_468_469,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_469_470,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_470_471,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_471_472,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_472_473,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_473_474,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_474_475,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_475_476,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_476_477,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_477_478,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_478_479,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_479_480,lemma,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ subset(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_480_481,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_481_482,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_482_483,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_483_484,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_484_485,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_485_486,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_486_487,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_487_488,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_488_489,lemma,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_489_490,lemma,
( element(X1,powerset(X2))
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_490_491,lemma,
( in(esk21_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_491_492,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_492_493,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_493_494,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_494_495,lemma,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_495_496,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk7_1(X1),esk8_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_496_497,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk8_1(X1),esk7_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_497_498,lemma,
( transitive(X1)
| in(ordered_pair(esk4_1(X1),esk5_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_498_499,lemma,
( transitive(X1)
| in(ordered_pair(esk5_1(X1),esk6_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_499_500,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_500_501,lemma,
( in(X1,esk12_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk12_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_501_502,lemma,
( X1 = empty_set
| in(ordered_pair(esk26_1(X1),esk27_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_502_503,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_503_504,lemma,
( in(X1,esk12_1(X2))
| are_equipotent(X1,esk12_1(X2))
| ~ subset(X1,esk12_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_504_505,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_505_506,lemma,
( X2 = empty_set
| in(esk16_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_506_507,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_507_508,lemma,
( X1 = identity_relation(X2)
| in(esk17_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_508_509,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_509_510,lemma,
( ~ in(X1,X2)
| ~ in(X3,X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_510_511,lemma,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_511_512,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_512_513,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_513_514,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_514_515,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_515_516,lemma,
( X2 = empty_set
| relation_inverse_image(X1,X2) != empty_set
| ~ subset(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_516_517,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk19_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_517_518,lemma,
( X2 = empty_set
| ordinal(esk16_2(X2,X1))
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_518_519,lemma,
( relation_restriction(X1,X2) = relation_rng_restriction(X2,relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_519_520,lemma,
( relation_restriction(X1,X2) = relation_dom_restriction(relation_rng_restriction(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_520_521,lemma,
( in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(succ(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_521_522,lemma,
( element(X1,powerset(X2))
| in(esk11_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_522_523,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_523_524,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_524_525,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_525_526,lemma,
( in(powerset(X1),esk12_1(X2))
| ~ in(X1,esk12_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_526_527,lemma,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_527_528,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_528_529,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_529_530,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_530_531,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_531_532,lemma,
( disjoint(X1,X2)
| in(esk18_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_532_533,lemma,
( disjoint(X1,X2)
| in(esk18_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_533_534,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_534_535,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_535_536,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_536_537,lemma,
( ordinal(X1)
| ~ subset(esk15_1(X1),X1)
| ~ ordinal(esk15_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_537_538,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_538_539,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_539_540,lemma,
( relation_dom(X2) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_540_541,lemma,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_541_542,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_542_543,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_543_544,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_544_545,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_545_546,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_546_547,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_547_548,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_548_549,lemma,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_549_550,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_550_551,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_551_552,lemma,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_orders(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_552_553,lemma,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_553_554,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_554_555,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_555_556,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_556_557,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_557_558,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_558_559,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_559_560,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_560_561,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_561_562,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_562_563,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_563_564,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_564_565,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_565_566,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_566_567,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_567_568,lemma,
( connected(X1)
| in(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_568_569,lemma,
( connected(X1)
| in(esk10_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_569_570,lemma,
( reflexive(X1)
| in(esk1_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_570_571,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_571_572,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_572_573,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_573_574,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_574_575,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_575_576,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_576_577,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_577_578,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_578_579,lemma,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_579_580,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_580_581,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_581_582,lemma,
( well_orders(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_582_583,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_583_584,lemma,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_584_585,lemma,
( being_limit_ordinal(X1)
| in(esk19_1(X1),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_585_586,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_586_587,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_587_588,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_588_589,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_589_590,lemma,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| X1 != succ(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_590_591,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_591_592,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_592_593,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_593_594,lemma,
( ordinal(X1)
| in(esk15_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_594_595,lemma,
( connected(X1)
| ~ relation(X1)
| esk9_1(X1) != esk10_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_595_596,lemma,
( antisymmetric(X1)
| ~ relation(X1)
| esk7_1(X1) != esk8_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_596_597,lemma,
( being_limit_ordinal(X1)
| X1 = succ(esk20_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_597_598,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_598_599,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_599_600,lemma,
( being_limit_ordinal(X1)
| ordinal(esk20_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_600_601,lemma,
( being_limit_ordinal(X1)
| ordinal(esk19_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_601_602,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_602_603,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_603_604,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_604_605,lemma,
in(X1,esk12_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_605_606,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_606_607,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_607_608,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_608_609,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_609_610,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_610_611,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_611_612,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_612_613,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_613_614,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_614_615,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_615_616,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_616_617,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_617_618,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_618_619,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_619_620,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_620_621,lemma,
( X1 = relation_dom_restriction(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3)
| apply(X1,esk28_3(X3,X1,X2)) != apply(X2,esk28_3(X3,X1,X2)) ),
c_0_390,
[final] ).
cnf(c_0_621_622,lemma,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk23_2(X1,X2)) != esk22_2(X1,X2)
| ~ in(esk23_2(X1,X2),relation_dom(X1))
| apply(X2,esk24_2(X1,X2)) != esk25_2(X1,X2)
| ~ in(esk24_2(X1,X2),relation_rng(X1)) ),
c_0_391,
[final] ).
cnf(c_0_622_623,lemma,
( in(ordered_pair(X2,esk14_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_392,
[final] ).
cnf(c_0_623_624,lemma,
( in(ordered_pair(esk13_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_393,
[final] ).
cnf(c_0_624_625,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk22_2(X1,X2)) = esk23_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X2,esk24_2(X1,X2)) != esk25_2(X1,X2)
| ~ in(esk24_2(X1,X2),relation_rng(X1)) ),
c_0_394,
[final] ).
cnf(c_0_625_626,lemma,
( X2 = function_inverse(X1)
| apply(X1,esk25_2(X1,X2)) = esk24_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk23_2(X1,X2)) != esk22_2(X1,X2)
| ~ in(esk23_2(X1,X2),relation_dom(X1)) ),
c_0_395,
[final] ).
cnf(c_0_626_627,lemma,
( X2 = function_inverse(X1)
| in(esk22_2(X1,X2),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X2,esk24_2(X1,X2)) != esk25_2(X1,X2)
| ~ in(esk24_2(X1,X2),relation_rng(X1)) ),
c_0_396,
[final] ).
cnf(c_0_627_628,lemma,
( X2 = function_inverse(X1)
| in(esk25_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk23_2(X1,X2)) != esk22_2(X1,X2)
| ~ in(esk23_2(X1,X2),relation_dom(X1)) ),
c_0_397,
[final] ).
cnf(c_0_628_629,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_398,
[final] ).
cnf(c_0_629_630,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk28_3(X3,X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3) ),
c_0_399,
[final] ).
cnf(c_0_630_631,lemma,
( in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X2)) ),
c_0_400,
[final] ).
cnf(c_0_631_632,lemma,
( in(esk14_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_401,
[final] ).
cnf(c_0_632_633,lemma,
( in(esk13_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_402,
[final] ).
cnf(c_0_633_634,lemma,
( in(esk14_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_403,
[final] ).
cnf(c_0_634_635,lemma,
( in(esk13_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_404,
[final] ).
cnf(c_0_635_636,lemma,
( in(apply(X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
c_0_405,
[final] ).
cnf(c_0_636_637,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1) ),
c_0_406,
[final] ).
cnf(c_0_637_638,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| ~ transitive(X1) ),
c_0_407,
[final] ).
cnf(c_0_638_639,lemma,
( subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) = union_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_408,
[final] ).
cnf(c_0_639_640,lemma,
( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_409,
[final] ).
cnf(c_0_640_641,lemma,
( in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4) ),
c_0_410,
[final] ).
cnf(c_0_641_642,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_411,
[final] ).
cnf(c_0_642_643,lemma,
( in(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,relation_rng(X1)) ),
c_0_412,
[final] ).
cnf(c_0_643_644,lemma,
( in(X2,relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,X2),X1)
| ~ in(X4,relation_dom(X1)) ),
c_0_413,
[final] ).
cnf(c_0_644_645,lemma,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
c_0_414,
[final] ).
cnf(c_0_645_646,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk22_2(X1,X2)) = esk23_2(X1,X2)
| apply(X1,esk25_2(X1,X2)) = esk24_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_415,
[final] ).
cnf(c_0_646_647,lemma,
( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X1)
| X3 = X2
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ in(X3,relation_field(X1))
| ~ connected(X1) ),
c_0_416,
[final] ).
cnf(c_0_647_648,lemma,
( X2 = function_inverse(X1)
| in(esk22_2(X1,X2),relation_rng(X1))
| apply(X1,esk25_2(X1,X2)) = esk24_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_417,
[final] ).
cnf(c_0_648_649,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk22_2(X1,X2)) = esk23_2(X1,X2)
| in(esk25_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_418,
[final] ).
cnf(c_0_649_650,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_419,
[final] ).
cnf(c_0_650_651,lemma,
( X2 = function_inverse(X1)
| in(esk22_2(X1,X2),relation_rng(X1))
| in(esk25_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_420,
[final] ).
cnf(c_0_651_652,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_421,
[final] ).
cnf(c_0_652_653,lemma,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ antisymmetric(X1) ),
c_0_422,
[final] ).
cnf(c_0_653_654,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
c_0_423,
[final] ).
cnf(c_0_654_655,lemma,
( in(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_424,
[final] ).
cnf(c_0_655_656,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X2,relation_dom(X1)) ),
c_0_425,
[final] ).
cnf(c_0_656_657,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_426,
[final] ).
cnf(c_0_657_658,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_427,
[final] ).
cnf(c_0_658_659,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_428,
[final] ).
cnf(c_0_659_660,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_429,
[final] ).
cnf(c_0_660_661,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_430,
[final] ).
cnf(c_0_661_662,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
c_0_431,
[final] ).
cnf(c_0_662_663,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
c_0_432,
[final] ).
cnf(c_0_663_664,lemma,
( in(X2,relation_restriction(X1,X3))
| ~ relation(X1)
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
c_0_433,
[final] ).
cnf(c_0_664_665,lemma,
( subset(X1,relation_inverse_image(X2,relation_image(X2,X1)))
| ~ subset(X1,relation_dom(X2))
| ~ relation(X2) ),
c_0_434,
[final] ).
cnf(c_0_665_666,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
c_0_435,
[final] ).
cnf(c_0_666_667,lemma,
( in(X3,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
c_0_436,
[final] ).
cnf(c_0_667_668,lemma,
( in(X3,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_437,
[final] ).
cnf(c_0_668_669,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_438,
[final] ).
cnf(c_0_669_670,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_439,
[final] ).
cnf(c_0_670_671,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_440,
[final] ).
cnf(c_0_671_672,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_441,
[final] ).
cnf(c_0_672_673,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
c_0_442,
[final] ).
cnf(c_0_673_674,lemma,
( X4 = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
c_0_443,
[final] ).
cnf(c_0_674_675,lemma,
( X4 = apply(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_444,
[final] ).
cnf(c_0_675_676,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk9_1(X1),esk10_1(X1)),X1) ),
c_0_445,
[final] ).
cnf(c_0_676_677,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk10_1(X1),esk9_1(X1)),X1) ),
c_0_446,
[final] ).
cnf(c_0_677_678,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk4_1(X1),esk6_1(X1)),X1) ),
c_0_447,
[final] ).
cnf(c_0_678_679,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk1_1(X1),esk1_1(X1)),X1) ),
c_0_448,
[final] ).
cnf(c_0_679_680,lemma,
( apply(X1,X4) = apply(X2,X4)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3)
| ~ in(X4,relation_dom(X1)) ),
c_0_449,
[final] ).
cnf(c_0_680_681,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk17_2(X2,X1)) != esk17_2(X2,X1) ),
c_0_450,
[final] ).
cnf(c_0_681_682,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_451,
[final] ).
cnf(c_0_682_683,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_452,
[final] ).
cnf(c_0_683_684,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_453,
[final] ).
cnf(c_0_684_685,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
c_0_454,
[final] ).
cnf(c_0_685_686,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1)) ),
c_0_455,
[final] ).
cnf(c_0_686_687,lemma,
( in(X2,cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_456,
[final] ).
cnf(c_0_687_688,lemma,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
c_0_457,
[final] ).
cnf(c_0_688_689,lemma,
( apply(relation_composition(function_inverse(X1),X1),X2) = X2
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
c_0_458,
[final] ).
cnf(c_0_689_690,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_459,
[final] ).
cnf(c_0_690_691,lemma,
( X2 = empty_set
| ordinal_subset(esk16_2(X2,X1),X3)
| ~ ordinal(X1)
| ~ subset(X2,X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
c_0_460,
[final] ).
cnf(c_0_691_692,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(esk2_0,esk3_0)),relation_dom(esk3_0)),
c_0_461,
[final] ).
cnf(c_0_692_693,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_462,
[final] ).
cnf(c_0_693_694,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
c_0_463,
[final] ).
cnf(c_0_694_695,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_464,
[final] ).
cnf(c_0_695_696,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_465,
[final] ).
cnf(c_0_696_697,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_466,
[final] ).
cnf(c_0_697_698,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_467,
[final] ).
cnf(c_0_698_699,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_468,
[final] ).
cnf(c_0_699_700,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_469,
[final] ).
cnf(c_0_700_701,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_470,
[final] ).
cnf(c_0_701_702,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_471,
[final] ).
cnf(c_0_702_703,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
c_0_472,
[final] ).
cnf(c_0_703_704,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_473,
[final] ).
cnf(c_0_704_705,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_474,
[final] ).
cnf(c_0_705_706,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_475,
[final] ).
cnf(c_0_706_707,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_476,
[final] ).
cnf(c_0_707_708,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_477,
[final] ).
cnf(c_0_708_709,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_478,
[final] ).
cnf(c_0_709_710,lemma,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ subset(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_479,
[final] ).
cnf(c_0_710_711,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
c_0_480,
[final] ).
cnf(c_0_711_712,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
c_0_481,
[final] ).
cnf(c_0_712_713,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_482,
[final] ).
cnf(c_0_713_714,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_483,
[final] ).
cnf(c_0_714_715,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_484,
[final] ).
cnf(c_0_715_716,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_485,
[final] ).
cnf(c_0_716_717,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
c_0_486,
[final] ).
cnf(c_0_717_718,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
c_0_487,
[final] ).
cnf(c_0_718_719,lemma,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_488,
[final] ).
cnf(c_0_719_720,lemma,
( element(X1,powerset(X2))
| ~ in(esk11_2(X1,X2),X2) ),
c_0_489,
[final] ).
cnf(c_0_720_721,lemma,
( in(esk21_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_490,
[final] ).
cnf(c_0_721_722,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
c_0_491,
[final] ).
cnf(c_0_722_723,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_492,
[final] ).
cnf(c_0_723_724,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_493,
[final] ).
cnf(c_0_724_725,lemma,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3) ),
c_0_494,
[final] ).
cnf(c_0_725_726,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk7_1(X1),esk8_1(X1)),X1)
| ~ relation(X1) ),
c_0_495,
[final] ).
cnf(c_0_726_727,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk8_1(X1),esk7_1(X1)),X1)
| ~ relation(X1) ),
c_0_496,
[final] ).
cnf(c_0_727_728,lemma,
( transitive(X1)
| in(ordered_pair(esk4_1(X1),esk5_1(X1)),X1)
| ~ relation(X1) ),
c_0_497,
[final] ).
cnf(c_0_728_729,lemma,
( transitive(X1)
| in(ordered_pair(esk5_1(X1),esk6_1(X1)),X1)
| ~ relation(X1) ),
c_0_498,
[final] ).
cnf(c_0_729_730,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_499,
[final] ).
cnf(c_0_730_731,lemma,
( in(X1,esk12_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk12_1(X2)) ),
c_0_500,
[final] ).
cnf(c_0_731_732,lemma,
( X1 = empty_set
| in(ordered_pair(esk26_1(X1),esk27_1(X1)),X1)
| ~ relation(X1) ),
c_0_501,
[final] ).
cnf(c_0_732_733,lemma,
( relation_image(X1,set_intersection2(relation_dom(X1),X2)) = relation_image(X1,X2)
| ~ relation(X1) ),
c_0_502,
[final] ).
cnf(c_0_733_734,lemma,
( in(X1,esk12_1(X2))
| are_equipotent(X1,esk12_1(X2))
| ~ subset(X1,esk12_1(X2)) ),
c_0_503,
[final] ).
cnf(c_0_734_735,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
c_0_504,
[final] ).
cnf(c_0_735_736,lemma,
( X2 = empty_set
| in(esk16_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
c_0_505,
[final] ).
cnf(c_0_736_737,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
c_0_506,
[final] ).
cnf(c_0_737_738,lemma,
( X1 = identity_relation(X2)
| in(esk17_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
c_0_507,
[final] ).
cnf(c_0_738_739,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_508,
[final] ).
cnf(c_0_739_740,lemma,
( ~ in(X1,X2)
| ~ in(X3,X1)
| ~ in(X2,X3) ),
c_0_509,
[final] ).
cnf(c_0_740_741,lemma,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X1) ),
c_0_510,
[final] ).
cnf(c_0_741_742,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_511,
[final] ).
cnf(c_0_742_743,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_512,
[final] ).
cnf(c_0_743_744,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_513,
[final] ).
cnf(c_0_744_745,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_514,
[final] ).
cnf(c_0_745_746,lemma,
( X2 = empty_set
| relation_inverse_image(X1,X2) != empty_set
| ~ subset(X2,relation_rng(X1))
| ~ relation(X1) ),
c_0_515,
[final] ).
cnf(c_0_746_747,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk19_1(X1)),X1) ),
c_0_516,
[final] ).
cnf(c_0_747_748,lemma,
( X2 = empty_set
| ordinal(esk16_2(X2,X1))
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
c_0_517,
[final] ).
cnf(c_0_748_749,lemma,
( relation_rng_restriction(X2,relation_dom_restriction(X1,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_518,
[final] ).
cnf(c_0_749_750,lemma,
( relation_dom_restriction(relation_rng_restriction(X2,X1),X2) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_519,
[final] ).
cnf(c_0_750_751,lemma,
( in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(succ(X1),X2) ),
c_0_520,
[final] ).
cnf(c_0_751_752,lemma,
( element(X1,powerset(X2))
| in(esk11_2(X1,X2),X1) ),
c_0_521,
[final] ).
cnf(c_0_752_753,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
c_0_522,
[final] ).
cnf(c_0_753_754,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_523,
[final] ).
cnf(c_0_754_755,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_524,
[final] ).
cnf(c_0_755_756,lemma,
( in(powerset(X1),esk12_1(X2))
| ~ in(X1,esk12_1(X2)) ),
c_0_525,
[final] ).
cnf(c_0_756_757,lemma,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
c_0_526,
[final] ).
cnf(c_0_757_758,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
c_0_527,
[final] ).
cnf(c_0_758_759,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
c_0_528,
[final] ).
cnf(c_0_759_760,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_529,
[final] ).
cnf(c_0_760_761,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_530,
[final] ).
cnf(c_0_761_762,lemma,
( disjoint(X1,X2)
| in(esk18_2(X1,X2),X1) ),
c_0_531,
[final] ).
cnf(c_0_762_763,lemma,
( disjoint(X1,X2)
| in(esk18_2(X1,X2),X2) ),
c_0_532,
[final] ).
cnf(c_0_763_764,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_533,
[final] ).
cnf(c_0_764_765,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_534,
[final] ).
cnf(c_0_765_766,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_535,
[final] ).
cnf(c_0_766_767,lemma,
( ordinal(X1)
| ~ subset(esk15_1(X1),X1)
| ~ ordinal(esk15_1(X1)) ),
c_0_536,
[final] ).
cnf(c_0_767_768,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
c_0_537,
[final] ).
cnf(c_0_768_769,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
c_0_538,
[final] ).
cnf(c_0_769_770,lemma,
( relation_dom(X2) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1) ),
c_0_539,
[final] ).
cnf(c_0_770_771,lemma,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
c_0_540,
[final] ).
cnf(c_0_771_772,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_541,
[final] ).
cnf(c_0_772_773,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
c_0_542,
[final] ).
cnf(c_0_773_774,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
c_0_543,
[final] ).
cnf(c_0_774_775,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_544,
[final] ).
cnf(c_0_775_776,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_545,
[final] ).
cnf(c_0_776_777,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_546,
[final] ).
cnf(c_0_777_778,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_547,
[final] ).
cnf(c_0_778_779,lemma,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
c_0_548,
[final] ).
cnf(c_0_779_780,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_549,
[final] ).
cnf(c_0_780_781,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_550,
[final] ).
cnf(c_0_781_782,lemma,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_orders(X1,relation_field(X1)) ),
c_0_551,
[final] ).
cnf(c_0_782_783,lemma,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
c_0_552,
[final] ).
cnf(c_0_783_784,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_553,
[final] ).
cnf(c_0_784_785,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
c_0_554,
[final] ).
cnf(c_0_785_786,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_555,
[final] ).
cnf(c_0_786_787,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_556,
[final] ).
cnf(c_0_787_788,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_557,
[final] ).
cnf(c_0_788_789,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_558,
[final] ).
cnf(c_0_789_790,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_559,
[final] ).
cnf(c_0_790_791,lemma,
( relation_composition(identity_relation(X2),X1) = relation_dom_restriction(X1,X2)
| ~ relation(X1) ),
c_0_560,
[final] ).
cnf(c_0_791_792,lemma,
subset(X1,set_union2(X1,X2)),
c_0_561,
[final] ).
cnf(c_0_792_793,lemma,
subset(set_difference(X1,X2),X1),
c_0_562,
[final] ).
cnf(c_0_793_794,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_563,
[final] ).
cnf(c_0_794_795,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_564,
[final] ).
cnf(c_0_795_796,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_565,
[final] ).
cnf(c_0_796_797,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_566,
[final] ).
cnf(c_0_797_798,lemma,
( connected(X1)
| in(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_567,
[final] ).
cnf(c_0_798_799,lemma,
( connected(X1)
| in(esk10_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_568,
[final] ).
cnf(c_0_799_800,lemma,
( reflexive(X1)
| in(esk1_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_569,
[final] ).
cnf(c_0_800_801,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_570,
[final] ).
cnf(c_0_801_802,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_571,
[final] ).
cnf(c_0_802_803,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_572,
[final] ).
cnf(c_0_803_804,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_573,
[final] ).
cnf(c_0_804_805,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_574,
[final] ).
cnf(c_0_805_806,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_575,
[final] ).
cnf(c_0_806_807,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_576,
[final] ).
cnf(c_0_807_808,lemma,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_577,
[final] ).
cnf(c_0_808_809,lemma,
( relation_rng(function_inverse(X1)) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_578,
[final] ).
cnf(c_0_809_810,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_579,
[final] ).
cnf(c_0_810_811,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_580,
[final] ).
cnf(c_0_811_812,lemma,
( well_orders(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_581,
[final] ).
cnf(c_0_812_813,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
c_0_582,
[final] ).
cnf(c_0_813_814,lemma,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
c_0_583,
[final] ).
cnf(c_0_814_815,lemma,
( being_limit_ordinal(X1)
| in(esk19_1(X1),X1)
| ~ ordinal(X1) ),
c_0_584,
[final] ).
cnf(c_0_815_816,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_585,
[final] ).
cnf(c_0_816_817,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_586,
[final] ).
cnf(c_0_817_818,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_587,
[final] ).
cnf(c_0_818_819,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_588,
[final] ).
cnf(c_0_819_820,lemma,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| X1 != succ(X2)
| ~ ordinal(X2) ),
c_0_589,
[final] ).
cnf(c_0_820_821,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_590,
[final] ).
cnf(c_0_821_822,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_591,
[final] ).
cnf(c_0_822_823,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
c_0_592,
[final] ).
cnf(c_0_823_824,lemma,
( ordinal(X1)
| in(esk15_1(X1),X1) ),
c_0_593,
[final] ).
cnf(c_0_824_825,lemma,
( connected(X1)
| ~ relation(X1)
| esk9_1(X1) != esk10_1(X1) ),
c_0_594,
[final] ).
cnf(c_0_825_826,lemma,
( antisymmetric(X1)
| ~ relation(X1)
| esk8_1(X1) != esk7_1(X1) ),
c_0_595,
[final] ).
cnf(c_0_826_827,lemma,
( being_limit_ordinal(X1)
| succ(esk20_1(X1)) = X1
| ~ ordinal(X1) ),
c_0_596,
[final] ).
cnf(c_0_827_828,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_597,
[final] ).
cnf(c_0_828_829,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_598,
[final] ).
cnf(c_0_829_830,lemma,
( being_limit_ordinal(X1)
| ordinal(esk20_1(X1))
| ~ ordinal(X1) ),
c_0_599,
[final] ).
cnf(c_0_830_831,lemma,
( being_limit_ordinal(X1)
| ordinal(esk19_1(X1))
| ~ ordinal(X1) ),
c_0_600,
[final] ).
cnf(c_0_831_832,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_601,
[final] ).
cnf(c_0_832_833,lemma,
( relation_dom(relation_inverse(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_602,
[final] ).
cnf(c_0_833_834,lemma,
( relation_rng(relation_inverse(X1)) = relation_dom(X1)
| ~ relation(X1) ),
c_0_603,
[final] ).
cnf(c_0_834_835,lemma,
in(X1,esk12_1(X1)),
c_0_604,
[final] ).
cnf(c_0_835_836,lemma,
in(X1,succ(X1)),
c_0_605,
[final] ).
cnf(c_0_836_837,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_606,
[final] ).
cnf(c_0_837_838,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_607,
[final] ).
cnf(c_0_838_839,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_608,
[final] ).
cnf(c_0_839_840,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_609,
[final] ).
cnf(c_0_840_841,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_610,
[final] ).
cnf(c_0_841_842,lemma,
subset(empty_set,X1),
c_0_611,
[final] ).
cnf(c_0_842_843,lemma,
union(powerset(X1)) = X1,
c_0_612,
[final] ).
cnf(c_0_843_844,lemma,
relation_dom(identity_relation(X1)) = X1,
c_0_613,
[final] ).
cnf(c_0_844_845,lemma,
relation_rng(identity_relation(X1)) = X1,
c_0_614,
[final] ).
cnf(c_0_845_846,lemma,
singleton(X1) != empty_set,
c_0_615,
[final] ).
cnf(c_0_846_847,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_616,
[final] ).
cnf(c_0_847_848,lemma,
relation_dom(empty_set) = empty_set,
c_0_617,
[final] ).
cnf(c_0_848_849,lemma,
relation_rng(empty_set) = empty_set,
c_0_618,
[final] ).
cnf(c_0_849_850,negated_conjecture,
relation(esk3_0),
c_0_619,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1386,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X1),relation_dom(X0))
| ~ subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_363524.p',c_0_743) ).
cnf(c_2161,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X1),relation_dom(X0))
| ~ subset(X1,X0) ),
inference(copy,[status(esa)],[c_1386]) ).
cnf(c_2494,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X1),relation_dom(X0))
| ~ subset(X1,X0) ),
inference(copy,[status(esa)],[c_2161]) ).
cnf(c_2699,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X1),relation_dom(X0))
| ~ subset(X1,X0) ),
inference(copy,[status(esa)],[c_2494]) ).
cnf(c_3418,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X1),relation_dom(X0))
| ~ subset(X1,X0) ),
inference(copy,[status(esa)],[c_2699]) ).
cnf(c_7682,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X1),relation_dom(X0))
| ~ subset(X1,X0) ),
inference(copy,[status(esa)],[c_3418]) ).
cnf(c_1475,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0)),relation_dom(sk2_esk3_0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_363524.p',c_0_691) ).
cnf(c_2373,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0)),relation_dom(sk2_esk3_0)),
inference(copy,[status(esa)],[c_1475]) ).
cnf(c_2573,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0)),relation_dom(sk2_esk3_0)),
inference(copy,[status(esa)],[c_2373]) ).
cnf(c_2620,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0)),relation_dom(sk2_esk3_0)),
inference(copy,[status(esa)],[c_2573]) ).
cnf(c_3496,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0)),relation_dom(sk2_esk3_0)),
inference(copy,[status(esa)],[c_2620]) ).
cnf(c_7838,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0)),relation_dom(sk2_esk3_0)),
inference(copy,[status(esa)],[c_3496]) ).
cnf(c_72428,plain,
( ~ relation(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0))
| ~ relation(sk2_esk3_0)
| ~ subset(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0),sk2_esk3_0) ),
inference(resolution,[status(thm)],[c_7682,c_7838]) ).
cnf(c_72429,plain,
( ~ relation(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0))
| ~ relation(sk2_esk3_0)
| ~ subset(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0),sk2_esk3_0) ),
inference(rewriting,[status(thm)],[c_72428]) ).
cnf(c_1493,negated_conjecture,
relation(sk2_esk3_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_363524.p',c_0_849) ).
cnf(c_2375,negated_conjecture,
relation(sk2_esk3_0),
inference(copy,[status(esa)],[c_1493]) ).
cnf(c_2591,negated_conjecture,
relation(sk2_esk3_0),
inference(copy,[status(esa)],[c_2375]) ).
cnf(c_2602,negated_conjecture,
relation(sk2_esk3_0),
inference(copy,[status(esa)],[c_2591]) ).
cnf(c_3514,negated_conjecture,
relation(sk2_esk3_0),
inference(copy,[status(esa)],[c_2602]) ).
cnf(c_7874,negated_conjecture,
relation(sk2_esk3_0),
inference(copy,[status(esa)],[c_3514]) ).
cnf(c_295,plain,
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_363524.p',c_0_1206_1) ).
cnf(c_5618,plain,
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(copy,[status(esa)],[c_295]) ).
cnf(c_72711,plain,
~ subset(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0),sk2_esk3_0),
inference(forward_subsumption_resolution,[status(thm)],[c_72429,c_7874,c_5618]) ).
cnf(c_72712,plain,
~ subset(relation_rng_restriction(sk2_esk2_0,sk2_esk3_0),sk2_esk3_0),
inference(rewriting,[status(thm)],[c_72711]) ).
cnf(c_1413,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_363524.p',c_0_773) ).
cnf(c_2215,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
inference(copy,[status(esa)],[c_1413]) ).
cnf(c_2520,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
inference(copy,[status(esa)],[c_2215]) ).
cnf(c_2673,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
inference(copy,[status(esa)],[c_2520]) ).
cnf(c_3448,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
inference(copy,[status(esa)],[c_2673]) ).
cnf(c_7742,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
inference(copy,[status(esa)],[c_3448]) ).
cnf(c_72714,plain,
~ relation(sk2_esk3_0),
inference(resolution,[status(thm)],[c_72712,c_7742]) ).
cnf(c_72715,plain,
~ relation(sk2_esk3_0),
inference(rewriting,[status(thm)],[c_72714]) ).
cnf(c_72719,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_72715,c_7874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU248+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n014.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 : Sun Jun 19 18:54:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.20/0.47 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.47 % FOF problem with conjecture
% 0.20/0.47 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_257b0c.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_363524.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_9ad66a | grep -v "SZS"
% 0.20/0.49
% 0.20/0.49 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.49
% 0.20/0.49 %
% 0.20/0.49 % ------ iProver source info
% 0.20/0.49
% 0.20/0.49 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.49 % git: non_committed_changes: true
% 0.20/0.49 % git: last_make_outside_of_git: true
% 0.20/0.49
% 0.20/0.49 %
% 0.20/0.49 % ------ Input Options
% 0.20/0.49
% 0.20/0.49 % --out_options all
% 0.20/0.49 % --tptp_safe_out true
% 0.20/0.49 % --problem_path ""
% 0.20/0.49 % --include_path ""
% 0.20/0.49 % --clausifier .//eprover
% 0.20/0.49 % --clausifier_options --tstp-format
% 0.20/0.49 % --stdin false
% 0.20/0.49 % --dbg_backtrace false
% 0.20/0.49 % --dbg_dump_prop_clauses false
% 0.20/0.49 % --dbg_dump_prop_clauses_file -
% 0.20/0.49 % --dbg_out_stat false
% 0.20/0.49
% 0.20/0.49 % ------ General Options
% 0.20/0.49
% 0.20/0.49 % --fof false
% 0.20/0.49 % --time_out_real 150.
% 0.20/0.49 % --time_out_prep_mult 0.2
% 0.20/0.49 % --time_out_virtual -1.
% 0.20/0.49 % --schedule none
% 0.20/0.49 % --ground_splitting input
% 0.20/0.49 % --splitting_nvd 16
% 0.20/0.49 % --non_eq_to_eq false
% 0.20/0.49 % --prep_gs_sim true
% 0.20/0.49 % --prep_unflatten false
% 0.20/0.49 % --prep_res_sim true
% 0.20/0.49 % --prep_upred true
% 0.20/0.49 % --res_sim_input true
% 0.20/0.49 % --clause_weak_htbl true
% 0.20/0.49 % --gc_record_bc_elim false
% 0.20/0.49 % --symbol_type_check false
% 0.20/0.49 % --clausify_out false
% 0.20/0.49 % --large_theory_mode false
% 0.20/0.49 % --prep_sem_filter none
% 0.20/0.49 % --prep_sem_filter_out false
% 0.20/0.49 % --preprocessed_out false
% 0.20/0.49 % --sub_typing false
% 0.20/0.49 % --brand_transform false
% 0.20/0.49 % --pure_diseq_elim true
% 0.20/0.49 % --min_unsat_core false
% 0.20/0.49 % --pred_elim true
% 0.20/0.49 % --add_important_lit false
% 0.20/0.49 % --soft_assumptions false
% 0.20/0.49 % --reset_solvers false
% 0.20/0.49 % --bc_imp_inh []
% 0.20/0.49 % --conj_cone_tolerance 1.5
% 0.20/0.49 % --prolific_symb_bound 500
% 0.20/0.49 % --lt_threshold 2000
% 0.20/0.49
% 0.20/0.49 % ------ SAT Options
% 0.20/0.49
% 0.20/0.49 % --sat_mode false
% 0.20/0.49 % --sat_fm_restart_options ""
% 0.20/0.49 % --sat_gr_def false
% 0.20/0.49 % --sat_epr_types true
% 0.20/0.49 % --sat_non_cyclic_types false
% 0.20/0.49 % --sat_finite_models false
% 0.20/0.49 % --sat_fm_lemmas false
% 0.20/0.49 % --sat_fm_prep false
% 0.20/0.49 % --sat_fm_uc_incr true
% 0.20/0.49 % --sat_out_model small
% 0.20/0.49 % --sat_out_clauses false
% 0.20/0.49
% 0.20/0.49 % ------ QBF Options
% 0.20/0.49
% 0.20/0.49 % --qbf_mode false
% 0.20/0.49 % --qbf_elim_univ true
% 0.20/0.49 % --qbf_sk_in true
% 0.20/0.49 % --qbf_pred_elim true
% 0.20/0.49 % --qbf_split 32
% 0.20/0.49
% 0.20/0.49 % ------ BMC1 Options
% 0.20/0.49
% 0.20/0.49 % --bmc1_incremental false
% 0.20/0.49 % --bmc1_axioms reachable_all
% 0.20/0.49 % --bmc1_min_bound 0
% 0.20/0.49 % --bmc1_max_bound -1
% 0.20/0.49 % --bmc1_max_bound_default -1
% 0.20/0.49 % --bmc1_symbol_reachability true
% 0.20/0.49 % --bmc1_property_lemmas false
% 0.20/0.49 % --bmc1_k_induction false
% 0.20/0.49 % --bmc1_non_equiv_states false
% 0.20/0.49 % --bmc1_deadlock false
% 0.20/0.49 % --bmc1_ucm false
% 0.20/0.49 % --bmc1_add_unsat_core none
% 0.20/0.49 % --bmc1_unsat_core_children false
% 0.20/0.49 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.49 % --bmc1_out_stat full
% 0.20/0.49 % --bmc1_ground_init false
% 0.20/0.49 % --bmc1_pre_inst_next_state false
% 0.20/0.49 % --bmc1_pre_inst_state false
% 0.20/0.49 % --bmc1_pre_inst_reach_state false
% 0.20/0.49 % --bmc1_out_unsat_core false
% 0.20/0.49 % --bmc1_aig_witness_out false
% 0.20/0.49 % --bmc1_verbose false
% 0.20/0.49 % --bmc1_dump_clauses_tptp false
% 0.20/0.51 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.51 % --bmc1_dump_file -
% 0.20/0.51 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.51 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.51 % --bmc1_ucm_extend_mode 1
% 0.20/0.51 % --bmc1_ucm_init_mode 2
% 0.20/0.51 % --bmc1_ucm_cone_mode none
% 0.20/0.51 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.51 % --bmc1_ucm_relax_model 4
% 0.20/0.51 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.51 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.51 % --bmc1_ucm_layered_model none
% 0.20/0.51 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.51
% 0.20/0.51 % ------ AIG Options
% 0.20/0.51
% 0.20/0.51 % --aig_mode false
% 0.20/0.51
% 0.20/0.51 % ------ Instantiation Options
% 0.20/0.51
% 0.20/0.51 % --instantiation_flag true
% 0.20/0.51 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.51 % --inst_solver_per_active 750
% 0.20/0.51 % --inst_solver_calls_frac 0.5
% 0.20/0.51 % --inst_passive_queue_type priority_queues
% 0.20/0.51 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.51 % --inst_passive_queues_freq [25;2]
% 0.20/0.51 % --inst_dismatching true
% 0.20/0.51 % --inst_eager_unprocessed_to_passive true
% 0.20/0.51 % --inst_prop_sim_given true
% 0.20/0.51 % --inst_prop_sim_new false
% 0.20/0.51 % --inst_orphan_elimination true
% 0.20/0.51 % --inst_learning_loop_flag true
% 0.20/0.51 % --inst_learning_start 3000
% 0.20/0.51 % --inst_learning_factor 2
% 0.20/0.51 % --inst_start_prop_sim_after_learn 3
% 0.20/0.51 % --inst_sel_renew solver
% 0.20/0.51 % --inst_lit_activity_flag true
% 0.20/0.51 % --inst_out_proof true
% 0.20/0.51
% 0.20/0.51 % ------ Resolution Options
% 0.20/0.51
% 0.20/0.51 % --resolution_flag true
% 0.20/0.51 % --res_lit_sel kbo_max
% 0.20/0.51 % --res_to_prop_solver none
% 0.20/0.51 % --res_prop_simpl_new false
% 0.20/0.51 % --res_prop_simpl_given false
% 0.20/0.51 % --res_passive_queue_type priority_queues
% 0.20/0.51 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.51 % --res_passive_queues_freq [15;5]
% 0.20/0.51 % --res_forward_subs full
% 0.20/0.51 % --res_backward_subs full
% 0.20/0.51 % --res_forward_subs_resolution true
% 0.20/0.51 % --res_backward_subs_resolution true
% 0.20/0.51 % --res_orphan_elimination false
% 0.20/0.51 % --res_time_limit 1000.
% 0.20/0.51 % --res_out_proof true
% 0.20/0.51 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_257b0c.s
% 0.20/0.51 % --modulo true
% 0.20/0.51
% 0.20/0.51 % ------ Combination Options
% 0.20/0.51
% 0.20/0.51 % --comb_res_mult 1000
% 0.20/0.51 % --comb_inst_mult 300
% 0.20/0.51 % ------
% 0.20/0.51
% 0.20/0.51 % ------ Parsing...%
% 0.20/0.51
% 0.20/0.51
% 0.20/0.51 % ------ Statistics
% 0.20/0.51
% 0.20/0.51 % ------ General
% 0.20/0.51
% 0.20/0.51 % num_of_input_clauses: 480
% 0.20/0.51 % num_of_input_neg_conjectures: 0
% 0.20/0.51 % num_of_splits: 0
% 0.20/0.51 % num_of_split_atoms: 0
% 0.20/0.51 % num_of_sem_filtered_clauses: 0
% 0.20/0.51 % num_of_subtypes: 0
% 0.20/0.51 % monotx_restored_types: 0
% 0.20/0.51 % sat_num_of_epr_types: 0
% 0.20/0.51 % sat_num_of_non_cyclic_types: 0
% 0.20/0.51 % sat_guarded_non_collapsed_types: 0
% 0.20/0.51 % is_epr: 0
% 0.20/0.51 % is_horn: 0
% 0.20/0.51 % has_eq: 0
% 0.20/0.51 % num_pure_diseq_elim: 0
% 0.20/0.51 % simp_replaced_by: 0
% 0.20/0.51 % res_preprocessed: 0
% 0.20/0.51 % prep_upred: 0
% 0.20/0.51 % prep_unflattend: 0
% 0.20/0.51 % pred_elim_cands: 0
% 0.20/0.51 % pred_elim: 0
% 0.20/0.51 % pred_elim_cl: 0
% 0.20/0.51 % pred_elim_cycles: 0
% 0.20/0.51 % forced_gc_time: 0
% 0.20/0.51 % gc_basic_clause_elim: 0
% 0.20/0.51 % parsing_time: 0.
% 0.20/0.51 % sem_filter_time: 0.
% 0.20/0.51 % pred_elim_time: 0.
% 0.20/0.51 % out_proof_time: 0.
% 0.20/0.51 % monotx_time: 0.
% 0.20/0.51 % subtype_inf_time: 0.
% 0.20/0.51 % unif_index_cands_time: 0.
% 0.20/0.51 % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_363524.p line: 483 near token: '!='")
% 0.20/0.51 nif_index_add_time: 0.
% 0.20/0.51 % total_time: 0.033
% 0.20/0.51 % num_of_symbols: 127
% 0.20/0.51 % num_of_terms: 811
% 0.20/0.51
% 0.20/0.51 % ------ Propositional Solver
% 0.20/0.51
% 0.20/0.51 % prop_solver_calls: 0
% 0.20/0.51 % prop_fast_solver_calls: 0
% 0.20/0.51 % prop_num_of_clauses: 0
% 0.20/0.51 % prop_preprocess_simplified: 0
% 0.20/0.51 % prop_fo_subsumed: 0
% 0.20/0.51 % prop_solver_time: 0.
% 0.20/0.51 % prop_fast_solver_time: 0.
% 0.20/0.51 % prop_unsat_core_time: 0.
% 0.20/0.51
% 0.20/0.51 % ------ QBF
% 0.20/0.51
% 0.20/0.51 % qbf_q_res: 0
% 0.20/0.51 % qbf_num_tautologies: 0
% 0.20/0.51 % qbf_prep_cycles: 0
% 0.20/0.51
% 0.20/0.51 % ------ BMC1
% 0.20/0.51
% 0.20/0.51 % bmc1_current_bound: -1
% 0.20/0.51 % bmc1_last_solved_bound: -1
% 0.20/0.51 % bmc1_unsat_core_size: -1
% 0.20/0.51 % bmc1_unsat_core_parents_size: -1
% 0.20/0.51 % bmc1_merge_next_fun: 0
% 0.20/0.51 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.51
% 0.20/0.51 % ------ Instantiation
% 0.20/0.51
% 0.20/0.51 % inst_num_of_clauses: undef
% 0.20/0.51 % inst_num_in_passive: undef
% 0.20/0.51 % inst_num_in_active: 0
% 0.20/0.51 % inst_num_in_unprocessed: 0
% 0.20/0.51 % inst_num_of_loops: 0
% 0.20/0.51 % inst_num_of_learning_restarts: 0
% 0.20/0.51 % inst_num_moves_active_passive: 0
% 0.20/0.51 % inst_lit_activity: 0
% 0.20/0.51 % inst_lit_activity_moves: 0
% 0.20/0.51 % inst_num_tautologies: 0
% 0.20/0.51 % inst_num_prop_implied: 0
% 0.20/0.51 % inst_num_existing_simplified: 0
% 0.20/0.51 % inst_num_eq_res_simplified: 0
% 0.20/0.51 % inst_num_child_elim: 0
% 0.20/0.51 % inst_num_of_dismatching_blockings: 0
% 0.20/0.51 % inst_num_of_non_proper_insts: 0
% 0.20/0.51 % inst_num_of_duplicates: 0
% 0.20/0.51 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.51 % inst_dismatching_checking_time: 0.
% 0.20/0.51
% 0.20/0.51 % ------ Resolution
% 0.20/0.51
% 0.20/0.51 % res_num_of_clauses: undef
% 0.20/0.51 % res_num_in_passive: undef
% 0.20/0.51 % res_num_in_active: 0
% 0.20/0.51 % res_num_of_loops: 0
% 0.20/0.51 % res_forward_subset_subsumed: 0
% 0.20/0.51 % res_backward_subset_subsumed: 0
% 0.20/0.51 % res_forward_subsumed: 0
% 0.20/0.51 % res_backward_subsumed: 0
% 0.20/0.51 % res_forward_subsumption_resolution: 0
% 0.20/0.51 % res_backward_subsumption_resolution: 0
% 0.20/0.51 % res_clause_to_clause_subsumption: 0
% 0.20/0.51 % res_orphan_elimination: 0
% 0.20/0.51 % res_tautology_del: 0
% 0.20/0.51 % res_num_eq_res_simplified: 0
% 0.20/0.51 % res_num_sel_changes: 0
% 0.20/0.51 % res_moves_from_active_to_pass: 0
% 0.20/0.51
% 0.20/0.51 % Status Unknown
% 0.37/0.63 % Orienting using strategy ClausalAll
% 0.37/0.63 % FOF problem with conjecture
% 0.37/0.63 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_257b0c.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_363524.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_7f4c8f | grep -v "SZS"
% 0.37/0.65
% 0.37/0.65 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.37/0.65
% 0.37/0.65 %
% 0.37/0.65 % ------ iProver source info
% 0.37/0.65
% 0.37/0.65 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.37/0.65 % git: non_committed_changes: true
% 0.37/0.65 % git: last_make_outside_of_git: true
% 0.37/0.65
% 0.37/0.65 %
% 0.37/0.65 % ------ Input Options
% 0.37/0.65
% 0.37/0.65 % --out_options all
% 0.37/0.65 % --tptp_safe_out true
% 0.37/0.65 % --problem_path ""
% 0.37/0.65 % --include_path ""
% 0.37/0.65 % --clausifier .//eprover
% 0.37/0.65 % --clausifier_options --tstp-format
% 0.37/0.65 % --stdin false
% 0.37/0.65 % --dbg_backtrace false
% 0.37/0.65 % --dbg_dump_prop_clauses false
% 0.37/0.65 % --dbg_dump_prop_clauses_file -
% 0.37/0.65 % --dbg_out_stat false
% 0.37/0.65
% 0.37/0.65 % ------ General Options
% 0.37/0.65
% 0.37/0.65 % --fof false
% 0.37/0.65 % --time_out_real 150.
% 0.37/0.65 % --time_out_prep_mult 0.2
% 0.37/0.65 % --time_out_virtual -1.
% 0.37/0.65 % --schedule none
% 0.37/0.65 % --ground_splitting input
% 0.37/0.65 % --splitting_nvd 16
% 0.37/0.65 % --non_eq_to_eq false
% 0.37/0.65 % --prep_gs_sim true
% 0.37/0.65 % --prep_unflatten false
% 0.37/0.65 % --prep_res_sim true
% 0.37/0.65 % --prep_upred true
% 0.37/0.65 % --res_sim_input true
% 0.37/0.65 % --clause_weak_htbl true
% 0.37/0.65 % --gc_record_bc_elim false
% 0.37/0.65 % --symbol_type_check false
% 0.37/0.65 % --clausify_out false
% 0.37/0.65 % --large_theory_mode false
% 0.37/0.65 % --prep_sem_filter none
% 0.37/0.65 % --prep_sem_filter_out false
% 0.37/0.65 % --preprocessed_out false
% 0.37/0.65 % --sub_typing false
% 0.37/0.65 % --brand_transform false
% 0.37/0.65 % --pure_diseq_elim true
% 0.37/0.65 % --min_unsat_core false
% 0.37/0.65 % --pred_elim true
% 0.37/0.65 % --add_important_lit false
% 0.37/0.65 % --soft_assumptions false
% 0.37/0.65 % --reset_solvers false
% 0.37/0.65 % --bc_imp_inh []
% 0.37/0.65 % --conj_cone_tolerance 1.5
% 0.37/0.65 % --prolific_symb_bound 500
% 0.37/0.65 % --lt_threshold 2000
% 0.37/0.65
% 0.37/0.65 % ------ SAT Options
% 0.37/0.65
% 0.37/0.65 % --sat_mode false
% 0.37/0.65 % --sat_fm_restart_options ""
% 0.37/0.65 % --sat_gr_def false
% 0.37/0.65 % --sat_epr_types true
% 0.37/0.65 % --sat_non_cyclic_types false
% 0.37/0.65 % --sat_finite_models false
% 0.37/0.65 % --sat_fm_lemmas false
% 0.37/0.65 % --sat_fm_prep false
% 0.37/0.65 % --sat_fm_uc_incr true
% 0.37/0.65 % --sat_out_model small
% 0.37/0.65 % --sat_out_clauses false
% 0.37/0.65
% 0.37/0.65 % ------ QBF Options
% 0.37/0.65
% 0.37/0.65 % --qbf_mode false
% 0.37/0.65 % --qbf_elim_univ true
% 0.37/0.65 % --qbf_sk_in true
% 0.37/0.65 % --qbf_pred_elim true
% 0.37/0.65 % --qbf_split 32
% 0.37/0.65
% 0.37/0.65 % ------ BMC1 Options
% 0.37/0.65
% 0.37/0.65 % --bmc1_incremental false
% 0.37/0.65 % --bmc1_axioms reachable_all
% 0.37/0.65 % --bmc1_min_bound 0
% 0.37/0.65 % --bmc1_max_bound -1
% 0.37/0.65 % --bmc1_max_bound_default -1
% 0.37/0.65 % --bmc1_symbol_reachability true
% 0.37/0.65 % --bmc1_property_lemmas false
% 0.37/0.65 % --bmc1_k_induction false
% 0.37/0.65 % --bmc1_non_equiv_states false
% 0.37/0.65 % --bmc1_deadlock false
% 0.37/0.65 % --bmc1_ucm false
% 0.37/0.65 % --bmc1_add_unsat_core none
% 0.37/0.65 % --bmc1_unsat_core_children false
% 0.37/0.65 % --bmc1_unsat_core_extrapolate_axioms false
% 0.37/0.65 % --bmc1_out_stat full
% 0.37/0.65 % --bmc1_ground_init false
% 0.37/0.65 % --bmc1_pre_inst_next_state false
% 0.37/0.65 % --bmc1_pre_inst_state false
% 0.37/0.65 % --bmc1_pre_inst_reach_state false
% 0.37/0.65 % --bmc1_out_unsat_core false
% 0.37/0.65 % --bmc1_aig_witness_out false
% 0.37/0.65 % --bmc1_verbose false
% 0.37/0.65 % --bmc1_dump_clauses_tptp false
% 0.98/1.30 % --bmc1_dump_unsat_core_tptp false
% 0.98/1.30 % --bmc1_dump_file -
% 0.98/1.30 % --bmc1_ucm_expand_uc_limit 128
% 0.98/1.30 % --bmc1_ucm_n_expand_iterations 6
% 0.98/1.30 % --bmc1_ucm_extend_mode 1
% 0.98/1.30 % --bmc1_ucm_init_mode 2
% 0.98/1.30 % --bmc1_ucm_cone_mode none
% 0.98/1.30 % --bmc1_ucm_reduced_relation_type 0
% 0.98/1.30 % --bmc1_ucm_relax_model 4
% 0.98/1.30 % --bmc1_ucm_full_tr_after_sat true
% 0.98/1.30 % --bmc1_ucm_expand_neg_assumptions false
% 0.98/1.30 % --bmc1_ucm_layered_model none
% 0.98/1.30 % --bmc1_ucm_max_lemma_size 10
% 0.98/1.30
% 0.98/1.30 % ------ AIG Options
% 0.98/1.30
% 0.98/1.30 % --aig_mode false
% 0.98/1.30
% 0.98/1.30 % ------ Instantiation Options
% 0.98/1.30
% 0.98/1.30 % --instantiation_flag true
% 0.98/1.30 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.98/1.30 % --inst_solver_per_active 750
% 0.98/1.30 % --inst_solver_calls_frac 0.5
% 0.98/1.30 % --inst_passive_queue_type priority_queues
% 0.98/1.30 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.98/1.30 % --inst_passive_queues_freq [25;2]
% 0.98/1.30 % --inst_dismatching true
% 0.98/1.30 % --inst_eager_unprocessed_to_passive true
% 0.98/1.30 % --inst_prop_sim_given true
% 0.98/1.30 % --inst_prop_sim_new false
% 0.98/1.30 % --inst_orphan_elimination true
% 0.98/1.30 % --inst_learning_loop_flag true
% 0.98/1.30 % --inst_learning_start 3000
% 0.98/1.30 % --inst_learning_factor 2
% 0.98/1.30 % --inst_start_prop_sim_after_learn 3
% 0.98/1.30 % --inst_sel_renew solver
% 0.98/1.30 % --inst_lit_activity_flag true
% 0.98/1.30 % --inst_out_proof true
% 0.98/1.30
% 0.98/1.30 % ------ Resolution Options
% 0.98/1.30
% 0.98/1.30 % --resolution_flag true
% 0.98/1.30 % --res_lit_sel kbo_max
% 0.98/1.30 % --res_to_prop_solver none
% 0.98/1.30 % --res_prop_simpl_new false
% 0.98/1.30 % --res_prop_simpl_given false
% 0.98/1.30 % --res_passive_queue_type priority_queues
% 0.98/1.30 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.98/1.30 % --res_passive_queues_freq [15;5]
% 0.98/1.30 % --res_forward_subs full
% 0.98/1.30 % --res_backward_subs full
% 0.98/1.30 % --res_forward_subs_resolution true
% 0.98/1.30 % --res_backward_subs_resolution true
% 0.98/1.30 % --res_orphan_elimination false
% 0.98/1.30 % --res_time_limit 1000.
% 0.98/1.30 % --res_out_proof true
% 0.98/1.30 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_257b0c.s
% 0.98/1.30 % --modulo true
% 0.98/1.30
% 0.98/1.30 % ------ Combination Options
% 0.98/1.30
% 0.98/1.30 % --comb_res_mult 1000
% 0.98/1.30 % --comb_inst_mult 300
% 0.98/1.30 % ------
% 0.98/1.30
% 0.98/1.30 % ------ Parsing...% successful
% 0.98/1.30
% 0.98/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e snvd_s sp: 0 0s snvd_e %
% 0.98/1.30
% 0.98/1.30 % ------ Proving...
% 0.98/1.30 % ------ Problem Properties
% 0.98/1.30
% 0.98/1.30 %
% 0.98/1.30 % EPR false
% 0.98/1.30 % Horn false
% 0.98/1.30 % Has equality true
% 0.98/1.30
% 0.98/1.30 % % ------ Input Options Time Limit: Unbounded
% 0.98/1.30
% 0.98/1.30
% 0.98/1.30 Compiling...
% 0.98/1.30 Loading plugin: done.
% 0.98/1.30 Compiling...
% 0.98/1.30 Loading plugin: done.
% 0.98/1.30 Compiling...
% 0.98/1.30 Loading plugin: done.
% 0.98/1.30 Compiling...
% 0.98/1.30 Loading plugin: done.
% 0.98/1.30 Compiling...
% 0.98/1.30 Loading plugin: done.
% 0.98/1.30 % warning: Clause {~(relation(X0));~(function(X0));in(ordered_pair(X1,X2),X0);~(in(X1,relation_dom(X0)));~(equality_sorted($i,X2,apply(X0,X1)))} has no selected literals
% 0.98/1.30 cnf(c_3363,plain,
% 0.98/1.30 ( ~ relation(X0)
% 0.98/1.30 | ~ function(X0)
% 0.98/1.30 | in(ordered_pair(X1,X2),X0)
% 0.98/1.30 | ~ in(X1,relation_dom(X0))
% 0.98/1.30 | X2 != apply(X0,X1) ),
% 0.98/1.30 inference(copy,[status(esa)],[c_2755]) ).
% 0.98/1.30
% 0.98/1.30 cnf(c_2755,plain,
% 0.98/1.30 ( ~ relation(X0)
% 0.98/1.30 | ~ function(X0)
% 0.98/1.30 | in(ordered_pair(X1,X2),X0)
% 0.98/1.30 | ~ in(X1,relation_dom(X0))
% 0.98/1.30 | X2 != apply(X0,X1) ),
% 0.98/1.30 inference(copy,[status(esa)],[c_2438]) ).
% 0.98/1.30
% 0.98/1.30 cnf(c_2438,plain,
% 0.98/1.30 ( ~ relation(X0)
% 0.98/1.30 | ~ function(X0)
% 0.98/1.30 | in(ordered_pair(X1,X2),X0)
% 0.98/1.30 | ~ in(X1,relation_dom(X0))
% 0.98/1.30 | X2 != apply(X0,X1) ),
% 0.98/1.30 inference(copy,[status(esa)],[c_2047]) ).
% 0.98/1.30
% 0.98/1.30 cnf(c_2047,plain,
% 0.98/1.30 ( ~ relation(X0)
% 0.98/1.30 | ~ function(X0)
% 0.98/1.31 | in(ordered_pair(X1,X2),X0)
% 0.98/1.31 | ~ in(X1,relation_dom(X0))
% 0.98/1.31 | X2 != apply(X0,X1) ),
% 0.98/1.31 inference(copy,[status(esa)],[c_1329]) ).
% 0.98/1.31
% 0.98/1.31 cnf(c_1329,plain,
% 0.98/1.31 ( ~ relation(X0)
% 0.98/1.31 | ~ function(X0)
% 0.98/1.31 | in(ordered_pair(X1,X2),X0)
% 0.98/1.31 | ~ in(X1,relation_dom(X0))
% 0.98/1.31 | X2 != apply(X0,X1) ),
% 0.98/1.31 file('/export/starexec/sandbox/tmp/iprover_modulo_363524.p', c_0_685) ).
% 0.98/1.31
% 0.98/1.31 % % ------ Current options:
% 0.98/1.31
% 0.98/1.31 % ------ Input Options
% 0.98/1.31
% 0.98/1.31 % --out_options all
% 0.98/1.31 % --tptp_safe_out true
% 0.98/1.31 % --problem_path ""
% 0.98/1.31 % --include_path ""
% 0.98/1.31 % --clausifier .//eprover
% 0.98/1.31 % --clausifier_options --tstp-format
% 0.98/1.31 % --stdin false
% 0.98/1.31 % --dbg_backtrace false
% 0.98/1.31 % --dbg_dump_prop_clauses false
% 0.98/1.31 % --dbg_dump_prop_clauses_file -
% 0.98/1.31 % --dbg_out_stat false
% 0.98/1.31
% 0.98/1.31 % ------ General Options
% 0.98/1.31
% 0.98/1.31 % --fof false
% 0.98/1.31 % --time_out_real 150.
% 0.98/1.31 % --time_out_prep_mult 0.2
% 0.98/1.31 % --time_out_virtual -1.
% 0.98/1.31 % --schedule none
% 0.98/1.31 % --ground_splitting input
% 0.98/1.31 % --splitting_nvd 16
% 0.98/1.31 % --non_eq_to_eq false
% 0.98/1.31 % --prep_gs_sim true
% 0.98/1.31 % --prep_unflatten false
% 0.98/1.31 % --prep_res_sim true
% 0.98/1.31 % --prep_upred true
% 0.98/1.31 % --res_sim_input true
% 0.98/1.31 % --clause_weak_htbl true
% 0.98/1.31 % --gc_record_bc_elim false
% 0.98/1.31 % --symbol_type_check false
% 0.98/1.31 % --clausify_out false
% 0.98/1.31 % --large_theory_mode false
% 0.98/1.31 % --prep_sem_filter none
% 0.98/1.31 % --prep_sem_filter_out false
% 0.98/1.31 % --preprocessed_out false
% 0.98/1.31 % --sub_typing false
% 0.98/1.31 % --brand_transform false
% 0.98/1.31 % --pure_diseq_elim true
% 0.98/1.31 % --min_unsat_core false
% 0.98/1.31 % --pred_elim true
% 0.98/1.31 % --add_important_lit false
% 0.98/1.31 % --soft_assumptions false
% 0.98/1.31 % --reset_solvers false
% 0.98/1.31 % --bc_imp_inh []
% 0.98/1.31 % --conj_cone_tolerance 1.5
% 0.98/1.31 % --prolific_symb_bound 500
% 0.98/1.31 % --lt_threshold 2000
% 0.98/1.31
% 0.98/1.31 % ------ SAT Options
% 0.98/1.31
% 0.98/1.31 % --sat_mode false
% 0.98/1.31 % --sat_fm_restart_options ""
% 0.98/1.31 % --sat_gr_def false
% 0.98/1.31 % --sat_epr_types true
% 0.98/1.31 % --sat_non_cyclic_types false
% 0.98/1.31 % --sat_finite_models false
% 0.98/1.31 % --sat_fm_lemmas false
% 0.98/1.31 % --sat_fm_prep false
% 0.98/1.31 % --sat_fm_uc_incr true
% 0.98/1.31 % --sat_out_model small
% 0.98/1.31 % --sat_out_clauses false
% 0.98/1.31
% 0.98/1.31 % ------ QBF Options
% 0.98/1.31
% 0.98/1.31 % --qbf_mode false
% 0.98/1.31 % --qbf_elim_univ true
% 0.98/1.31 % --qbf_sk_in true
% 0.98/1.31 % --qbf_pred_elim true
% 0.98/1.31 % --qbf_split 32
% 0.98/1.31
% 0.98/1.31 % ------ BMC1 Options
% 0.98/1.31
% 0.98/1.31 % --bmc1_incremental false
% 0.98/1.31 % --bmc1_axioms reachable_all
% 0.98/1.31 % --bmc1_min_bound 0
% 0.98/1.31 % --bmc1_max_bound -1
% 0.98/1.31 % --bmc1_max_bound_default -1
% 0.98/1.31 % --bmc1_symbol_reachability true
% 0.98/1.31 % --bmc1_property_lemmas false
% 0.98/1.31 % --bmc1_k_induction false
% 0.98/1.31 % --bmc1_non_equiv_states false
% 0.98/1.31 % --bmc1_deadlock false
% 0.98/1.31 % --bmc1_ucm false
% 0.98/1.31 % --bmc1_add_unsat_core none
% 0.98/1.31 % --bmc1_unsat_core_children false
% 0.98/1.31 % --bmc1_unsat_core_extrapolate_axioms false
% 0.98/1.31 % --bmc1_out_stat full
% 0.98/1.31 % --bmc1_ground_init false
% 0.98/1.31 % --bmc1_pre_inst_next_state false
% 0.98/1.31 % --bmc1_pre_inst_state false
% 0.98/1.31 % --bmc1_pre_inst_reach_state false
% 2.44/2.73 % --bmc1_out_unsat_core false
% 2.44/2.73 % --bmc1_aig_witness_out false
% 2.44/2.73 % --bmc1_verbose false
% 2.44/2.73 % --bmc1_dump_clauses_tptp false
% 2.44/2.73 % --bmc1_dump_unsat_core_tptp false
% 2.44/2.73 % --bmc1_dump_file -
% 2.44/2.73 % --bmc1_ucm_expand_uc_limit 128
% 2.44/2.73 % --bmc1_ucm_n_expand_iterations 6
% 2.44/2.73 % --bmc1_ucm_extend_mode 1
% 2.44/2.73 % --bmc1_ucm_init_mode 2
% 2.44/2.73 % --bmc1_ucm_cone_mode none
% 2.44/2.73 % --bmc1_ucm_reduced_relation_type 0
% 2.44/2.73 % --bmc1_ucm_relax_model 4
% 2.44/2.73 % --bmc1_ucm_full_tr_after_sat true
% 2.44/2.73 % --bmc1_ucm_expand_neg_assumptions false
% 2.44/2.73 % --bmc1_ucm_layered_model none
% 2.44/2.73 % --bmc1_ucm_max_lemma_size 10
% 2.44/2.73
% 2.44/2.73 % ------ AIG Options
% 2.44/2.73
% 2.44/2.73 % --aig_mode false
% 2.44/2.73
% 2.44/2.73 % ------ Instantiation Options
% 2.44/2.73
% 2.44/2.73 % --instantiation_flag true
% 2.44/2.73 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 2.44/2.73 % --inst_solver_per_active 750
% 2.44/2.73 % --inst_solver_calls_frac 0.5
% 2.44/2.73 % --inst_passive_queue_type priority_queues
% 2.44/2.73 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.44/2.73 % --inst_passive_queues_freq [25;2]
% 2.44/2.73 % --inst_dismatching true
% 2.44/2.73 % --inst_eager_unprocessed_to_passive true
% 2.44/2.73 % --inst_prop_sim_given true
% 2.44/2.73 % --inst_prop_sim_new false
% 2.44/2.73 % --inst_orphan_elimination true
% 2.44/2.73 % --inst_learning_loop_flag true
% 2.44/2.73 % --inst_learning_start 3000
% 2.44/2.73 % --inst_learning_factor 2
% 2.44/2.73 % --inst_start_prop_sim_after_learn 3
% 2.44/2.73 % --inst_sel_renew solver
% 2.44/2.73 % --inst_lit_activity_flag true
% 2.44/2.73 % --inst_out_proof true
% 2.44/2.73
% 2.44/2.73 % ------ Resolution Options
% 2.44/2.73
% 2.44/2.73 % --resolution_flag true
% 2.44/2.73 % --res_lit_sel kbo_max
% 2.44/2.73 % --res_to_prop_solver none
% 2.44/2.73 % --res_prop_simpl_new false
% 2.44/2.73 % --res_prop_simpl_given false
% 2.44/2.73 % --res_passive_queue_type priority_queues
% 2.44/2.73 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.44/2.73 % --res_passive_queues_freq [15;5]
% 2.44/2.73 % --res_forward_subs full
% 2.44/2.73 % --res_backward_subs full
% 2.44/2.73 % --res_forward_subs_resolution true
% 2.44/2.73 % --res_backward_subs_resolution true
% 2.44/2.73 % --res_orphan_elimination false
% 2.44/2.73 % --res_time_limit 1000.
% 2.44/2.73 % --res_out_proof true
% 2.44/2.73 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_257b0c.s
% 2.44/2.73 % --modulo true
% 2.44/2.73
% 2.44/2.73 % ------ Combination Options
% 2.44/2.73
% 2.44/2.73 % --comb_res_mult 1000
% 2.44/2.73 % --comb_inst_mult 300
% 2.44/2.73 % ------
% 2.44/2.73
% 2.44/2.73
% 2.44/2.73
% 2.44/2.73 % ------ Proving...
% 2.44/2.73 %
% 2.44/2.73
% 2.44/2.73
% 2.44/2.73 % Resolution empty clause
% 2.44/2.73
% 2.44/2.73 % ------ Statistics
% 2.44/2.73
% 2.44/2.73 % ------ General
% 2.44/2.73
% 2.44/2.73 % num_of_input_clauses: 1494
% 2.44/2.73 % num_of_input_neg_conjectures: 2
% 2.44/2.73 % num_of_splits: 0
% 2.44/2.73 % num_of_split_atoms: 0
% 2.44/2.73 % num_of_sem_filtered_clauses: 0
% 2.44/2.73 % num_of_subtypes: 0
% 2.44/2.73 % monotx_restored_types: 0
% 2.44/2.73 % sat_num_of_epr_types: 0
% 2.44/2.73 % sat_num_of_non_cyclic_types: 0
% 2.44/2.73 % sat_guarded_non_collapsed_types: 0
% 2.44/2.73 % is_epr: 0
% 2.44/2.73 % is_horn: 0
% 2.44/2.73 % has_eq: 1
% 2.44/2.73 % num_pure_diseq_elim: 0
% 2.44/2.73 % simp_replaced_by: 0
% 2.44/2.73 % res_preprocessed: 232
% 2.44/2.73 % prep_upred: 0
% 2.44/2.73 % prep_unflattend: 16
% 2.44/2.73 % pred_elim_cands: 19
% 2.44/2.73 % pred_elim: 7
% 2.44/2.73 % pred_elim_cl: 7
% 2.44/2.73 % pred_elim_cycles: 13
% 2.44/2.73 % forced_gc_time: 0
% 2.44/2.73 % gc_basic_clause_elim: 0
% 2.44/2.73 % parsing_time: 0.069
% 2.44/2.73 % sem_filter_time: 0.
% 2.44/2.73 % pred_elim_time: 0.011
% 2.44/2.73 % out_proof_time: 0.
% 2.44/2.73 % monotx_time: 0.
% 2.44/2.73 % subtype_inf_time: 0.
% 2.44/2.73 % unif_index_cands_time: 0.003
% 2.44/2.73 % unif_index_add_time: 0.002
% 2.44/2.73 % total_time: 2.091
% 2.44/2.73 % num_of_symbols: 209
% 2.44/2.73 % num_of_terms: 98129
% 2.44/2.73
% 2.44/2.73 % ------ Propositional Solver
% 2.44/2.73
% 2.44/2.73 % prop_solver_calls: 1
% 2.44/2.73 % prop_fast_solver_calls: 1651
% 2.44/2.73 % prop_num_of_clauses: 1284
% 2.44/2.73 % prop_preprocess_simplified: 6893
% 2.44/2.73 % prop_fo_subsumed: 14
% 2.44/2.73 % prop_solver_time: 0.
% 2.44/2.73 % prop_fast_solver_time: 0.001
% 2.44/2.73 % prop_unsat_core_time: 0.
% 2.44/2.73
% 2.44/2.73 % ------ QBF
% 2.44/2.73
% 2.44/2.73 % qbf_q_res: 0
% 2.44/2.73 % qbf_num_tautologies: 0
% 2.44/2.73 % qbf_prep_cycles: 0
% 2.44/2.73
% 2.44/2.73 % ------ BMC1
% 2.44/2.73
% 2.44/2.73 % bmc1_current_bound: -1
% 2.44/2.73 % bmc1_last_solved_bound: -1
% 2.44/2.73 % bmc1_unsat_core_size: -1
% 2.44/2.73 % bmc1_unsat_core_parents_size: -1
% 2.44/2.73 % bmc1_merge_next_fun: 0
% 2.44/2.73 % bmc1_unsat_core_clauses_time: 0.
% 2.44/2.73
% 2.44/2.73 % ------ Instantiation
% 2.44/2.73
% 2.44/2.73 % inst_num_of_clauses: 1435
% 2.44/2.73 % inst_num_in_passive: 0
% 2.44/2.73 % inst_num_in_active: 0
% 2.44/2.73 % inst_num_in_unprocessed: 1473
% 2.44/2.73 % inst_num_of_loops: 0
% 2.44/2.73 % inst_num_of_learning_restarts: 0
% 2.44/2.73 % inst_num_moves_active_passive: 0
% 2.44/2.73 % inst_lit_activity: 0
% 2.44/2.73 % inst_lit_activity_moves: 0
% 2.44/2.73 % inst_num_tautologies: 0
% 2.44/2.73 % inst_num_prop_implied: 0
% 2.44/2.73 % inst_num_existing_simplified: 0
% 2.44/2.73 % inst_num_eq_res_simplified: 0
% 2.44/2.73 % inst_num_child_elim: 0
% 2.44/2.73 % inst_num_of_dismatching_blockings: 0
% 2.44/2.73 % inst_num_of_non_proper_insts: 0
% 2.44/2.73 % inst_num_of_duplicates: 0
% 2.44/2.73 % inst_inst_num_from_inst_to_res: 0
% 2.44/2.73 % inst_dismatching_checking_time: 0.
% 2.44/2.73
% 2.44/2.73 % ------ Resolution
% 2.44/2.73
% 2.44/2.73 % res_num_of_clauses: 31265
% 2.44/2.73 % res_num_in_passive: 29361
% 2.44/2.73 % res_num_in_active: 1039
% 2.44/2.73 % res_num_of_loops: 542
% 2.44/2.73 % res_forward_subset_subsumed: 2052
% 2.44/2.73 % res_backward_subset_subsumed: 124
% 2.44/2.73 % res_forward_subsumed: 15
% 2.44/2.73 % res_backward_subsumed: 0
% 2.44/2.73 % res_forward_subsumption_resolution: 9
% 2.44/2.73 % res_backward_subsumption_resolution: 1
% 2.44/2.73 % res_clause_to_clause_subsumption: 1214
% 2.44/2.73 % res_orphan_elimination: 0
% 2.44/2.73 % res_tautology_del: 62
% 2.44/2.73 % res_num_eq_res_simplified: 0
% 2.44/2.73 % res_num_sel_changes: 0
% 2.44/2.73 % res_moves_from_active_to_pass: 0
% 2.44/2.73
% 2.44/2.73 % Status Unsatisfiable
% 2.44/2.73 % SZS status Theorem
% 2.44/2.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------