TSTP Solution File: SEU295+2 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU295+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n029.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 10:26:57 EDT 2022
% Result : Theorem 1.72s 1.93s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 402
% Syntax : Number of formulae : 7831 ( 667 unt; 0 def)
% Number of atoms : 41486 (9093 equ)
% Maximal formula atoms : 1044 ( 5 avg)
% Number of connectives : 56480 (22825 ~;30437 |;2087 &)
% ( 293 <=>; 838 =>; 0 <=; 0 <~>)
% Maximal formula depth : 161 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 36 usr; 2 prp; 0-3 aty)
% Number of functors : 459 ( 459 usr; 41 con; 0-8 aty)
% Number of variables : 25429 ( 702 sgn2879 !; 232 ?)
% 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,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ! [X3] :
( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( ordered_pair(X7,X8) = X5
& in(X7,X1)
& ? [X9] :
( X7 = X9
& in(X8,X9)
& ! [X10] :
( in(X10,X9)
=> in(ordered_pair(X8,X10),X2) ) ) )
& X4 = X6
& ? [X11,X12] :
( ordered_pair(X11,X12) = X6
& in(X11,X1)
& ? [X13] :
( X11 = X13
& in(X12,X13)
& ! [X14] :
( in(X14,X13)
=> in(ordered_pair(X12,X14),X2) ) ) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(X1,X3))
& X6 = X5
& ? [X15,X16] :
( ordered_pair(X15,X16) = X5
& in(X15,X1)
& ? [X17] :
( X15 = X17
& in(X16,X17)
& ! [X18] :
( in(X18,X17)
=> in(ordered_pair(X16,X18),X2) ) ) ) ) ) ) ),
file('<stdin>',s1_tarski__e10_24__wellord2__2) ).
fof(c_0_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& in(X3,X1)
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X1)
& in(X5,X1)
& ? [X10] :
( X5 = X10
& in(X4,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X4,X11),X2) ) ) ) ) ) ),
file('<stdin>',s1_tarski__e10_24__wellord2__1) ).
fof(c_0_2,axiom,
! [X1,X2,X3] :
( ( relation(X2)
& relation(X3)
& function(X3) )
=> ( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( X5 = ordered_pair(X7,X8)
& in(ordered_pair(apply(X3,X7),apply(X3,X8)),X2) )
& X4 = X6
& ? [X9,X10] :
( X6 = ordered_pair(X9,X10)
& in(ordered_pair(apply(X3,X9),apply(X3,X10)),X2) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(X1,X1))
& X6 = X5
& ? [X11,X12] :
( X5 = ordered_pair(X11,X12)
& in(ordered_pair(apply(X3,X11),apply(X3,X12)),X2) ) ) ) ) ),
file('<stdin>',s1_tarski__e6_21__wellord2__1) ).
fof(c_0_3,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_4,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
<=> ( relation_dom(X3) = relation_field(X1)
& relation_rng(X3) = relation_field(X2)
& one_to_one(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
<=> ( in(X4,relation_field(X1))
& in(X5,relation_field(X1))
& in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2) ) ) ) ) ) ) ),
file('<stdin>',d7_wellord1) ).
fof(c_0_5,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_6,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_7,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_8,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_9,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_10,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_11,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_12,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_13,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = fiber(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 != X2
& in(ordered_pair(X4,X2),X1) ) ) ) ),
file('<stdin>',d1_wellord1) ).
fof(c_0_14,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_15,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_16,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_17,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_18,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_19,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_20,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = inclusion_relation(X1)
<=> ( relation_field(X2) = X1
& ! [X3,X4] :
( ( in(X3,X1)
& in(X4,X1) )
=> ( in(ordered_pair(X3,X4),X2)
<=> subset(X3,X4) ) ) ) ) ),
file('<stdin>',d1_wellord2) ).
fof(c_0_21,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_22,axiom,
! [X1,X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& X7 = singleton(X6) )
& X3 = X5
& ? [X8,X9] :
( ordered_pair(X8,X9) = X5
& in(X8,X1)
& X9 = singleton(X8) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,cartesian_product2(X1,X2))
& X5 = X4
& ? [X10,X11] :
( ordered_pair(X10,X11) = X4
& in(X10,X1)
& X11 = singleton(X10) ) ) ) ),
file('<stdin>',s1_tarski__e16_22__wellord2__2) ).
fof(c_0_23,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_24,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_25,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_26,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_27,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_28,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_29,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_30,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_31,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X1) )
& X3 = X5
& ? [X7] :
( ordinal(X7)
& X5 = X7
& in(X7,X1) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,succ(X2))
& X5 = X4
& ? [X8] :
( ordinal(X8)
& X4 = X8
& in(X8,X1) ) ) ) ) ),
file('<stdin>',s1_tarski__e8_6__wellord2__1) ).
fof(c_0_32,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('<stdin>',d1_funct_2) ).
fof(c_0_33,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_34,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
file('<stdin>',dt_k5_relset_1) ).
fof(c_0_35,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
file('<stdin>',dt_k4_relset_1) ).
fof(c_0_36,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_37,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_38,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_39,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('<stdin>',dt_m2_relset_1) ).
fof(c_0_40,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_41,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
file('<stdin>',redefinition_k5_relset_1) ).
fof(c_0_42,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('<stdin>',redefinition_k4_relset_1) ).
fof(c_0_43,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('<stdin>',redefinition_m2_relset_1) ).
fof(c_0_44,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_45,axiom,
! [X1] :
( function(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) ),
file('<stdin>',d1_funct_1) ).
fof(c_0_46,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_47,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_48,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_49,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_50,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_51,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('<stdin>',d1_relset_1) ).
fof(c_0_52,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_53,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('<stdin>',cc1_relset_1) ).
fof(c_0_54,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_55,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('<stdin>',t7_tarski) ).
fof(c_0_56,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_57,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_58,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('<stdin>',d1_relat_1) ).
fof(c_0_59,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_second(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X4 ) ) ),
file('<stdin>',d2_mcart_1) ).
fof(c_0_60,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_first(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X3 ) ) ),
file('<stdin>',d1_mcart_1) ).
fof(c_0_61,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_62,axiom,
! [X1] :
( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& in(X2,X1)
& X4 = singleton(X2) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(X4,X1)
& X3 = singleton(X4) ) ) ),
file('<stdin>',s1_tarski__e16_22__wellord2__1) ).
fof(c_0_63,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_64,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_65,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_66,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3) ),
file('<stdin>',rc2_partfun1) ).
fof(c_0_67,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3)
& quasi_total(X3,X1,X2) ),
file('<stdin>',rc1_funct_2) ).
fof(c_0_68,axiom,
! [X1,X2] :
? [X3] : relation_of2_as_subset(X3,X1,X2),
file('<stdin>',existence_m2_relset_1) ).
fof(c_0_69,axiom,
! [X1,X2] :
? [X3] : relation_of2(X3,X1,X2),
file('<stdin>',existence_m1_relset_1) ).
fof(c_0_70,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k3_subset_1) ).
fof(c_0_71,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_72,axiom,
! [X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ordinal(X3)
& X2 = X4
& ordinal(X4) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& X4 = X3
& ordinal(X3) ) ) ),
file('<stdin>',s1_tarski__e6_22__wellord2__1) ).
fof(c_0_73,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k3_subset_1) ).
fof(c_0_74,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_75,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('<stdin>',redefinition_k5_setfam_1) ).
fof(c_0_76,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('<stdin>',t4_subset) ).
fof(c_0_77,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_78,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('<stdin>',d6_wellord1) ).
fof(c_0_79,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('<stdin>',d5_subset_1) ).
fof(c_0_80,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_81,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_82,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('<stdin>',fc4_subset_1) ).
fof(c_0_83,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> ? [X3] :
( relation(X3)
& function(X3)
& one_to_one(X3)
& relation_dom(X3) = X1
& relation_rng(X3) = X2 ) ),
file('<stdin>',d4_wellord2) ).
fof(c_0_84,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_85,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_86,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('<stdin>',redefinition_r1_ordinal1) ).
fof(c_0_87,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('<stdin>',fc3_subset_1) ).
fof(c_0_88,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_89,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_90,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_91,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('<stdin>',t3_subset) ).
fof(c_0_92,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_93,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_94,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_95,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_96,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_97,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
file('<stdin>',fc3_relat_1) ).
fof(c_0_98,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('<stdin>',fc2_relat_1) ).
fof(c_0_99,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('<stdin>',fc1_relat_1) ).
fof(c_0_100,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_101,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_102,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('<stdin>',dt_k5_relat_1) ).
fof(c_0_103,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('<stdin>',d2_ordinal1) ).
fof(c_0_104,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('<stdin>',d9_relat_2) ).
fof(c_0_105,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
file('<stdin>',d16_relat_2) ).
fof(c_0_106,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('<stdin>',d14_relat_2) ).
fof(c_0_107,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('<stdin>',d12_relat_2) ).
fof(c_0_108,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('<stdin>',cc2_finset_1) ).
fof(c_0_109,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('<stdin>',connectedness_r1_ordinal1) ).
fof(c_0_110,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('<stdin>',t2_subset) ).
fof(c_0_111,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_112,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_113,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('<stdin>',fc11_finset_1) ).
fof(c_0_114,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
file('<stdin>',fc10_finset_1) ).
fof(c_0_115,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('<stdin>',dt_k8_relat_1) ).
fof(c_0_116,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('<stdin>',dt_k7_relat_1) ).
fof(c_0_117,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('<stdin>',dt_k2_wellord1) ).
fof(c_0_118,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('<stdin>',d6_relat_1) ).
fof(c_0_119,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('<stdin>',t1_subset) ).
fof(c_0_120,axiom,
! [X1,X2] :
( equipotent(X1,X2)
=> equipotent(X2,X1) ),
file('<stdin>',symmetry_r2_wellord2) ).
fof(c_0_121,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_122,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> are_equipotent(X1,X2) ),
file('<stdin>',redefinition_r2_wellord2) ).
fof(c_0_123,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_124,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
file('<stdin>',cc1_arytm_3) ).
fof(c_0_125,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_126,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('<stdin>',rc3_finset_1) ).
fof(c_0_127,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_128,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_129,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('<stdin>',d9_funct_1) ).
fof(c_0_130,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('<stdin>',reflexivity_r1_ordinal1) ).
fof(c_0_131,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('<stdin>',fc6_relat_1) ).
fof(c_0_132,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('<stdin>',fc5_relat_1) ).
fof(c_0_133,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_134,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_135,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_136,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_137,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('<stdin>',rc2_finset_1) ).
fof(c_0_138,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('<stdin>',dt_k2_subset_1) ).
fof(c_0_139,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_140,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_141,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('<stdin>',dt_k2_funct_1) ).
fof(c_0_142,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('<stdin>',d1_ordinal1) ).
fof(c_0_143,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_144,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_145,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_146,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('<stdin>',d4_ordinal1) ).
fof(c_0_147,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('<stdin>',cc2_ordinal1) ).
fof(c_0_148,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('<stdin>',cc2_arytm_3) ).
fof(c_0_149,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('<stdin>',involutiveness_k4_relat_1) ).
fof(c_0_150,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('<stdin>',fc8_relat_1) ).
fof(c_0_151,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('<stdin>',fc7_relat_1) ).
fof(c_0_152,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
file('<stdin>',fc4_ordinal1) ).
fof(c_0_153,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
file('<stdin>',fc11_relat_1) ).
fof(c_0_154,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('<stdin>',dt_k4_relat_1) ).
fof(c_0_155,axiom,
! [X1] : ~ empty(singleton(X1)),
file('<stdin>',fc2_subset_1) ).
fof(c_0_156,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_157,axiom,
! [X1] : ~ empty(succ(X1)),
file('<stdin>',fc1_ordinal1) ).
fof(c_0_158,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_159,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_160,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_161,axiom,
! [X1,X2] : equipotent(X1,X1),
file('<stdin>',reflexivity_r2_wellord2) ).
fof(c_0_162,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_163,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_164,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_165,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_166,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_167,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
file('<stdin>',d6_ordinal1) ).
fof(c_0_168,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('<stdin>',cc3_ordinal1) ).
fof(c_0_169,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('<stdin>',cc1_relat_1) ).
fof(c_0_170,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('<stdin>',cc1_ordinal1) ).
fof(c_0_171,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('<stdin>',cc1_funct_1) ).
fof(c_0_172,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('<stdin>',cc1_finset_1) ).
fof(c_0_173,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('<stdin>',fc2_funct_1) ).
fof(c_0_174,axiom,
! [X1] : relation(identity_relation(X1)),
file('<stdin>',dt_k6_relat_1) ).
fof(c_0_175,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('<stdin>',dt_k1_wellord2) ).
fof(c_0_176,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_177,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('<stdin>',d4_subset_1) ).
fof(c_0_178,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc3_ordinal1) ).
fof(c_0_179,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_180,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_181,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('<stdin>',rc1_finset_1) ).
fof(c_0_182,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('<stdin>',rc1_arytm_3) ).
fof(c_0_183,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('<stdin>',rc4_funct_1) ).
fof(c_0_184,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_185,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_186,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_187,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_188,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_189,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_190,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
file('<stdin>',rc1_partfun1) ).
fof(c_0_191,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc1_ordinal1) ).
fof(c_0_192,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_193,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('<stdin>',fc4_relat_1) ).
fof(c_0_194,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_195,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_196,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('<stdin>',fc12_relat_1) ).
fof(c_0_197,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_198,axiom,
$true,
file('<stdin>',dt_m1_relset_1) ).
fof(c_0_199,axiom,
$true,
file('<stdin>',dt_k9_relat_1) ).
fof(c_0_200,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_201,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_202,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_203,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_204,axiom,
$true,
file('<stdin>',dt_k3_relat_1) ).
fof(c_0_205,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_206,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_207,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_208,axiom,
$true,
file('<stdin>',dt_k2_relat_1) ).
fof(c_0_209,axiom,
$true,
file('<stdin>',dt_k2_mcart_1) ).
fof(c_0_210,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_211,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_212,axiom,
$true,
file('<stdin>',dt_k1_wellord1) ).
fof(c_0_213,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_214,axiom,
$true,
file('<stdin>',dt_k1_setfam_1) ).
fof(c_0_215,axiom,
$true,
file('<stdin>',dt_k1_relat_1) ).
fof(c_0_216,axiom,
$true,
file('<stdin>',dt_k1_ordinal1) ).
fof(c_0_217,axiom,
$true,
file('<stdin>',dt_k1_mcart_1) ).
fof(c_0_218,axiom,
$true,
file('<stdin>',dt_k1_funct_1) ).
fof(c_0_219,axiom,
$true,
file('<stdin>',dt_k1_enumset1) ).
fof(c_0_220,axiom,
$true,
file('<stdin>',dt_k10_relat_1) ).
fof(c_0_221,plain,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ! [X3] :
( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( ordered_pair(X7,X8) = X5
& in(X7,X1)
& ? [X9] :
( X7 = X9
& in(X8,X9)
& ! [X10] :
( in(X10,X9)
=> in(ordered_pair(X8,X10),X2) ) ) )
& X4 = X6
& ? [X11,X12] :
( ordered_pair(X11,X12) = X6
& in(X11,X1)
& ? [X13] :
( X11 = X13
& in(X12,X13)
& ! [X14] :
( in(X14,X13)
=> in(ordered_pair(X12,X14),X2) ) ) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(X1,X3))
& X6 = X5
& ? [X15,X16] :
( ordered_pair(X15,X16) = X5
& in(X15,X1)
& ? [X17] :
( X15 = X17
& in(X16,X17)
& ! [X18] :
( in(X18,X17)
=> in(ordered_pair(X16,X18),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_222,plain,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& in(X3,X1)
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X1)
& in(X5,X1)
& ? [X10] :
( X5 = X10
& in(X4,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X4,X11),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_223,axiom,
! [X1,X2,X3] :
( ( relation(X2)
& relation(X3)
& function(X3) )
=> ( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( X5 = ordered_pair(X7,X8)
& in(ordered_pair(apply(X3,X7),apply(X3,X8)),X2) )
& X4 = X6
& ? [X9,X10] :
( X6 = ordered_pair(X9,X10)
& in(ordered_pair(apply(X3,X9),apply(X3,X10)),X2) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(X1,X1))
& X6 = X5
& ? [X11,X12] :
( X5 = ordered_pair(X11,X12)
& in(ordered_pair(apply(X3,X11),apply(X3,X12)),X2) ) ) ) ) ),
c_0_2 ).
fof(c_0_224,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_3 ).
fof(c_0_225,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
<=> ( relation_dom(X3) = relation_field(X1)
& relation_rng(X3) = relation_field(X2)
& one_to_one(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
<=> ( in(X4,relation_field(X1))
& in(X5,relation_field(X1))
& in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2) ) ) ) ) ) ) ),
c_0_4 ).
fof(c_0_226,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_5 ).
fof(c_0_227,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_6 ).
fof(c_0_228,axiom,
! [X1,X2,X3,X4] :
( X4 = unordered_triple(X1,X2,X3)
<=> ! [X5] :
( in(X5,X4)
<=> ~ ( X5 != X1
& X5 != X2
& X5 != X3 ) ) ),
c_0_7 ).
fof(c_0_229,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_8 ).
fof(c_0_230,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_9 ).
fof(c_0_231,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_10 ).
fof(c_0_232,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_11 ).
fof(c_0_233,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_12 ).
fof(c_0_234,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = fiber(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 != X2
& in(ordered_pair(X4,X2),X1) ) ) ) ),
c_0_13 ).
fof(c_0_235,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_14 ).
fof(c_0_236,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_15 ).
fof(c_0_237,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_16]) ).
fof(c_0_238,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_17 ).
fof(c_0_239,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_18 ).
fof(c_0_240,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_19 ).
fof(c_0_241,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = inclusion_relation(X1)
<=> ( relation_field(X2) = X1
& ! [X3,X4] :
( ( in(X3,X1)
& in(X4,X1) )
=> ( in(ordered_pair(X3,X4),X2)
<=> subset(X3,X4) ) ) ) ) ),
c_0_20 ).
fof(c_0_242,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
c_0_21 ).
fof(c_0_243,axiom,
! [X1,X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& X7 = singleton(X6) )
& X3 = X5
& ? [X8,X9] :
( ordered_pair(X8,X9) = X5
& in(X8,X1)
& X9 = singleton(X8) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,cartesian_product2(X1,X2))
& X5 = X4
& ? [X10,X11] :
( ordered_pair(X10,X11) = X4
& in(X10,X1)
& X11 = singleton(X10) ) ) ) ),
c_0_22 ).
fof(c_0_244,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_23 ).
fof(c_0_245,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_24 ).
fof(c_0_246,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
c_0_25 ).
fof(c_0_247,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
c_0_26 ).
fof(c_0_248,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_27 ).
fof(c_0_249,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_28 ).
fof(c_0_250,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_29]) ).
fof(c_0_251,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
c_0_30 ).
fof(c_0_252,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X1) )
& X3 = X5
& ? [X7] :
( ordinal(X7)
& X5 = X7
& in(X7,X1) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,succ(X2))
& X5 = X4
& ? [X8] :
( ordinal(X8)
& X4 = X8
& in(X8,X1) ) ) ) ) ),
c_0_31 ).
fof(c_0_253,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
c_0_32 ).
fof(c_0_254,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_33 ).
fof(c_0_255,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
c_0_34 ).
fof(c_0_256,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
c_0_35 ).
fof(c_0_257,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_36 ).
fof(c_0_258,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
c_0_37 ).
fof(c_0_259,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_38 ).
fof(c_0_260,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
c_0_39 ).
fof(c_0_261,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_40 ).
fof(c_0_262,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
c_0_41 ).
fof(c_0_263,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
c_0_42 ).
fof(c_0_264,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
c_0_43 ).
fof(c_0_265,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_44 ).
fof(c_0_266,axiom,
! [X1] :
( function(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) ),
c_0_45 ).
fof(c_0_267,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_46 ).
fof(c_0_268,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
c_0_47 ).
fof(c_0_269,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_48 ).
fof(c_0_270,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_49 ).
fof(c_0_271,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_50 ).
fof(c_0_272,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
c_0_51 ).
fof(c_0_273,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_52]) ).
fof(c_0_274,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
c_0_53 ).
fof(c_0_275,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
c_0_54 ).
fof(c_0_276,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
c_0_55 ).
fof(c_0_277,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
c_0_56 ).
fof(c_0_278,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
c_0_57 ).
fof(c_0_279,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
c_0_58 ).
fof(c_0_280,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_second(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X4 ) ) ),
c_0_59 ).
fof(c_0_281,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_first(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X3 ) ) ),
c_0_60 ).
fof(c_0_282,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_61]) ).
fof(c_0_283,axiom,
! [X1] :
( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& in(X2,X1)
& X4 = singleton(X2) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(X4,X1)
& X3 = singleton(X4) ) ) ),
c_0_62 ).
fof(c_0_284,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_63 ).
fof(c_0_285,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
c_0_64 ).
fof(c_0_286,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_65]) ).
fof(c_0_287,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3) ),
c_0_66 ).
fof(c_0_288,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3)
& quasi_total(X3,X1,X2) ),
c_0_67 ).
fof(c_0_289,axiom,
! [X1,X2] :
? [X3] : relation_of2_as_subset(X3,X1,X2),
c_0_68 ).
fof(c_0_290,axiom,
! [X1,X2] :
? [X3] : relation_of2(X3,X1,X2),
c_0_69 ).
fof(c_0_291,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
c_0_70 ).
fof(c_0_292,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_71 ).
fof(c_0_293,axiom,
! [X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ordinal(X3)
& X2 = X4
& ordinal(X4) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& X4 = X3
& ordinal(X3) ) ) ),
c_0_72 ).
fof(c_0_294,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
c_0_73 ).
fof(c_0_295,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
c_0_74 ).
fof(c_0_296,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
c_0_75 ).
fof(c_0_297,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
c_0_76 ).
fof(c_0_298,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_77 ).
fof(c_0_299,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
c_0_78 ).
fof(c_0_300,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
c_0_79 ).
fof(c_0_301,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_80 ).
fof(c_0_302,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
c_0_81 ).
fof(c_0_303,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_304,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> ? [X3] :
( relation(X3)
& function(X3)
& one_to_one(X3)
& relation_dom(X3) = X1
& relation_rng(X3) = X2 ) ),
c_0_83 ).
fof(c_0_305,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_306,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_307,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
c_0_86 ).
fof(c_0_308,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_309,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_310,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_89 ).
fof(c_0_311,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
c_0_90 ).
fof(c_0_312,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
c_0_91 ).
fof(c_0_313,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_314,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_315,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
c_0_94 ).
fof(c_0_316,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
c_0_95 ).
fof(c_0_317,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
c_0_96 ).
fof(c_0_318,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
c_0_97 ).
fof(c_0_319,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
c_0_98 ).
fof(c_0_320,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
c_0_99 ).
fof(c_0_321,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_100 ).
fof(c_0_322,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
c_0_101 ).
fof(c_0_323,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
c_0_102 ).
fof(c_0_324,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
c_0_103 ).
fof(c_0_325,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
c_0_104 ).
fof(c_0_326,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
c_0_105 ).
fof(c_0_327,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
c_0_106 ).
fof(c_0_328,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
c_0_107 ).
fof(c_0_329,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
c_0_108 ).
fof(c_0_330,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
c_0_109 ).
fof(c_0_331,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
c_0_110 ).
fof(c_0_332,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_111]) ).
fof(c_0_333,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_112 ).
fof(c_0_334,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
c_0_113 ).
fof(c_0_335,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
c_0_114 ).
fof(c_0_336,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
c_0_115 ).
fof(c_0_337,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
c_0_116 ).
fof(c_0_338,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
c_0_117 ).
fof(c_0_339,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
c_0_118 ).
fof(c_0_340,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
c_0_119 ).
fof(c_0_341,axiom,
! [X1,X2] :
( equipotent(X1,X2)
=> equipotent(X2,X1) ),
c_0_120 ).
fof(c_0_342,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_121 ).
fof(c_0_343,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> are_equipotent(X1,X2) ),
c_0_122 ).
fof(c_0_344,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_123 ).
fof(c_0_345,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
c_0_124 ).
fof(c_0_346,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
c_0_125 ).
fof(c_0_347,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_348,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_349,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_128 ).
fof(c_0_350,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
c_0_129 ).
fof(c_0_351,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
c_0_130 ).
fof(c_0_352,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_353,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_354,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_133 ).
fof(c_0_355,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_134 ).
fof(c_0_356,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_135 ).
fof(c_0_357,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_136 ).
fof(c_0_358,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
c_0_137 ).
fof(c_0_359,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
c_0_138 ).
fof(c_0_360,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_139 ).
fof(c_0_361,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_362,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
c_0_141 ).
fof(c_0_363,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
c_0_142 ).
fof(c_0_364,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_143]) ).
fof(c_0_365,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_366,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_145 ).
fof(c_0_367,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
c_0_146 ).
fof(c_0_368,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
c_0_147 ).
fof(c_0_369,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
c_0_148 ).
fof(c_0_370,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
c_0_149 ).
fof(c_0_371,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
c_0_150 ).
fof(c_0_372,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
c_0_151 ).
fof(c_0_373,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
c_0_152 ).
fof(c_0_374,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
c_0_153 ).
fof(c_0_375,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
c_0_154 ).
fof(c_0_376,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_377,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_378,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_379,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_158 ).
fof(c_0_380,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_159 ).
fof(c_0_381,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_160 ).
fof(c_0_382,axiom,
! [X1,X2] : equipotent(X1,X1),
c_0_161 ).
fof(c_0_383,axiom,
! [X1,X2] : subset(X1,X1),
c_0_162 ).
fof(c_0_384,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_163 ).
fof(c_0_385,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_164 ).
fof(c_0_386,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_165 ).
fof(c_0_387,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_166 ).
fof(c_0_388,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
c_0_167 ).
fof(c_0_389,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
c_0_168 ).
fof(c_0_390,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
c_0_169 ).
fof(c_0_391,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
c_0_170 ).
fof(c_0_392,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
c_0_171 ).
fof(c_0_393,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
c_0_172 ).
fof(c_0_394,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
c_0_173 ).
fof(c_0_395,axiom,
! [X1] : relation(identity_relation(X1)),
c_0_174 ).
fof(c_0_396,axiom,
! [X1] : relation(inclusion_relation(X1)),
c_0_175 ).
fof(c_0_397,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_176 ).
fof(c_0_398,axiom,
! [X1] : cast_to_subset(X1) = X1,
c_0_177 ).
fof(c_0_399,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_400,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_401,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_402,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_403,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_404,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
c_0_183 ).
fof(c_0_405,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_184 ).
fof(c_0_406,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_185 ).
fof(c_0_407,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_186 ).
fof(c_0_408,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_187 ).
fof(c_0_409,axiom,
? [X1] : empty(X1),
c_0_188 ).
fof(c_0_410,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_189 ).
fof(c_0_411,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
c_0_190 ).
fof(c_0_412,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_191 ).
fof(c_0_413,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_192 ).
fof(c_0_414,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_193 ).
fof(c_0_415,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_194 ).
fof(c_0_416,axiom,
empty(empty_set),
c_0_195 ).
fof(c_0_417,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_196 ).
fof(c_0_418,axiom,
$true,
c_0_197 ).
fof(c_0_419,axiom,
$true,
c_0_198 ).
fof(c_0_420,axiom,
$true,
c_0_199 ).
fof(c_0_421,axiom,
$true,
c_0_200 ).
fof(c_0_422,axiom,
$true,
c_0_201 ).
fof(c_0_423,axiom,
$true,
c_0_202 ).
fof(c_0_424,axiom,
$true,
c_0_203 ).
fof(c_0_425,axiom,
$true,
c_0_204 ).
fof(c_0_426,axiom,
$true,
c_0_205 ).
fof(c_0_427,axiom,
$true,
c_0_206 ).
fof(c_0_428,axiom,
$true,
c_0_207 ).
fof(c_0_429,axiom,
$true,
c_0_208 ).
fof(c_0_430,axiom,
$true,
c_0_209 ).
fof(c_0_431,axiom,
$true,
c_0_210 ).
fof(c_0_432,axiom,
$true,
c_0_211 ).
fof(c_0_433,axiom,
$true,
c_0_212 ).
fof(c_0_434,axiom,
$true,
c_0_213 ).
fof(c_0_435,axiom,
$true,
c_0_214 ).
fof(c_0_436,axiom,
$true,
c_0_215 ).
fof(c_0_437,axiom,
$true,
c_0_216 ).
fof(c_0_438,axiom,
$true,
c_0_217 ).
fof(c_0_439,axiom,
$true,
c_0_218 ).
fof(c_0_440,axiom,
$true,
c_0_219 ).
fof(c_0_441,axiom,
$true,
c_0_220 ).
fof(c_0_442,plain,
! [X19,X20,X27,X31,X32,X34,X39,X40,X41,X42,X43,X44] :
( ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ordered_pair(esk126_2(X19,X20),esk127_2(X19,X20)) = esk124_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk126_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk126_2(X19,X20) = esk128_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk127_2(X19,X20),esk128_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ~ in(X27,esk128_2(X19,X20))
| in(ordered_pair(esk127_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk123_2(X19,X20) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ordered_pair(esk129_2(X19,X20),esk130_2(X19,X20)) = esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk129_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk129_2(X19,X20) = esk131_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| in(esk130_2(X19,X20),esk131_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| ~ in(X31,esk131_2(X19,X20))
| in(ordered_pair(esk130_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk133_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk133_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk134_4(X19,X20,X32,X34),esk135_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk134_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk134_4(X19,X20,X32,X34) = esk136_4(X19,X20,X32,X34)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk135_4(X19,X20,X32,X34),esk136_4(X19,X20,X32,X34))
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk136_4(X19,X20,X32,X34))
| in(ordered_pair(esk135_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk137_8(X19,X20,X32,X40,X41,X42,X43,X44),X44)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk137_8(X19,X20,X32,X40,X41,X42,X43,X44)),X20)
| ~ in(X43,X44)
| X42 != X44
| ~ in(X42,X19)
| ordered_pair(X42,X43) != X40
| X41 != X40
| ~ in(X41,cartesian_product2(X19,X32))
| in(X40,esk132_3(X19,X20,X32))
| esk124_2(X19,X20) != esk125_2(X19,X20)
| empty(X19)
| ~ relation(X20) ) ),
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_221])])])])])]) ).
fof(c_0_443,plain,
! [X12,X13,X18,X20,X22,X25,X26,X27,X28] :
( ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk117_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk115_2(X12,X13),esk117_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| ~ in(X18,esk117_2(X12,X13))
| in(ordered_pair(esk115_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk114_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| esk114_2(X12,X13) = esk118_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| in(esk116_2(X12,X13),esk118_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| ~ in(X20,esk118_2(X12,X13))
| in(ordered_pair(esk116_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk120_3(X12,X13,X22),X12)
| ~ in(X22,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( esk120_3(X12,X13,X22) = esk121_3(X12,X13,X22)
| ~ in(X22,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk121_3(X12,X13,X22))
| ~ in(X22,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk121_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk122_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk122_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk119_2(X12,X13))
| esk115_2(X12,X13) != esk116_2(X12,X13)
| empty(X12)
| ~ relation(X13) ) ),
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_444,plain,
! [X13,X14,X15,X24,X28,X29,X30,X31] :
( ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk155_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk155_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk155_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk155_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk155_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) = ordered_pair(esk157_3(X13,X14,X15),esk158_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) = ordered_pair(esk157_3(X13,X14,X15),esk158_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) = ordered_pair(esk157_3(X13,X14,X15),esk158_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) = ordered_pair(esk157_3(X13,X14,X15),esk158_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) = ordered_pair(esk157_3(X13,X14,X15),esk158_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk157_3(X13,X14,X15)),apply(X15,esk158_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk157_3(X13,X14,X15)),apply(X15,esk158_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk157_3(X13,X14,X15)),apply(X15,esk158_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk157_3(X13,X14,X15)),apply(X15,esk158_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk157_3(X13,X14,X15)),apply(X15,esk158_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| esk154_3(X13,X14,X15) = esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk156_3(X13,X14,X15) = ordered_pair(esk159_3(X13,X14,X15),esk160_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| esk156_3(X13,X14,X15) = ordered_pair(esk159_3(X13,X14,X15),esk160_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk156_3(X13,X14,X15) = ordered_pair(esk159_3(X13,X14,X15),esk160_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| esk156_3(X13,X14,X15) = ordered_pair(esk159_3(X13,X14,X15),esk160_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| esk156_3(X13,X14,X15) = ordered_pair(esk159_3(X13,X14,X15),esk160_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk159_3(X13,X14,X15)),apply(X15,esk160_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk159_3(X13,X14,X15)),apply(X15,esk160_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk159_3(X13,X14,X15)),apply(X15,esk160_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk159_3(X13,X14,X15)),apply(X15,esk160_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk159_3(X13,X14,X15)),apply(X15,esk160_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk162_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) != esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk162_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) != esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk163_4(X13,X14,X15,X24),esk164_4(X13,X14,X15,X24))
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) != esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk163_4(X13,X14,X15,X24)),apply(X15,esk164_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) != esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X29,cartesian_product2(X13,X13))
| X29 != X28
| X28 != ordered_pair(X30,X31)
| ~ in(ordered_pair(apply(X15,X30),apply(X15,X31)),X14)
| in(X28,esk161_3(X13,X14,X15))
| esk155_3(X13,X14,X15) != esk156_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) ) ),
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_223])])])])])]) ).
fof(c_0_445,plain,
! [X7,X8,X9,X10,X11,X13,X14,X15,X18] :
( ( in(ordered_pair(X10,esk82_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(esk82_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(esk83_3(X7,X8,X9),esk84_3(X7,X8,X9)),X9)
| ~ in(ordered_pair(esk83_3(X7,X8,X9),X18),X7)
| ~ in(ordered_pair(X18,esk84_3(X7,X8,X9)),X8)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk83_3(X7,X8,X9),esk85_3(X7,X8,X9)),X7)
| in(ordered_pair(esk83_3(X7,X8,X9),esk84_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk85_3(X7,X8,X9),esk84_3(X7,X8,X9)),X8)
| in(ordered_pair(esk83_3(X7,X8,X9),esk84_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_224])])])])])]) ).
fof(c_0_446,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( relation_dom(X8) = relation_field(X6)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( relation_rng(X8) = relation_field(X7)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( one_to_one(X8)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( in(X9,relation_field(X6))
| ~ in(ordered_pair(X9,X10),X6)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( in(X10,relation_field(X6))
| ~ in(ordered_pair(X9,X10),X6)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( in(ordered_pair(apply(X8,X9),apply(X8,X10)),X7)
| ~ in(ordered_pair(X9,X10),X6)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( ~ in(X11,relation_field(X6))
| ~ in(X12,relation_field(X6))
| ~ in(ordered_pair(apply(X8,X11),apply(X8,X12)),X7)
| in(ordered_pair(X11,X12),X6)
| ~ relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk78_3(X6,X7,X8),esk79_3(X6,X7,X8)),X6)
| ~ in(esk78_3(X6,X7,X8),relation_field(X6))
| ~ in(esk79_3(X6,X7,X8),relation_field(X6))
| ~ in(ordered_pair(apply(X8,esk78_3(X6,X7,X8)),apply(X8,esk79_3(X6,X7,X8))),X7)
| ~ one_to_one(X8)
| relation_rng(X8) != relation_field(X7)
| relation_dom(X8) != relation_field(X6)
| relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( in(esk78_3(X6,X7,X8),relation_field(X6))
| in(ordered_pair(esk78_3(X6,X7,X8),esk79_3(X6,X7,X8)),X6)
| ~ one_to_one(X8)
| relation_rng(X8) != relation_field(X7)
| relation_dom(X8) != relation_field(X6)
| relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( in(esk79_3(X6,X7,X8),relation_field(X6))
| in(ordered_pair(esk78_3(X6,X7,X8),esk79_3(X6,X7,X8)),X6)
| ~ one_to_one(X8)
| relation_rng(X8) != relation_field(X7)
| relation_dom(X8) != relation_field(X6)
| relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ relation(X6) )
& ( in(ordered_pair(apply(X8,esk78_3(X6,X7,X8)),apply(X8,esk79_3(X6,X7,X8))),X7)
| in(ordered_pair(esk78_3(X6,X7,X8),esk79_3(X6,X7,X8)),X6)
| ~ one_to_one(X8)
| relation_rng(X8) != relation_field(X7)
| relation_dom(X8) != relation_field(X6)
| relation_isomorphism(X6,X7,X8)
| ~ relation(X8)
| ~ function(X8)
| ~ relation(X7)
| ~ 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_225])])])])])]) ).
fof(c_0_447,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_226])])])])])]) ).
fof(c_0_448,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_227])])])])])]) ).
fof(c_0_449,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_228])])])])])]) ).
fof(c_0_450,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_229])])])])])]) ).
fof(c_0_451,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_230])])])])])]) ).
fof(c_0_452,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk45_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk46_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk45_4(X7,X8,X9,X10),esk46_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(esk47_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk47_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk48_3(X16,X17,X18),X16)
| in(esk47_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk49_3(X16,X17,X18),X17)
| in(esk47_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk47_3(X16,X17,X18) = ordered_pair(esk48_3(X16,X17,X18),esk49_3(X16,X17,X18))
| in(esk47_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_231])])])])])]) ).
fof(c_0_453,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_232])])])])])]) ).
fof(c_0_454,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(esk89_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk89_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk89_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk89_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk89_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_233])])])])]) ).
fof(c_0_455,plain,
! [X5,X6,X7,X8,X9,X10,X11] :
( ( X8 != X6
| ~ in(X8,X7)
| X7 != fiber(X5,X6)
| ~ relation(X5) )
& ( in(ordered_pair(X8,X6),X5)
| ~ in(X8,X7)
| X7 != fiber(X5,X6)
| ~ relation(X5) )
& ( X9 = X6
| ~ in(ordered_pair(X9,X6),X5)
| in(X9,X7)
| X7 != fiber(X5,X6)
| ~ relation(X5) )
& ( ~ in(esk31_3(X5,X10,X11),X11)
| esk31_3(X5,X10,X11) = X10
| ~ in(ordered_pair(esk31_3(X5,X10,X11),X10),X5)
| X11 = fiber(X5,X10)
| ~ relation(X5) )
& ( esk31_3(X5,X10,X11) != X10
| in(esk31_3(X5,X10,X11),X11)
| X11 = fiber(X5,X10)
| ~ relation(X5) )
& ( in(ordered_pair(esk31_3(X5,X10,X11),X10),X5)
| in(esk31_3(X5,X10,X11),X11)
| X11 = fiber(X5,X10)
| ~ 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_234])])])])])]) ).
fof(c_0_456,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(esk57_3(X10,X11,X12),X12)
| ~ in(esk57_3(X10,X11,X12),X10)
| ~ in(esk57_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk57_3(X10,X11,X12),X10)
| in(esk57_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk57_3(X10,X11,X12),X11)
| in(esk57_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_235])])])])])]) ).
fof(c_0_457,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_236])])])])])]) ).
fof(c_0_458,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(esk67_3(X10,X11,X12),X12)
| ~ in(esk67_3(X10,X11,X12),X10)
| in(esk67_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk67_3(X10,X11,X12),X10)
| in(esk67_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk67_3(X10,X11,X12),X11)
| in(esk67_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_237])])])])])]) ).
fof(c_0_459,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(esk76_2(X5,X6),esk77_2(X5,X6)),X6)
| ~ in(ordered_pair(esk77_2(X5,X6),esk76_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk76_2(X5,X6),esk77_2(X5,X6)),X6)
| in(ordered_pair(esk77_2(X5,X6),esk76_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_238])])])])])]) ).
fof(c_0_460,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(esk39_2(X5,X6),esk40_2(X5,X6)),X5)
| ~ in(ordered_pair(esk39_2(X5,X6),esk40_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk39_2(X5,X6),esk40_2(X5,X6)),X5)
| in(ordered_pair(esk39_2(X5,X6),esk40_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_239])])])])])]) ).
fof(c_0_461,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(esk44_3(X10,X11,X12),X10)
| ~ in(esk44_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk44_3(X10,X11,X12),X11)
| ~ in(esk44_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk44_3(X10,X11,X12),X12)
| in(esk44_3(X10,X11,X12),X10)
| in(esk44_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_240])])])])])]) ).
fof(c_0_462,plain,
! [X5,X6,X7,X8] :
( ( relation_field(X6) = X5
| X6 != inclusion_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(X7,X8),X6)
| subset(X7,X8)
| ~ in(X7,X5)
| ~ in(X8,X5)
| X6 != inclusion_relation(X5)
| ~ relation(X6) )
& ( ~ subset(X7,X8)
| in(ordered_pair(X7,X8),X6)
| ~ in(X7,X5)
| ~ in(X8,X5)
| X6 != inclusion_relation(X5)
| ~ relation(X6) )
& ( in(esk32_2(X5,X6),X5)
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( in(esk33_2(X5,X6),X5)
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk32_2(X5,X6),esk33_2(X5,X6)),X6)
| ~ subset(esk32_2(X5,X6),esk33_2(X5,X6))
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( in(ordered_pair(esk32_2(X5,X6),esk33_2(X5,X6)),X6)
| subset(esk32_2(X5,X6),esk33_2(X5,X6))
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(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_241])])])])]) ).
fof(c_0_463,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_242])])])])])]) ).
fof(c_0_464,plain,
! [X12,X20,X22,X26,X27,X28,X29] :
( ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk144_1(X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk144_1(X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk144_1(X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk144_1(X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk144_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| esk143_1(X12) = esk144_1(X12) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk146_1(X12),esk147_1(X12)) = esk144_1(X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk146_1(X12),esk147_1(X12)) = esk144_1(X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk146_1(X12),esk147_1(X12)) = esk144_1(X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk146_1(X12),esk147_1(X12)) = esk144_1(X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk146_1(X12),esk147_1(X12)) = esk144_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| ordered_pair(esk146_1(X12),esk147_1(X12)) = esk144_1(X12) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| in(esk146_1(X12),X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| in(esk146_1(X12),X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| in(esk146_1(X12),X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| in(esk146_1(X12),X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| in(esk146_1(X12),X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| in(esk146_1(X12),X12) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| esk147_1(X12) = singleton(esk146_1(X12)) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk147_1(X12) = singleton(esk146_1(X12)) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk147_1(X12) = singleton(esk146_1(X12)) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| esk147_1(X12) = singleton(esk146_1(X12)) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| esk147_1(X12) = singleton(esk146_1(X12)) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| esk147_1(X12) = singleton(esk146_1(X12)) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk145_1(X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk145_1(X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk145_1(X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk145_1(X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| esk143_1(X12) = esk145_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| esk143_1(X12) = esk145_1(X12) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk148_1(X12),esk149_1(X12)) = esk145_1(X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk148_1(X12),esk149_1(X12)) = esk145_1(X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk148_1(X12),esk149_1(X12)) = esk145_1(X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk148_1(X12),esk149_1(X12)) = esk145_1(X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| ordered_pair(esk148_1(X12),esk149_1(X12)) = esk145_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| ordered_pair(esk148_1(X12),esk149_1(X12)) = esk145_1(X12) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| in(esk148_1(X12),X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| in(esk148_1(X12),X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| in(esk148_1(X12),X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| in(esk148_1(X12),X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| in(esk148_1(X12),X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| in(esk148_1(X12),X12) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| esk149_1(X12) = singleton(esk148_1(X12)) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk149_1(X12) = singleton(esk148_1(X12)) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk149_1(X12) = singleton(esk148_1(X12)) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| esk149_1(X12) = singleton(esk148_1(X12)) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| esk149_1(X12) = singleton(esk148_1(X12)) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| esk149_1(X12) = singleton(esk148_1(X12)) )
& ( in(esk151_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk150_2(X12,X20))
| esk144_1(X12) != esk145_1(X12) )
& ( esk151_3(X12,X20,X22) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk144_1(X12) != esk145_1(X12) )
& ( ordered_pair(esk152_3(X12,X20,X22),esk153_3(X12,X20,X22)) = X22
| ~ in(X22,esk150_2(X12,X20))
| esk144_1(X12) != esk145_1(X12) )
& ( in(esk152_3(X12,X20,X22),X12)
| ~ in(X22,esk150_2(X12,X20))
| esk144_1(X12) != esk145_1(X12) )
& ( esk153_3(X12,X20,X22) = singleton(esk152_3(X12,X20,X22))
| ~ in(X22,esk150_2(X12,X20))
| esk144_1(X12) != esk145_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk150_2(X12,X20))
| esk144_1(X12) != esk145_1(X12) ) ),
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_243])])])])])]) ).
fof(c_0_465,plain,
! [X5,X6,X7,X9,X11] :
( ( in(esk55_3(X5,X6,X7),X7)
| X7 = empty_set
| ~ subset(X7,X6)
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( disjoint(fiber(X5,esk55_3(X5,X6,X7)),X7)
| X7 = empty_set
| ~ subset(X7,X6)
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( subset(esk56_2(X5,X9),X9)
| is_well_founded_in(X5,X9)
| ~ relation(X5) )
& ( esk56_2(X5,X9) != empty_set
| is_well_founded_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(X11,esk56_2(X5,X9))
| ~ disjoint(fiber(X5,X11),esk56_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_244])])])])])]) ).
fof(c_0_466,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) )
& ( esk41_3(X10,X11,X12) != X10
| ~ in(esk41_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk41_3(X10,X11,X12) != X11
| ~ in(esk41_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk41_3(X10,X11,X12),X12)
| esk41_3(X10,X11,X12) = X10
| esk41_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_245])])])])])]) ).
fof(c_0_467,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk71_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(esk72_2(X5,X11),X11)
| ~ in(ordered_pair(X13,esk72_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk72_2(X5,X11),X11)
| in(ordered_pair(esk73_2(X5,X11),esk72_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_246])])])])])]) ).
fof(c_0_468,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk58_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(esk59_2(X5,X11),X11)
| ~ in(ordered_pair(esk59_2(X5,X11),X13),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk59_2(X5,X11),X11)
| in(ordered_pair(esk59_2(X5,X11),esk60_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_247])])])])])]) ).
fof(c_0_469,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(esk86_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(esk87_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(esk88_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(ordered_pair(esk86_2(X6,X11),esk87_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(ordered_pair(esk87_2(X6,X11),esk88_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk86_2(X6,X11),esk88_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_248])])])])])]) ).
fof(c_0_470,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(esk52_2(X5,X6),esk53_2(X5,X6)),X5)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk52_2(X5,X6),esk53_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_249])])])])]) ).
fof(c_0_471,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(esk74_2(X5,X9),X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( in(esk75_2(X5,X9),X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( esk74_2(X5,X9) != esk75_2(X5,X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk74_2(X5,X9),esk75_2(X5,X9)),X5)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk75_2(X5,X9),esk74_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_250])])])])])]) ).
fof(c_0_472,plain,
! [X4,X5,X6,X7] :
( ( ~ is_reflexive_in(X4,X5)
| ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ relation(X4) )
& ( in(esk26_2(X4,X7),X7)
| is_reflexive_in(X4,X7)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk26_2(X4,X7),esk26_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_251])])])])])]) ).
fof(c_0_473,plain,
! [X9,X10,X17,X20,X21,X22] :
( ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk171_2(X9,X10)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk171_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk171_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk171_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk171_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk171_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk173_2(X9,X10))
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk173_2(X9,X10))
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk173_2(X9,X10))
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk173_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk173_2(X9,X10))
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| ordinal(esk173_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) = esk173_2(X9,X10)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) = esk173_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) = esk173_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) = esk173_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) = esk173_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| esk171_2(X9,X10) = esk173_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| in(esk173_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| in(esk173_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| in(esk173_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| in(esk173_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| in(esk173_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| in(esk173_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| esk170_2(X9,X10) = esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk174_2(X9,X10))
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk174_2(X9,X10))
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk174_2(X9,X10))
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk174_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| ordinal(esk174_2(X9,X10))
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| ordinal(esk174_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| esk172_2(X9,X10) = esk174_2(X9,X10)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| esk172_2(X9,X10) = esk174_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| esk172_2(X9,X10) = esk174_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| esk172_2(X9,X10) = esk174_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| esk172_2(X9,X10) = esk174_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| esk172_2(X9,X10) = esk174_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| in(esk174_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| in(esk174_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| in(esk174_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| in(esk174_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| in(esk174_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| in(esk174_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk176_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) != esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( esk176_3(X9,X10,X17) = X17
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) != esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk177_3(X9,X10,X17))
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) != esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk177_3(X9,X10,X17)
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) != esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk177_3(X9,X10,X17),X9)
| ~ in(X17,esk175_2(X9,X10))
| esk171_2(X9,X10) != esk172_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk175_2(X9,X10))
| esk171_2(X9,X10) != esk172_2(X9,X10)
| ~ ordinal(X10) ) ),
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_474,plain,
! [X4,X5,X6] :
( ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6)
| X5 = empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5)
| X5 = empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6)
| X4 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5)
| X4 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( ~ quasi_total(X6,X4,X5)
| X6 = empty_set
| X4 = empty_set
| X5 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X6 != empty_set
| quasi_total(X6,X4,X5)
| X4 = empty_set
| X5 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_253])])]) ).
fof(c_0_475,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(esk27_3(X5,X6,X9),X5)
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( ~ in(X9,esk27_3(X5,X6,X9))
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk29_2(X5,X11),X5)
| ~ in(esk28_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( ~ in(esk28_2(X5,X11),esk29_2(X5,X11))
| ~ in(esk28_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( in(esk28_2(X5,X11),X11)
| ~ in(X14,X5)
| in(esk28_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_254])])])])])]) ).
fof(c_0_476,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| element(relation_rng_as_subset(X4,X5,X6),powerset(X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_255])]) ).
fof(c_0_477,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| element(relation_dom_as_subset(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_256])]) ).
fof(c_0_478,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(esk61_2(X5,X9),X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(esk62_2(X5,X9),X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(ordered_pair(esk61_2(X5,X9),esk62_2(X5,X9)),X5)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(ordered_pair(esk62_2(X5,X9),esk61_2(X5,X9)),X5)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( esk61_2(X5,X9) != esk62_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_257])])])])])]) ).
fof(c_0_479,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_258])]) ).
fof(c_0_480,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( in(esk68_3(X5,X6,X7),relation_dom(X5))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,esk68_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(esk69_2(X5,X11),X11)
| ~ in(X13,relation_dom(X5))
| esk69_2(X5,X11) != apply(X5,X13)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk70_2(X5,X11),relation_dom(X5))
| in(esk69_2(X5,X11),X11)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk69_2(X5,X11) = apply(X5,esk70_2(X5,X11))
| in(esk69_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_259])])])])])]) ).
fof(c_0_481,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_260])]) ).
fof(c_0_482,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk63_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk63_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk64_2(X11,X12),X12)
| ~ in(esk64_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk64_2(X11,X12),esk65_2(X11,X12))
| in(esk64_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk65_2(X11,X12),X11)
| in(esk64_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_261])])])])])]) ).
fof(c_0_483,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_rng_as_subset(X4,X5,X6) = relation_rng(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_262])]) ).
fof(c_0_484,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_dom_as_subset(X4,X5,X6) = relation_dom(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_263])]) ).
fof(c_0_485,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ relation_of2_as_subset(X6,X4,X5)
| relation_of2(X6,X4,X5) )
& ( ~ relation_of2(X9,X7,X8)
| relation_of2_as_subset(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_264])])])]) ).
fof(c_0_486,plain,
! [X4,X5,X8] :
( ( in(esk42_2(X4,X5),X5)
| X5 = empty_set
| ~ subset(X5,relation_field(X4))
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( disjoint(fiber(X4,esk42_2(X4,X5)),X5)
| X5 = empty_set
| ~ subset(X5,relation_field(X4))
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( subset(esk43_1(X4),relation_field(X4))
| well_founded_relation(X4)
| ~ relation(X4) )
& ( esk43_1(X4) != empty_set
| well_founded_relation(X4)
| ~ relation(X4) )
& ( ~ in(X8,esk43_1(X4))
| ~ disjoint(fiber(X4,X8),esk43_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_265])])])])]) ).
fof(c_0_487,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ function(X5)
| ~ in(ordered_pair(X6,X7),X5)
| ~ in(ordered_pair(X6,X8),X5)
| X7 = X8 )
& ( in(ordered_pair(esk18_1(X9),esk19_1(X9)),X9)
| function(X9) )
& ( in(ordered_pair(esk18_1(X9),esk20_1(X9)),X9)
| function(X9) )
& ( esk19_1(X9) != esk20_1(X9)
| function(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_266])])])])])]) ).
fof(c_0_488,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_267])])])])]) ).
fof(c_0_489,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_268])]) ).
fof(c_0_490,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(esk80_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk81_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk80_1(X4)) = apply(X4,esk81_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk80_1(X4) != esk81_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_269])])])])]) ).
fof(c_0_491,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(esk35_2(X8,X9),X9)
| ~ subset(esk35_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk35_2(X8,X9),X9)
| subset(esk35_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_270])])])])])]) ).
fof(c_0_492,plain,
! [X4,X5] :
( ( ~ in(esk178_2(X4,X5),X4)
| ~ in(esk178_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk178_2(X4,X5),X4)
| in(esk178_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_271])])])]) ).
fof(c_0_493,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ relation_of2(X6,X4,X5)
| subset(X6,cartesian_product2(X4,X5)) )
& ( ~ subset(X9,cartesian_product2(X7,X8))
| relation_of2(X9,X7,X8) ) ),
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_494,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_273])])])])]) ).
fof(c_0_495,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(cartesian_product2(X4,X5)))
| relation(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_274])]) ).
fof(c_0_496,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_275])]) ).
fof(c_0_497,plain,
! [X5,X6,X8] :
( ( in(esk179_2(X5,X6),X6)
| ~ in(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,esk179_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_276])])])])]) ).
fof(c_0_498,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_277])]) ).
fof(c_0_499,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_278])]) ).
fof(c_0_500,plain,
! [X5,X6,X9,X11,X12] :
( ( ~ relation(X5)
| ~ in(X6,X5)
| X6 = ordered_pair(esk23_2(X5,X6),esk24_2(X5,X6)) )
& ( in(esk25_1(X9),X9)
| relation(X9) )
& ( esk25_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_279])])])])])]) ).
fof(c_0_501,plain,
! [X5,X6,X7,X8,X9,X10,X11] :
( ( X8 != pair_second(X5)
| X5 != ordered_pair(X9,X10)
| X8 = X10
| X5 != ordered_pair(X6,X7) )
& ( X5 = ordered_pair(esk36_2(X5,X11),esk37_2(X5,X11))
| X11 = pair_second(X5)
| X5 != ordered_pair(X6,X7) )
& ( X11 != esk37_2(X5,X11)
| X11 = pair_second(X5)
| X5 != ordered_pair(X6,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_280])])])])])]) ).
fof(c_0_502,plain,
! [X5,X6,X7,X8,X9,X10,X11] :
( ( X8 != pair_first(X5)
| X5 != ordered_pair(X9,X10)
| X8 = X9
| X5 != ordered_pair(X6,X7) )
& ( X5 = ordered_pair(esk21_2(X5,X11),esk22_2(X5,X11))
| X11 = pair_first(X5)
| X5 != ordered_pair(X6,X7) )
& ( X11 != esk21_2(X5,X11)
| X11 = pair_first(X5)
| X5 != ordered_pair(X6,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_281])])])])])]) ).
fof(c_0_503,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk180_1(X6))
& ( ~ in(X8,esk180_1(X6))
| ~ subset(X9,X8)
| in(X9,esk180_1(X6)) )
& ( in(esk181_2(X6,X10),esk180_1(X6))
| ~ in(X10,esk180_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk181_2(X6,X10))
| ~ in(X10,esk180_1(X6)) )
& ( ~ subset(X13,esk180_1(X6))
| are_equipotent(X13,esk180_1(X6))
| in(X13,esk180_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_282])])])])]) ).
fof(c_0_504,plain,
! [X5,X10,X12,X13] :
( ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( X10 = singleton(esk142_2(X5,X10))
| ~ in(X10,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| esk139_1(X5) = singleton(esk138_1(X5)) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| esk139_1(X5) = singleton(esk138_1(X5)) )
& ( X10 = singleton(esk142_2(X5,X10))
| ~ in(X10,esk141_1(X5))
| esk139_1(X5) = singleton(esk138_1(X5)) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk141_1(X5))
| esk139_1(X5) = singleton(esk138_1(X5)) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( X10 = singleton(esk142_2(X5,X10))
| ~ in(X10,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk141_1(X5))
| in(esk138_1(X5),X5) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| esk140_1(X5) = singleton(esk138_1(X5)) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| esk140_1(X5) = singleton(esk138_1(X5)) )
& ( X10 = singleton(esk142_2(X5,X10))
| ~ in(X10,esk141_1(X5))
| esk140_1(X5) = singleton(esk138_1(X5)) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk141_1(X5))
| esk140_1(X5) = singleton(esk138_1(X5)) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| esk139_1(X5) != esk140_1(X5) )
& ( in(esk142_2(X5,X10),X5)
| ~ in(X10,esk141_1(X5))
| esk139_1(X5) != esk140_1(X5) )
& ( X10 = singleton(esk142_2(X5,X10))
| ~ in(X10,esk141_1(X5))
| esk139_1(X5) != esk140_1(X5) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk141_1(X5))
| esk139_1(X5) != esk140_1(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_283])])])])])]) ).
fof(c_0_505,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk30_2(X8,X9),X9)
| esk30_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk30_2(X8,X9),X9)
| esk30_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_284])])])])])]) ).
fof(c_0_506,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_285])]) ).
fof(c_0_507,plain,
! [X4,X5,X6,X7] :
( ( ~ epsilon_connected(X4)
| ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5) )
& ( in(esk50_1(X7),X7)
| epsilon_connected(X7) )
& ( in(esk51_1(X7),X7)
| epsilon_connected(X7) )
& ( ~ in(esk50_1(X7),esk51_1(X7))
| epsilon_connected(X7) )
& ( esk50_1(X7) != esk51_1(X7)
| epsilon_connected(X7) )
& ( ~ in(esk51_1(X7),esk50_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_286])])])])])]) ).
fof(c_0_508,plain,
! [X4,X5] :
( relation_of2(esk105_2(X4,X5),X4,X5)
& relation(esk105_2(X4,X5))
& function(esk105_2(X4,X5)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_287])]) ).
fof(c_0_509,plain,
! [X4,X5] :
( relation_of2(esk96_2(X4,X5),X4,X5)
& relation(esk96_2(X4,X5))
& function(esk96_2(X4,X5))
& quasi_total(esk96_2(X4,X5),X4,X5) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_288])]) ).
fof(c_0_510,plain,
! [X4,X5] : relation_of2_as_subset(esk92_2(X4,X5),X4,X5),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_289])]) ).
fof(c_0_511,plain,
! [X4,X5] : relation_of2(esk90_2(X4,X5),X4,X5),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_290])]) ).
fof(c_0_512,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_291])]) ).
fof(c_0_513,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk54_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk54_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_292])])])])])]) ).
fof(c_0_514,plain,
! [X8,X10,X12,X13] :
( ( in(esk169_2(X8,X10),X8)
| ~ in(X10,esk168_1(X8))
| esk165_0 = esk166_0 )
& ( esk169_2(X8,X10) = X10
| ~ in(X10,esk168_1(X8))
| esk165_0 = esk166_0 )
& ( ordinal(X10)
| ~ in(X10,esk168_1(X8))
| esk165_0 = esk166_0 )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk168_1(X8))
| esk165_0 = esk166_0 )
& ( in(esk169_2(X8,X10),X8)
| ~ in(X10,esk168_1(X8))
| ordinal(esk166_0) )
& ( esk169_2(X8,X10) = X10
| ~ in(X10,esk168_1(X8))
| ordinal(esk166_0) )
& ( ordinal(X10)
| ~ in(X10,esk168_1(X8))
| ordinal(esk166_0) )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk168_1(X8))
| ordinal(esk166_0) )
& ( in(esk169_2(X8,X10),X8)
| ~ in(X10,esk168_1(X8))
| esk165_0 = esk167_0 )
& ( esk169_2(X8,X10) = X10
| ~ in(X10,esk168_1(X8))
| esk165_0 = esk167_0 )
& ( ordinal(X10)
| ~ in(X10,esk168_1(X8))
| esk165_0 = esk167_0 )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk168_1(X8))
| esk165_0 = esk167_0 )
& ( in(esk169_2(X8,X10),X8)
| ~ in(X10,esk168_1(X8))
| ordinal(esk167_0) )
& ( esk169_2(X8,X10) = X10
| ~ in(X10,esk168_1(X8))
| ordinal(esk167_0) )
& ( ordinal(X10)
| ~ in(X10,esk168_1(X8))
| ordinal(esk167_0) )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk168_1(X8))
| ordinal(esk167_0) )
& ( in(esk169_2(X8,X10),X8)
| ~ in(X10,esk168_1(X8))
| esk166_0 != esk167_0 )
& ( esk169_2(X8,X10) = X10
| ~ in(X10,esk168_1(X8))
| esk166_0 != esk167_0 )
& ( ordinal(X10)
| ~ in(X10,esk168_1(X8))
| esk166_0 != esk167_0 )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk168_1(X8))
| esk166_0 != esk167_0 ) ),
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_293])])])])])]) ).
fof(c_0_515,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_294])]) ).
fof(c_0_516,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_295])]) ).
fof(c_0_517,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_296])]) ).
fof(c_0_518,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_297])]) ).
fof(c_0_519,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_298])])])]) ).
fof(c_0_520,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_299])])]) ).
fof(c_0_521,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_300])]) ).
fof(c_0_522,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_523,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_302])])]) ).
fof(c_0_524,plain,
! [X3,X4] :
( empty(X3)
| empty(X4)
| ~ empty(cartesian_product2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_303])]) ).
fof(c_0_525,plain,
! [X4,X5,X7,X8,X9] :
( ( relation(esk66_2(X4,X5))
| ~ equipotent(X4,X5) )
& ( function(esk66_2(X4,X5))
| ~ equipotent(X4,X5) )
& ( one_to_one(esk66_2(X4,X5))
| ~ equipotent(X4,X5) )
& ( relation_dom(esk66_2(X4,X5)) = X4
| ~ equipotent(X4,X5) )
& ( relation_rng(esk66_2(X4,X5)) = X5
| ~ equipotent(X4,X5) )
& ( ~ relation(X9)
| ~ function(X9)
| ~ one_to_one(X9)
| relation_dom(X9) != X7
| relation_rng(X9) != X8
| equipotent(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_304])])])])])]) ).
fof(c_0_526,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_305])])])]) ).
fof(c_0_527,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_306])])])]) ).
fof(c_0_528,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_307])])]) ).
fof(c_0_529,plain,
! [X3,X4] : ~ empty(unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_308]) ).
fof(c_0_530,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_309]) ).
fof(c_0_531,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_310])])])])]) ).
fof(c_0_532,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_311])])]) ).
fof(c_0_533,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_312])])])]) ).
fof(c_0_534,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_313])]) ).
fof(c_0_535,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_314])]) ).
fof(c_0_536,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_315])])]) ).
fof(c_0_537,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_316])])]) ).
fof(c_0_538,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_317])])])])]) ).
fof(c_0_539,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_difference(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_318])]) ).
fof(c_0_540,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_319])]) ).
fof(c_0_541,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_320])]) ).
fof(c_0_542,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_321])])])])]) ).
fof(c_0_543,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_322])])]) ).
fof(c_0_544,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(relation_composition(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_323])]) ).
fof(c_0_545,plain,
! [X3,X4,X5] :
( ( ~ epsilon_transitive(X3)
| ~ in(X4,X3)
| subset(X4,X3) )
& ( in(esk38_1(X5),X5)
| epsilon_transitive(X5) )
& ( ~ subset(esk38_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_324])])])])])]) ).
fof(c_0_546,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_325])])]) ).
fof(c_0_547,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_326])])]) ).
fof(c_0_548,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_327])])]) ).
fof(c_0_549,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_328])])]) ).
fof(c_0_550,plain,
! [X3,X4] :
( ~ finite(X3)
| ~ element(X4,powerset(X3))
| finite(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_329])])]) ).
fof(c_0_551,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_330])]) ).
fof(c_0_552,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_331])]) ).
fof(c_0_553,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_332])])])])]) ).
fof(c_0_554,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_333])])])])]) ).
fof(c_0_555,plain,
! [X3,X4] :
( ~ finite(X3)
| finite(set_intersection2(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_334])])])]) ).
fof(c_0_556,plain,
! [X3,X4] :
( ~ finite(X4)
| finite(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_335])]) ).
fof(c_0_557,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_336])]) ).
fof(c_0_558,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_337])])])]) ).
fof(c_0_559,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_338])])])]) ).
fof(c_0_560,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_339])]) ).
fof(c_0_561,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_340])]) ).
fof(c_0_562,plain,
! [X3,X4] :
( ~ equipotent(X3,X4)
| equipotent(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_341])]) ).
fof(c_0_563,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_342])]) ).
fof(c_0_564,plain,
! [X3,X4,X5,X6] :
( ( ~ equipotent(X3,X4)
| are_equipotent(X3,X4) )
& ( ~ are_equipotent(X5,X6)
| equipotent(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_343])])])]) ).
fof(c_0_565,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_344])])])]) ).
fof(c_0_566,plain,
! [X3,X4] :
( ( epsilon_transitive(X4)
| ~ element(X4,X3)
| ~ ordinal(X3) )
& ( epsilon_connected(X4)
| ~ element(X4,X3)
| ~ ordinal(X3) )
& ( ordinal(X4)
| ~ element(X4,X3)
| ~ ordinal(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_345])])])]) ).
fof(c_0_567,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_346])])]) ).
fof(c_0_568,plain,
! [X3] :
( ( element(esk109_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk109_1(X3))
| empty(X3) )
& ( finite(esk109_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_347])])])]) ).
fof(c_0_569,plain,
! [X3] :
( ( element(esk100_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk100_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_348])])])]) ).
fof(c_0_570,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_349])]) ).
fof(c_0_571,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_350])]) ).
fof(c_0_572,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_351])])])]) ).
fof(c_0_573,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_352])]) ).
fof(c_0_574,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_353])]) ).
fof(c_0_575,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_354]) ).
fof(c_0_576,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_355]) ).
fof(c_0_577,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_356]) ).
fof(c_0_578,plain,
! [X3] :
( element(esk107_1(X3),powerset(X3))
& empty(esk107_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_357])]) ).
fof(c_0_579,plain,
! [X3] :
( element(esk102_1(X3),powerset(X3))
& empty(esk102_1(X3))
& relation(esk102_1(X3))
& function(esk102_1(X3))
& one_to_one(esk102_1(X3))
& epsilon_transitive(esk102_1(X3))
& epsilon_connected(esk102_1(X3))
& ordinal(esk102_1(X3))
& natural(esk102_1(X3))
& finite(esk102_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_358])]) ).
fof(c_0_580,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_359]) ).
fof(c_0_581,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_360])])]) ).
fof(c_0_582,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk34_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_361])])])])]) ).
fof(c_0_583,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_362])])]) ).
fof(c_0_584,plain,
! [X2] : succ(X2) = set_union2(X2,singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_363]) ).
fof(c_0_585,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_364])])]) ).
fof(c_0_586,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_365]) ).
fof(c_0_587,plain,
! [X3] : element(esk91_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_366])]) ).
fof(c_0_588,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_367])])])])]) ).
fof(c_0_589,plain,
! [X2] :
( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_368])]) ).
fof(c_0_590,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ empty(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ empty(X2)
| ~ ordinal(X2) )
& ( ordinal(X2)
| ~ empty(X2)
| ~ ordinal(X2) )
& ( natural(X2)
| ~ empty(X2)
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_369])])]) ).
fof(c_0_591,plain,
! [X2] :
( ~ relation(X2)
| relation_inverse(relation_inverse(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_370])]) ).
fof(c_0_592,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_371])])]) ).
fof(c_0_593,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_372])])]) ).
fof(c_0_594,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_373])])]) ).
fof(c_0_595,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_374])])]) ).
fof(c_0_596,plain,
! [X2] :
( ~ relation(X2)
| relation(relation_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_375])]) ).
fof(c_0_597,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_376]) ).
fof(c_0_598,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_377]) ).
fof(c_0_599,plain,
! [X2] : ~ empty(succ(X2)),
inference(variable_rename,[status(thm)],[c_0_378]) ).
fof(c_0_600,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_379])])])]) ).
fof(c_0_601,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_380]) ).
fof(c_0_602,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_381]) ).
fof(c_0_603,plain,
! [X3,X4] : equipotent(X3,X3),
inference(variable_rename,[status(thm)],[c_0_382]) ).
fof(c_0_604,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_383]) ).
fof(c_0_605,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_384]) ).
fof(c_0_606,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_385]) ).
fof(c_0_607,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_386]) ).
fof(c_0_608,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_609,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_388])])])]) ).
fof(c_0_610,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_389])])]) ).
fof(c_0_611,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_390])]) ).
fof(c_0_612,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_391])])]) ).
fof(c_0_613,plain,
! [X2] :
( ~ empty(X2)
| function(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_392])]) ).
fof(c_0_614,plain,
! [X2] :
( ~ empty(X2)
| finite(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_393])]) ).
fof(c_0_615,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_394])])]) ).
fof(c_0_616,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_395]) ).
fof(c_0_617,plain,
! [X2] : relation(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_396]) ).
fof(c_0_618,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_397])]) ).
fof(c_0_619,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[c_0_398]) ).
fof(c_0_620,plain,
( ~ empty(esk111_0)
& epsilon_transitive(esk111_0)
& epsilon_connected(esk111_0)
& ordinal(esk111_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_399])]) ).
fof(c_0_621,plain,
~ empty(esk108_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_400])]) ).
fof(c_0_622,plain,
( ~ empty(esk106_0)
& relation(esk106_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_401])]) ).
fof(c_0_623,plain,
( ~ empty(esk94_0)
& finite(esk94_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_402])]) ).
fof(c_0_624,plain,
( ~ empty(esk93_0)
& epsilon_transitive(esk93_0)
& epsilon_connected(esk93_0)
& ordinal(esk93_0)
& natural(esk93_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_403])]) ).
fof(c_0_625,plain,
( relation(esk113_0)
& relation_empty_yielding(esk113_0)
& function(esk113_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_404])]) ).
fof(c_0_626,plain,
( relation(esk112_0)
& relation_empty_yielding(esk112_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_405])]) ).
fof(c_0_627,plain,
( relation(esk110_0)
& function(esk110_0)
& one_to_one(esk110_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_406])]) ).
fof(c_0_628,plain,
( relation(esk104_0)
& function(esk104_0)
& one_to_one(esk104_0)
& empty(esk104_0)
& epsilon_transitive(esk104_0)
& epsilon_connected(esk104_0)
& ordinal(esk104_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_407])]) ).
fof(c_0_629,plain,
( relation(esk103_0)
& empty(esk103_0)
& function(esk103_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_408])]) ).
fof(c_0_630,plain,
empty(esk101_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_409])]) ).
fof(c_0_631,plain,
( empty(esk99_0)
& relation(esk99_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_410])]) ).
fof(c_0_632,plain,
( relation(esk98_0)
& function(esk98_0)
& one_to_one(esk98_0)
& empty(esk98_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_411])]) ).
fof(c_0_633,plain,
( epsilon_transitive(esk97_0)
& epsilon_connected(esk97_0)
& ordinal(esk97_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_412])]) ).
fof(c_0_634,plain,
( relation(esk95_0)
& function(esk95_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_413])]) ).
fof(c_0_635,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_414 ).
fof(c_0_636,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_415 ).
fof(c_0_637,axiom,
empty(empty_set),
c_0_416 ).
fof(c_0_638,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_417 ).
fof(c_0_639,axiom,
$true,
c_0_418 ).
fof(c_0_640,axiom,
$true,
c_0_419 ).
fof(c_0_641,axiom,
$true,
c_0_420 ).
fof(c_0_642,axiom,
$true,
c_0_421 ).
fof(c_0_643,axiom,
$true,
c_0_422 ).
fof(c_0_644,axiom,
$true,
c_0_423 ).
fof(c_0_645,axiom,
$true,
c_0_424 ).
fof(c_0_646,axiom,
$true,
c_0_425 ).
fof(c_0_647,axiom,
$true,
c_0_426 ).
fof(c_0_648,axiom,
$true,
c_0_427 ).
fof(c_0_649,axiom,
$true,
c_0_428 ).
fof(c_0_650,axiom,
$true,
c_0_429 ).
fof(c_0_651,axiom,
$true,
c_0_430 ).
fof(c_0_652,axiom,
$true,
c_0_431 ).
fof(c_0_653,axiom,
$true,
c_0_432 ).
fof(c_0_654,axiom,
$true,
c_0_433 ).
fof(c_0_655,axiom,
$true,
c_0_434 ).
fof(c_0_656,axiom,
$true,
c_0_435 ).
fof(c_0_657,axiom,
$true,
c_0_436 ).
fof(c_0_658,axiom,
$true,
c_0_437 ).
fof(c_0_659,axiom,
$true,
c_0_438 ).
fof(c_0_660,axiom,
$true,
c_0_439 ).
fof(c_0_661,axiom,
$true,
c_0_440 ).
fof(c_0_662,axiom,
$true,
c_0_441 ).
cnf(c_0_663,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_664,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_665,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_666,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_667,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_668,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_669,plain,
( empty(X2)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_670,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_671,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_672,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_673,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_674,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_675,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_676,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| in(esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_677,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| in(esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_678,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_679,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_680,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_681,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_682,plain,
( empty(X2)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_683,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_684,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_685,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_686,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_687,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_688,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_689,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_690,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_691,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_692,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_693,plain,
( empty(X2)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_694,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_695,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_696,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_697,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_698,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_699,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_700,plain,
( in(ordered_pair(X4,esk82_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_445]) ).
cnf(c_0_701,plain,
( in(ordered_pair(esk82_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_445]) ).
cnf(c_0_702,plain,
( esk155_3(X3,X2,X1) = ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1))
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_703,plain,
( esk156_3(X3,X2,X1) = ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1))
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_704,plain,
( in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk155_3(X3,X2,X1) != esk156_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_705,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_706,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_707,plain,
( relation_isomorphism(X1,X2,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,esk78_3(X1,X2,X3)),apply(X3,esk79_3(X1,X2,X3))),X2)
| ~ in(esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_708,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_709,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_710,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_711,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_712,plain,
( empty(X2)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_713,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_714,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_715,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_716,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_717,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_718,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_719,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(ordered_pair(esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5))
| ~ in(X6,esk136_4(X2,X1,X5,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_720,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(ordered_pair(esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5))
| ~ in(X6,esk136_4(X2,X1,X5,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_721,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_722,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_723,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_724,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_725,plain,
( empty(X2)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_726,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_727,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_728,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_729,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_730,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_731,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_732,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_733,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_734,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_447]) ).
cnf(c_0_735,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_448]) ).
cnf(c_0_736,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1)
| in(ordered_pair(apply(X3,esk78_3(X1,X2,X3)),apply(X3,esk79_3(X1,X2,X3))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_737,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk84_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk83_3(X1,X2,X3),esk84_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_738,plain,
( esk155_3(X3,X2,X1) = ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1))
| X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_739,plain,
( esk156_3(X3,X2,X1) = ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1))
| X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_740,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_741,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_742,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_743,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_744,plain,
( X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk155_3(X3,X2,X1) != esk156_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_745,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| ordered_pair(esk134_4(X2,X1,X5,X4),esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_746,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| ordered_pair(esk134_4(X2,X1,X5,X4),esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_747,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk135_4(X2,X1,X5,X4),esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_748,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(esk135_4(X2,X1,X5,X4),esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_749,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_750,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| X4 = ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_751,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_449]) ).
cnf(c_0_752,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_753,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_754,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_755,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_756,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_757,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_758,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_759,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_760,plain,
( empty(X2)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_761,plain,
( empty(X2)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_762,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_763,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_764,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_449]) ).
cnf(c_0_765,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_449]) ).
cnf(c_0_766,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_449]) ).
cnf(c_0_767,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_768,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_769,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_770,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_771,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_772,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_773,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_774,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_775,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_776,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_777,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_450]) ).
cnf(c_0_778,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_451]) ).
cnf(c_0_779,plain,
( X4 = ordered_pair(esk45_4(X2,X3,X1,X4),esk46_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_780,plain,
( esk155_3(X3,X2,X1) = ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1))
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_781,plain,
( esk156_3(X3,X2,X1) = ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1))
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_782,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk83_3(X1,X2,X3),esk84_3(X1,X2,X3)),X3)
| in(ordered_pair(esk83_3(X1,X2,X3),esk85_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_783,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk83_3(X1,X2,X3),esk84_3(X1,X2,X3)),X3)
| in(ordered_pair(esk85_3(X1,X2,X3),esk84_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_784,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_447]) ).
cnf(c_0_785,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_448]) ).
cnf(c_0_786,plain,
( in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk155_3(X3,X2,X1) != esk156_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_787,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_788,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_789,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_790,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_791,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_792,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_793,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| esk134_4(X2,X1,X5,X4) = esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_794,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| esk134_4(X2,X1,X5,X4) = esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_795,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_453]) ).
cnf(c_0_796,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_797,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_798,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_799,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_800,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_801,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_802,plain,
( empty(X2)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_803,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_804,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_805,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_806,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_807,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_808,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_809,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_810,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_811,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_812,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_813,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_814,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_815,plain,
( empty(X2)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_816,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_817,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_818,plain,
( esk155_3(X3,X2,X1) = ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1))
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_819,plain,
( esk156_3(X3,X2,X1) = ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1))
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_820,plain,
( esk155_3(X3,X2,X1) = ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1))
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_821,plain,
( esk156_3(X3,X2,X1) = ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1))
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_822,plain,
( empty(X2)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_823,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_824,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_825,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_826,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_827,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_828,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_829,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_830,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_831,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_832,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_833,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1)
| in(esk78_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_834,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1)
| in(esk79_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_835,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk89_3(X2,X1,X3)),X1)
| ~ in(esk89_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_836,plain,
( X2 = fiber(X1,X3)
| esk31_3(X1,X3,X2) = X3
| ~ relation(X1)
| ~ in(ordered_pair(esk31_3(X1,X3,X2),X3),X1)
| ~ in(esk31_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_837,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_450]) ).
cnf(c_0_838,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_451]) ).
cnf(c_0_839,plain,
( esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk155_3(X3,X2,X1) != esk156_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_840,plain,
( in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk155_3(X3,X2,X1) != esk156_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_841,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_447]) ).
cnf(c_0_842,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_448]) ).
cnf(c_0_843,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_450]) ).
cnf(c_0_844,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_451]) ).
cnf(c_0_845,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_846,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_847,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk57_3(X2,X3,X1),X3)
| ~ in(esk57_3(X2,X3,X1),X2)
| ~ in(esk57_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_848,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_457]) ).
cnf(c_0_849,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_850,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_851,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_852,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_853,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_457]) ).
cnf(c_0_854,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_457]) ).
cnf(c_0_855,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_450]) ).
cnf(c_0_856,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_451]) ).
cnf(c_0_857,plain,
( in(esk45_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_858,plain,
( in(esk46_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_859,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_860,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_861,plain,
( X1 = set_difference(X2,X3)
| in(esk67_3(X2,X3,X1),X3)
| ~ in(esk67_3(X2,X3,X1),X2)
| ~ in(esk67_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_862,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_863,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_864,plain,
( empty(X2)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| esk124_2(X2,X1) != esk125_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_865,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk89_3(X2,X1,X3)),X1)
| in(esk89_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_866,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_867,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_868,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_869,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_870,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_871,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_872,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk77_2(X1,X2),esk76_2(X1,X2)),X1)
| ~ in(ordered_pair(esk76_2(X1,X2),esk77_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_873,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X2)
| ~ in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_874,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1))
| ~ in(X5,esk121_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_875,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1))
| ~ in(X5,esk121_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_876,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_877,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| esk47_3(X2,X3,X1) = ordered_pair(esk48_3(X2,X3,X1),esk49_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_878,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_453]) ).
cnf(c_0_879,plain,
( X2 = fiber(X1,X3)
| in(esk31_3(X1,X3,X2),X2)
| in(ordered_pair(esk31_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_880,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk44_3(X2,X3,X1),X1)
| ~ in(esk44_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_881,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk44_3(X2,X3,X1),X1)
| ~ in(esk44_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_882,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_457]) ).
cnf(c_0_883,plain,
( X1 = set_union2(X2,X3)
| in(esk44_3(X2,X3,X1),X3)
| in(esk44_3(X2,X3,X1),X2)
| in(esk44_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_884,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_885,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_886,plain,
( X1 = cartesian_product2(X2,X3)
| esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk47_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_887,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_888,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_889,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(X4,esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_890,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_891,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_892,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(X4,esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_893,plain,
( X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2
| ~ subset(esk32_2(X2,X1),esk33_2(X2,X1))
| ~ in(ordered_pair(esk32_2(X2,X1),esk33_2(X2,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_894,plain,
( empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_895,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_463]) ).
cnf(c_0_896,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_897,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_898,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| esk120_3(X2,X1,X4) = esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_899,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| esk120_3(X2,X1,X4) = esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_900,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_901,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_902,plain,
( X1 = set_difference(X2,X3)
| in(esk67_3(X2,X3,X1),X1)
| ~ in(esk67_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_903,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_457]) ).
cnf(c_0_904,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_905,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_906,plain,
( in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_907,plain,
( in(esk146_1(X1),X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_908,plain,
( in(esk148_1(X1),X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_909,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk55_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_910,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk77_2(X1,X2),esk76_2(X1,X2)),X1)
| in(ordered_pair(esk76_2(X1,X2),esk77_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_911,plain,
( esk147_1(X1) = singleton(esk146_1(X1))
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_912,plain,
( esk149_1(X1) = singleton(esk148_1(X1))
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_913,plain,
( ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| esk144_1(X1) != esk145_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_914,plain,
( X1 = X2
| in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X2)
| in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_915,plain,
( esk143_1(X1) = esk144_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_916,plain,
( esk143_1(X1) = esk145_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_917,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk41_3(X2,X3,X1),X1)
| esk41_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_918,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk41_3(X2,X3,X1),X1)
| esk41_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_919,plain,
( in(ordered_pair(esk71_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_920,plain,
( in(ordered_pair(X3,esk58_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_921,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_453]) ).
cnf(c_0_922,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_457]) ).
cnf(c_0_923,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_457]) ).
cnf(c_0_924,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_469]) ).
cnf(c_0_925,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_450]) ).
cnf(c_0_926,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_451]) ).
cnf(c_0_927,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_928,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_929,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_930,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_931,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_932,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_933,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_934,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_935,plain,
( X1 = set_difference(X2,X3)
| in(esk67_3(X2,X3,X1),X1)
| in(esk67_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_936,plain,
( X1 = set_intersection2(X2,X3)
| in(esk57_3(X2,X3,X1),X1)
| in(esk57_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_937,plain,
( X1 = set_intersection2(X2,X3)
| in(esk57_3(X2,X3,X1),X1)
| in(esk57_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_938,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk48_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_939,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk49_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_940,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk52_2(X1,X2),esk53_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_941,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_942,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_943,plain,
( in(esk146_1(X1),X1)
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_944,plain,
( in(esk148_1(X1),X1)
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_945,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk86_2(X1,X2),esk88_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_946,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk74_2(X1,X2),esk75_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_947,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk75_2(X1,X2),esk74_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_948,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk26_2(X1,X2),esk26_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_949,plain,
( X1 = unordered_pair(X2,X3)
| esk41_3(X2,X3,X1) = X3
| esk41_3(X2,X3,X1) = X2
| in(esk41_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_950,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk89_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_951,plain,
( esk147_1(X1) = singleton(esk146_1(X1))
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_952,plain,
( esk149_1(X1) = singleton(esk148_1(X1))
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_953,plain,
( in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| esk171_2(X2,X1) != esk172_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_954,plain,
( esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| esk144_1(X1) != esk145_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_955,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_956,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_957,plain,
( empty(X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_958,plain,
( empty(X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_959,plain,
( empty(X2)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_960,plain,
( in(esk173_2(X2,X1),X2)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_961,plain,
( in(esk174_2(X2,X1),X2)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_962,plain,
( esk143_1(X1) = esk144_1(X1)
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_963,plain,
( esk143_1(X1) = esk145_1(X1)
| esk153_3(X1,X3,X2) = singleton(esk152_3(X1,X3,X2))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_964,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_454]) ).
cnf(c_0_965,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_966,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_967,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_968,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_969,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_970,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_971,plain,
( in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| esk171_2(X2,X1) != esk172_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_972,plain,
( in(esk173_2(X2,X1),X2)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_973,plain,
( in(esk174_2(X2,X1),X2)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_974,plain,
( X1 = inclusion_relation(X2)
| subset(esk32_2(X2,X1),esk33_2(X2,X1))
| in(ordered_pair(esk32_2(X2,X1),esk33_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_975,plain,
( in(esk146_1(X1),X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_976,plain,
( in(esk148_1(X1),X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_977,plain,
( X2 = fiber(X1,X3)
| in(esk31_3(X1,X3,X2),X2)
| ~ relation(X1)
| esk31_3(X1,X3,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_978,plain,
( quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| X2 != relation_dom_as_subset(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_979,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_980,plain,
( X3 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != relation_dom_as_subset(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_981,plain,
( X3 = empty_set
| X2 = relation_dom_as_subset(X2,X3,X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_982,plain,
( empty(X2)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| esk115_2(X2,X1) != esk116_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_983,plain,
( ordinal(esk173_2(X2,X1))
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_984,plain,
( ordinal(esk174_2(X2,X1))
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_985,plain,
( ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| esk171_2(X2,X1) != esk172_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_986,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_987,plain,
( esk171_2(X2,X1) = esk173_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_988,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_989,plain,
( esk172_2(X2,X1) = esk174_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_990,plain,
( esk147_1(X1) = singleton(esk146_1(X1))
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_991,plain,
( esk149_1(X1) = singleton(esk148_1(X1))
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_992,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_993,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_994,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_995,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_996,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_997,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_998,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_999,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_1000,plain,
( in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| esk144_1(X1) != esk145_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1001,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_454]) ).
cnf(c_0_1002,plain,
( ordinal(esk173_2(X2,X1))
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1003,plain,
( in(esk173_2(X2,X1),X2)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1004,plain,
( ordinal(esk174_2(X2,X1))
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1005,plain,
( in(esk174_2(X2,X1),X2)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1006,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk72_2(X1,X2)),X1)
| ~ in(esk72_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_1007,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk59_2(X1,X2),X3),X1)
| ~ in(esk59_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1008,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1009,plain,
( esk171_2(X2,X1) = esk173_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1010,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1011,plain,
( esk172_2(X2,X1) = esk174_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1012,plain,
( esk143_1(X1) = esk144_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1013,plain,
( esk143_1(X1) = esk145_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1014,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1015,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1016,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk27_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1017,plain,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_1018,plain,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_1019,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_445]) ).
cnf(c_0_1020,plain,
( ordinal(esk173_2(X2,X1))
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1021,plain,
( ordinal(esk174_2(X2,X1))
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1022,plain,
( empty(X2)
| esk114_2(X2,X1) = esk117_2(X2,X1)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_1023,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_1024,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1025,plain,
( esk171_2(X2,X1) = esk173_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1026,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1027,plain,
( esk172_2(X2,X1) = esk174_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1028,plain,
( in(esk146_1(X1),X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1029,plain,
( in(esk148_1(X1),X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1030,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_478]) ).
cnf(c_0_1031,plain,
( esk147_1(X1) = singleton(esk146_1(X1))
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1032,plain,
( esk149_1(X1) = singleton(esk148_1(X1))
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1033,plain,
( in(X4,relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1034,plain,
( in(X5,relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1035,plain,
( in(esk152_3(X1,X3,X2),X1)
| esk144_1(X1) != esk145_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1036,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk73_2(X1,X2),esk72_2(X1,X2)),X1)
| in(esk72_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_1037,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk59_2(X1,X2),esk60_2(X1,X2)),X1)
| in(esk59_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1038,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_463]) ).
cnf(c_0_1039,plain,
( esk143_1(X1) = esk144_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1040,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1041,plain,
( esk143_1(X1) = esk145_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1042,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1043,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_1044,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk56_2(X1,X2))
| ~ in(X3,esk56_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_1045,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_463]) ).
cnf(c_0_1046,plain,
( in(esk146_1(X1),X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1047,plain,
( in(esk148_1(X1),X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1048,plain,
( X2 = empty_set
| X1 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_1049,plain,
( esk147_1(X1) = singleton(esk146_1(X1))
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1050,plain,
( esk149_1(X1) = singleton(esk148_1(X1))
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1051,plain,
( in(X2,esk150_2(X1,X3))
| esk144_1(X1) != esk145_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1052,plain,
( X3 = empty_set
| in(esk55_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_1053,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk28_2(X1,X2),X2)
| ~ in(esk28_2(X1,X2),esk29_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1054,plain,
( subset(X1,X2)
| in(ordered_pair(esk52_2(X1,X2),esk53_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_1055,plain,
( in(esk68_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_480]) ).
cnf(c_0_1056,plain,
( esk143_1(X1) = esk144_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1057,plain,
( esk143_1(X1) = esk145_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1058,plain,
( esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| esk171_2(X2,X1) != esk172_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1059,plain,
( X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| esk171_2(X2,X1) != esk172_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1060,plain,
( X3 = apply(X1,esk68_3(X1,X2,X3))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_1061,plain,
( in(esk173_2(X2,X1),X2)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1062,plain,
( in(esk173_2(X2,X1),X2)
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1063,plain,
( in(esk174_2(X2,X1),X2)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1064,plain,
( in(esk174_2(X2,X1),X2)
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1065,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk86_2(X1,X2),esk87_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1066,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk87_2(X1,X2),esk88_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1067,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk61_2(X1,X2),esk62_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1068,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk62_2(X1,X2),esk61_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1069,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_447]) ).
cnf(c_0_1070,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_448]) ).
cnf(c_0_1071,plain,
( in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| esk171_2(X2,X1) != esk172_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1072,plain,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| esk69_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(esk69_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_1073,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_1074,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_471]) ).
cnf(c_0_1075,plain,
( in(esk173_2(X2,X1),X2)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1076,plain,
( in(esk174_2(X2,X1),X2)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1077,plain,
( ordinal(esk173_2(X2,X1))
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1078,plain,
( ordinal(esk173_2(X2,X1))
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1079,plain,
( ordinal(esk174_2(X2,X1))
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1080,plain,
( ordinal(esk174_2(X2,X1))
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1081,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk64_2(X2,X1),X3)
| ~ in(esk64_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1082,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1083,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1084,plain,
( esk171_2(X2,X1) = esk173_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1085,plain,
( esk171_2(X2,X1) = esk173_2(X2,X1)
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1086,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1087,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1088,plain,
( esk172_2(X2,X1) = esk174_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1089,plain,
( esk172_2(X2,X1) = esk174_2(X2,X1)
| X3 = esk177_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1090,plain,
( in(X3,esk63_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1091,plain,
( in(esk63_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1092,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1093,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1094,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_453]) ).
cnf(c_0_1095,plain,
( ordinal(esk173_2(X2,X1))
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1096,plain,
( ordinal(esk174_2(X2,X1))
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1097,plain,
( X2 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_1098,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk27_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1099,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1100,plain,
( esk171_2(X2,X1) = esk173_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1101,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1102,plain,
( esk172_2(X2,X1) = esk174_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1103,plain,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_1104,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_1105,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_447]) ).
cnf(c_0_1106,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_448]) ).
cnf(c_0_1107,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_1108,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_1109,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_470]) ).
cnf(c_0_1110,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk42_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1111,plain,
( in(esk146_1(X1),X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1112,plain,
( in(esk148_1(X1),X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1113,plain,
( subset(X4,X3)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_1114,plain,
( X1 = X2
| ~ in(ordered_pair(X3,X2),X4)
| ~ in(ordered_pair(X3,X1),X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1115,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_488]) ).
cnf(c_0_1116,plain,
( esk147_1(X1) = singleton(esk146_1(X1))
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1117,plain,
( esk149_1(X1) = singleton(esk148_1(X1))
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1118,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_489]) ).
cnf(c_0_1119,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_490]) ).
cnf(c_0_1120,plain,
( esk151_3(X1,X3,X2) = X2
| esk144_1(X1) != esk145_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1121,plain,
( X1 = powerset(X2)
| ~ subset(esk35_2(X2,X1),X2)
| ~ in(esk35_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_1122,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_450]) ).
cnf(c_0_1123,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_451]) ).
cnf(c_0_1124,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_457]) ).
cnf(c_0_1125,plain,
( X1 = X2
| ~ in(esk178_2(X1,X2),X2)
| ~ in(esk178_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_1126,plain,
( esk143_1(X1) = esk144_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1127,plain,
( esk143_1(X1) = esk145_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1128,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_459]) ).
cnf(c_0_1129,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_459]) ).
cnf(c_0_1130,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_1131,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_494]) ).
cnf(c_0_1132,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_1133,plain,
( relation_dom(X3) = relation_field(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1134,plain,
( relation_rng(X3) = relation_field(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1135,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_460]) ).
cnf(c_0_1136,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_460]) ).
cnf(c_0_1137,plain,
( one_to_one(X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1138,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_1139,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_1140,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk43_1(X1))
| ~ in(X2,esk43_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1141,plain,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_1142,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_447]) ).
cnf(c_0_1143,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_448]) ).
cnf(c_0_1144,plain,
( X2 = relation_rng(X1)
| in(esk69_2(X1,X2),X2)
| esk69_2(X1,X2) = apply(X1,esk70_2(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_1145,plain,
( X1 = union(X2)
| in(esk64_2(X2,X1),X1)
| in(esk64_2(X2,X1),esk65_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1146,plain,
( in(X4,X2)
| X4 = X3
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1147,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_494]) ).
cnf(c_0_1148,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk29_2(X1,X2),X1)
| ~ in(esk28_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1149,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk28_2(X1,X2),X3)
| in(esk28_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1150,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_1151,plain,
( ~ in(X1,X2)
| ~ in(X3,esk179_2(X1,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1152,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_452]) ).
cnf(c_0_1153,plain,
( X2 = relation_rng(X1)
| in(esk69_2(X1,X2),X2)
| in(esk70_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_1154,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_1155,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_1156,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_1157,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_453]) ).
cnf(c_0_1158,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_1159,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_1160,plain,
( X1 = ordered_pair(esk23_2(X2,X1),esk24_2(X2,X1))
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_1161,plain,
( X4 = pair_second(X1)
| X1 = ordered_pair(esk36_2(X1,X4),esk37_2(X1,X4))
| X1 != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_1162,plain,
( X4 = pair_first(X1)
| X1 = ordered_pair(esk21_2(X1,X4),esk22_2(X1,X4))
| X1 != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1163,plain,
( in(X3,esk181_2(X2,X1))
| ~ in(X1,esk180_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1164,plain,
( in(esk138_1(X1),X1)
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1165,plain,
( in(esk138_1(X1),X1)
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1166,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1167,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_1168,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_480]) ).
cnf(c_0_1169,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1170,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_1171,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1172,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1173,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1174,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1175,plain,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1176,plain,
( X1 = singleton(X2)
| esk30_2(X2,X1) != X2
| ~ in(esk30_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_1177,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1178,plain,
( esk139_1(X1) = singleton(esk138_1(X1))
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1179,plain,
( esk140_1(X1) = singleton(esk138_1(X1))
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1180,plain,
( X2 = empty_set
| in(esk42_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1181,plain,
( in(X2,esk141_1(X1))
| esk139_1(X1) != esk140_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1182,plain,
( esk139_1(X1) = singleton(esk138_1(X1))
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1183,plain,
( esk139_1(X1) = singleton(esk138_1(X1))
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1184,plain,
( esk140_1(X1) = singleton(esk138_1(X1))
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1185,plain,
( esk140_1(X1) = singleton(esk138_1(X1))
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1186,plain,
( X1 = union(X2)
| in(esk64_2(X2,X1),X1)
| in(esk65_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1187,plain,
( X1 = powerset(X2)
| subset(esk35_2(X2,X1),X2)
| in(esk35_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_1188,plain,
( in(esk142_2(X1,X2),X1)
| esk139_1(X1) != esk140_1(X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1189,plain,
( in(esk142_2(X1,X2),X1)
| esk139_1(X1) != esk140_1(X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1190,plain,
( in(esk138_1(X1),X1)
| X2 = singleton(esk142_2(X1,X2))
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1191,plain,
( in(esk138_1(X1),X1)
| X2 = singleton(esk142_2(X1,X2))
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1192,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_1193,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_507]) ).
cnf(c_0_1194,plain,
( X1 = X2
| in(esk178_2(X1,X2),X2)
| in(esk178_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_1195,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_463]) ).
cnf(c_0_1196,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_453]) ).
cnf(c_0_1197,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_1198,plain,
relation_of2(esk105_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_1199,plain,
relation_of2(esk96_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1200,plain,
quasi_total(esk96_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1201,plain,
relation_of2_as_subset(esk92_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_510]) ).
cnf(c_0_1202,plain,
relation_of2(esk90_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_1203,plain,
( in(esk181_2(X2,X1),esk180_1(X2))
| ~ in(X1,esk180_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1204,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_512]) ).
cnf(c_0_1205,plain,
( esk139_1(X1) = singleton(esk138_1(X1))
| X2 = singleton(esk142_2(X1,X2))
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1206,plain,
( esk140_1(X1) = singleton(esk138_1(X1))
| X2 = singleton(esk142_2(X1,X2))
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1207,plain,
( subset(X1,X2)
| ~ in(esk54_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_1208,plain,
( X2 = singleton(esk142_2(X1,X2))
| esk139_1(X1) != esk140_1(X1)
| ~ in(X2,esk141_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1209,plain,
( ordinal(esk166_0)
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1210,plain,
( ordinal(esk167_0)
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1211,plain,
( in(X1,esk180_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk180_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1212,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_1213,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_1214,plain,
( in(esk169_2(X2,X1),X2)
| esk166_0 != esk167_0
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1215,plain,
( in(X1,esk180_1(X2))
| are_equipotent(X1,esk180_1(X2))
| ~ subset(X1,esk180_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1216,plain,
( esk165_0 = esk166_0
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1217,plain,
( esk165_0 = esk167_0
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1218,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_1219,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1220,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_1221,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_1222,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_518]) ).
cnf(c_0_1223,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_1224,plain,
( function(X1)
| in(ordered_pair(esk18_1(X1),esk19_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1225,plain,
( function(X1)
| in(ordered_pair(esk18_1(X1),esk20_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1226,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1227,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| esk74_2(X1,X2) != esk75_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_1228,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| esk61_2(X1,X2) != esk62_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1229,plain,
( in(esk179_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1230,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_1231,plain,
( is_transitive_in(X1,X2)
| in(esk86_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1232,plain,
( is_transitive_in(X1,X2)
| in(esk87_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1233,plain,
( is_transitive_in(X1,X2)
| in(esk88_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1234,plain,
( is_connected_in(X1,X2)
| in(esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_1235,plain,
( is_connected_in(X1,X2)
| in(esk75_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_1236,plain,
( is_antisymmetric_in(X1,X2)
| in(esk61_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1237,plain,
( is_antisymmetric_in(X1,X2)
| in(esk62_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1238,plain,
( is_well_founded_in(X1,X2)
| subset(esk56_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_1239,plain,
( is_reflexive_in(X1,X2)
| in(esk26_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1240,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_1241,plain,
( X1 = inclusion_relation(X2)
| in(esk32_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_1242,plain,
( X1 = inclusion_relation(X2)
| in(esk33_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_1243,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_1244,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_1245,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_1246,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_1247,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_1248,plain,
( X1 = singleton(X2)
| esk30_2(X2,X1) = X2
| in(esk30_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_1249,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_521]) ).
cnf(c_0_1250,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_1251,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_522]) ).
cnf(c_0_1252,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_1253,plain,
( one_to_one(X1)
| apply(X1,esk80_1(X1)) = apply(X1,esk81_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_1254,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_1255,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_1256,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X6,X5)
| X4 != pair_second(X1) ),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_1257,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X5,X6)
| X4 != pair_first(X1) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1258,plain,
( ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1259,plain,
( ordinal(esk166_0)
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1260,plain,
( ordinal(esk167_0)
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1261,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_1262,plain,
( in(X1,esk168_1(X2))
| esk166_0 != esk167_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1263,plain,
( esk165_0 = esk166_0
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1264,plain,
( esk165_0 = esk167_0
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1265,plain,
( subset(X1,X2)
| in(esk54_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_1266,plain,
( relation_dom(esk66_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1267,plain,
( relation_rng(esk66_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1268,plain,
( relation(esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1269,plain,
( function(esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1270,plain,
( one_to_one(esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1271,plain,
( X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3)
| X4 != esk37_2(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_1272,plain,
( X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3)
| X4 != esk21_2(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1273,plain,
( equipotent(X1,X2)
| relation_rng(X3) != X2
| relation_dom(X3) != X1
| ~ one_to_one(X3)
| ~ function(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1274,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_1275,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_1276,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_1277,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_528]) ).
cnf(c_0_1278,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_528]) ).
cnf(c_0_1279,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_1280,plain,
( ordinal(esk166_0)
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1281,plain,
( ordinal(esk167_0)
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1282,plain,
( esk169_2(X2,X1) = X1
| esk166_0 != esk167_0
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1283,plain,
( esk165_0 = esk166_0
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1284,plain,
( esk165_0 = esk167_0
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1285,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_529]) ).
cnf(c_0_1286,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_530]) ).
cnf(c_0_1287,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1288,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_532]) ).
cnf(c_0_1289,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_1290,plain,
( epsilon_connected(X1)
| ~ in(esk50_1(X1),esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1291,plain,
( epsilon_connected(X1)
| ~ in(esk51_1(X1),esk50_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1292,plain,
( one_to_one(X1)
| in(esk80_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_1293,plain,
( one_to_one(X1)
| in(esk81_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_1294,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_1295,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_1296,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_534]) ).
cnf(c_0_1297,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_535]) ).
cnf(c_0_1298,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_536]) ).
cnf(c_0_1299,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_536]) ).
cnf(c_0_1300,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_537]) ).
cnf(c_0_1301,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_537]) ).
cnf(c_0_1302,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_538]) ).
cnf(c_0_1303,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_538]) ).
cnf(c_0_1304,plain,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_539]) ).
cnf(c_0_1305,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_540]) ).
cnf(c_0_1306,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_1307,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_542]) ).
cnf(c_0_1308,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_542]) ).
cnf(c_0_1309,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_543]) ).
cnf(c_0_1310,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_543]) ).
cnf(c_0_1311,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_544]) ).
cnf(c_0_1312,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1313,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1314,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1315,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1316,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1317,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk56_2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_1318,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_545]) ).
cnf(c_0_1319,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_546]) ).
cnf(c_0_1320,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_547]) ).
cnf(c_0_1321,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_548]) ).
cnf(c_0_1322,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_1323,plain,
( finite(X1)
| ~ element(X1,powerset(X2))
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_550]) ).
cnf(c_0_1324,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_1325,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_1326,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_1327,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_1328,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_552]) ).
cnf(c_0_1329,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_1330,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_1331,plain,
( ordinal(esk166_0)
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1332,plain,
( ordinal(esk167_0)
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1333,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_1334,plain,
( well_founded_relation(X1)
| subset(esk43_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1335,plain,
( ordinal(X1)
| esk166_0 != esk167_0
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1336,plain,
( esk165_0 = esk166_0
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1337,plain,
( esk165_0 = esk167_0
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1338,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_555]) ).
cnf(c_0_1339,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_556]) ).
cnf(c_0_1340,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_557]) ).
cnf(c_0_1341,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_558]) ).
cnf(c_0_1342,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_559]) ).
cnf(c_0_1343,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_560]) ).
cnf(c_0_1344,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_561]) ).
cnf(c_0_1345,plain,
( equipotent(X1,X2)
| ~ equipotent(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_562]) ).
cnf(c_0_1346,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_563]) ).
cnf(c_0_1347,plain,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_564]) ).
cnf(c_0_1348,plain,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_564]) ).
cnf(c_0_1349,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_1350,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_565]) ).
cnf(c_0_1351,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_565]) ).
cnf(c_0_1352,plain,
( epsilon_transitive(X1)
| ~ subset(esk38_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_545]) ).
cnf(c_0_1353,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_546]) ).
cnf(c_0_1354,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_547]) ).
cnf(c_0_1355,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_548]) ).
cnf(c_0_1356,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_1357,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_1358,plain,
( epsilon_transitive(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_1359,plain,
( epsilon_connected(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_1360,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_1361,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_1362,plain,
( relation(X1)
| esk25_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_1363,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_567]) ).
cnf(c_0_1364,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_567]) ).
cnf(c_0_1365,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk80_1(X1) != esk81_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_1366,plain,
( empty(X1)
| element(esk109_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_1367,plain,
( empty(X1)
| element(esk100_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_569]) ).
cnf(c_0_1368,plain,
relation(esk105_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_1369,plain,
function(esk105_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_1370,plain,
relation(esk96_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1371,plain,
function(esk96_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1372,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_570]) ).
cnf(c_0_1373,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_571]) ).
cnf(c_0_1374,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_572]) ).
cnf(c_0_1375,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_1376,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_573]) ).
cnf(c_0_1377,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1378,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_575]) ).
cnf(c_0_1379,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1380,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_577]) ).
cnf(c_0_1381,plain,
element(esk107_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_578]) ).
cnf(c_0_1382,plain,
element(esk102_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1383,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1384,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_1385,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_1386,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_1387,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_1388,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_1389,plain,
( epsilon_connected(X1)
| in(esk50_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1390,plain,
( epsilon_connected(X1)
| in(esk51_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1391,plain,
( epsilon_transitive(X1)
| in(esk38_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_545]) ).
cnf(c_0_1392,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1393,plain,
( relation(X1)
| in(esk25_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_1394,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_1395,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_1396,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1397,plain,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_1398,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_586]) ).
cnf(c_0_1399,plain,
( X1 = empty_set
| in(esk34_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1400,plain,
( empty(X1)
| ~ empty(esk109_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_1401,plain,
( empty(X1)
| ~ empty(esk100_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_569]) ).
cnf(c_0_1402,plain,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_1403,plain,
in(X1,esk180_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1404,plain,
element(esk91_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_1405,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1406,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1407,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1408,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1409,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1410,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_588]) ).
cnf(c_0_1411,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk43_1(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1412,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_589]) ).
cnf(c_0_1413,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1414,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1415,plain,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1416,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1417,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1418,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1419,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1420,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_592]) ).
cnf(c_0_1421,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_592]) ).
cnf(c_0_1422,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_1423,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_1424,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1425,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1426,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1427,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_1428,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_1429,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_1430,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1431,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1432,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_596]) ).
cnf(c_0_1433,plain,
( epsilon_connected(X1)
| esk50_1(X1) != esk51_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1434,plain,
( function(X1)
| esk19_1(X1) != esk20_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1435,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1436,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_598]) ).
cnf(c_0_1437,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_599]) ).
cnf(c_0_1438,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1439,plain,
( empty(X1)
| finite(esk109_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_1440,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_1441,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1442,plain,
equipotent(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_603]) ).
cnf(c_0_1443,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_1444,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1445,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_1446,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1447,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_1448,plain,
( being_limit_ordinal(X1)
| X1 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_1449,plain,
( X1 = union(X1)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_1450,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1451,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_588]) ).
cnf(c_0_1452,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_588]) ).
cnf(c_0_1453,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1454,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1455,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1456,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_611]) ).
cnf(c_0_1457,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1458,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1459,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_613]) ).
cnf(c_0_1460,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1461,plain,
empty(esk107_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_578]) ).
cnf(c_0_1462,plain,
empty(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1463,plain,
relation(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1464,plain,
function(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1465,plain,
one_to_one(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1466,plain,
epsilon_transitive(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1467,plain,
epsilon_connected(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1468,plain,
ordinal(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1469,plain,
natural(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1470,plain,
finite(esk102_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_1471,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_615]) ).
cnf(c_0_1472,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_615]) ).
cnf(c_0_1473,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_616]) ).
cnf(c_0_1474,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1475,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1476,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_618]) ).
cnf(c_0_1477,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_619]) ).
cnf(c_0_1478,plain,
~ empty(esk111_0),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_1479,plain,
~ empty(esk108_0),
inference(split_conjunct,[status(thm)],[c_0_621]) ).
cnf(c_0_1480,plain,
~ empty(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1481,plain,
~ empty(esk94_0),
inference(split_conjunct,[status(thm)],[c_0_623]) ).
cnf(c_0_1482,plain,
~ empty(esk93_0),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_1483,plain,
relation(esk113_0),
inference(split_conjunct,[status(thm)],[c_0_625]) ).
cnf(c_0_1484,plain,
relation_empty_yielding(esk113_0),
inference(split_conjunct,[status(thm)],[c_0_625]) ).
cnf(c_0_1485,plain,
function(esk113_0),
inference(split_conjunct,[status(thm)],[c_0_625]) ).
cnf(c_0_1486,plain,
relation(esk112_0),
inference(split_conjunct,[status(thm)],[c_0_626]) ).
cnf(c_0_1487,plain,
relation_empty_yielding(esk112_0),
inference(split_conjunct,[status(thm)],[c_0_626]) ).
cnf(c_0_1488,plain,
epsilon_transitive(esk111_0),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_1489,plain,
epsilon_connected(esk111_0),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_1490,plain,
ordinal(esk111_0),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_1491,plain,
relation(esk110_0),
inference(split_conjunct,[status(thm)],[c_0_627]) ).
cnf(c_0_1492,plain,
function(esk110_0),
inference(split_conjunct,[status(thm)],[c_0_627]) ).
cnf(c_0_1493,plain,
one_to_one(esk110_0),
inference(split_conjunct,[status(thm)],[c_0_627]) ).
cnf(c_0_1494,plain,
relation(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1495,plain,
relation(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1496,plain,
function(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1497,plain,
one_to_one(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1498,plain,
empty(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1499,plain,
epsilon_transitive(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1500,plain,
epsilon_connected(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1501,plain,
ordinal(esk104_0),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1502,plain,
relation(esk103_0),
inference(split_conjunct,[status(thm)],[c_0_629]) ).
cnf(c_0_1503,plain,
empty(esk103_0),
inference(split_conjunct,[status(thm)],[c_0_629]) ).
cnf(c_0_1504,plain,
function(esk103_0),
inference(split_conjunct,[status(thm)],[c_0_629]) ).
cnf(c_0_1505,plain,
empty(esk101_0),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_1506,plain,
empty(esk99_0),
inference(split_conjunct,[status(thm)],[c_0_631]) ).
cnf(c_0_1507,plain,
relation(esk99_0),
inference(split_conjunct,[status(thm)],[c_0_631]) ).
cnf(c_0_1508,plain,
relation(esk98_0),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1509,plain,
function(esk98_0),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1510,plain,
one_to_one(esk98_0),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1511,plain,
empty(esk98_0),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1512,plain,
epsilon_transitive(esk97_0),
inference(split_conjunct,[status(thm)],[c_0_633]) ).
cnf(c_0_1513,plain,
epsilon_connected(esk97_0),
inference(split_conjunct,[status(thm)],[c_0_633]) ).
cnf(c_0_1514,plain,
ordinal(esk97_0),
inference(split_conjunct,[status(thm)],[c_0_633]) ).
cnf(c_0_1515,plain,
relation(esk95_0),
inference(split_conjunct,[status(thm)],[c_0_634]) ).
cnf(c_0_1516,plain,
function(esk95_0),
inference(split_conjunct,[status(thm)],[c_0_634]) ).
cnf(c_0_1517,plain,
finite(esk94_0),
inference(split_conjunct,[status(thm)],[c_0_623]) ).
cnf(c_0_1518,plain,
epsilon_transitive(esk93_0),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_1519,plain,
epsilon_connected(esk93_0),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_1520,plain,
ordinal(esk93_0),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_1521,plain,
natural(esk93_0),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_1522,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_635]) ).
cnf(c_0_1523,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_635]) ).
cnf(c_0_1524,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1525,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1526,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1527,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1528,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1529,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1530,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1531,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1532,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_1533,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1534,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1535,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1536,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_639]) ).
cnf(c_0_1537,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_1538,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_1539,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_642]) ).
cnf(c_0_1540,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_643]) ).
cnf(c_0_1541,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_644]) ).
cnf(c_0_1542,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_645]) ).
cnf(c_0_1543,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_646]) ).
cnf(c_0_1544,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_647]) ).
cnf(c_0_1545,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_648]) ).
cnf(c_0_1546,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_649]) ).
cnf(c_0_1547,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_650]) ).
cnf(c_0_1548,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_651]) ).
cnf(c_0_1549,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_652]) ).
cnf(c_0_1550,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_653]) ).
cnf(c_0_1551,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_654]) ).
cnf(c_0_1552,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_1553,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1554,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_1555,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_658]) ).
cnf(c_0_1556,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_1557,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_660]) ).
cnf(c_0_1558,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_1559,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_662]) ).
cnf(c_0_1560,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
c_0_663,
[final] ).
cnf(c_0_1561,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
c_0_664,
[final] ).
cnf(c_0_1562,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_665,
[final] ).
cnf(c_0_1563,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_666,
[final] ).
cnf(c_0_1564,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_667,
[final] ).
cnf(c_0_1565,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_668,
[final] ).
cnf(c_0_1566,plain,
( empty(X2)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_669,
[final] ).
cnf(c_0_1567,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_670,
[final] ).
cnf(c_0_1568,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_671,
[final] ).
cnf(c_0_1569,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_672,
[final] ).
cnf(c_0_1570,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_673,
[final] ).
cnf(c_0_1571,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_674,
[final] ).
cnf(c_0_1572,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_675,
[final] ).
cnf(c_0_1573,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| in(esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
c_0_676,
[final] ).
cnf(c_0_1574,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(X4,esk132_3(X2,X1,X5))
| in(esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
c_0_677,
[final] ).
cnf(c_0_1575,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_678,
[final] ).
cnf(c_0_1576,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_679,
[final] ).
cnf(c_0_1577,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_680,
[final] ).
cnf(c_0_1578,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_681,
[final] ).
cnf(c_0_1579,plain,
( empty(X2)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_682,
[final] ).
cnf(c_0_1580,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_683,
[final] ).
cnf(c_0_1581,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_684,
[final] ).
cnf(c_0_1582,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_685,
[final] ).
cnf(c_0_1583,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_686,
[final] ).
cnf(c_0_1584,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_687,
[final] ).
cnf(c_0_1585,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(X3,esk132_3(X2,X1,X4))
| in(esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
c_0_688,
[final] ).
cnf(c_0_1586,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk122_5(X2,X1,X4,X5,X6)),X1) ),
c_0_689,
[final] ).
cnf(c_0_1587,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk122_5(X2,X1,X4,X5,X6)),X1) ),
c_0_690,
[final] ).
cnf(c_0_1588,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_691,
[final] ).
cnf(c_0_1589,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_692,
[final] ).
cnf(c_0_1590,plain,
( empty(X2)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_693,
[final] ).
cnf(c_0_1591,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_694,
[final] ).
cnf(c_0_1592,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_695,
[final] ).
cnf(c_0_1593,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_696,
[final] ).
cnf(c_0_1594,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk122_5(X2,X1,X3,X4,X5)),X1) ),
c_0_697,
[final] ).
cnf(c_0_1595,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_698,
[final] ).
cnf(c_0_1596,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_699,
[final] ).
cnf(c_0_1597,plain,
( in(ordered_pair(X4,esk82_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_700,
[final] ).
cnf(c_0_1598,plain,
( in(ordered_pair(esk82_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_701,
[final] ).
cnf(c_0_1599,plain,
( ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1)) = esk155_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_702,
[final] ).
cnf(c_0_1600,plain,
( ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1)) = esk156_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_703,
[final] ).
cnf(c_0_1601,plain,
( in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk156_3(X3,X2,X1) != esk155_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_704,
[final] ).
cnf(c_0_1602,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_705,
[final] ).
cnf(c_0_1603,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk163_4(X3,X2,X1,X4)),apply(X1,esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_706,
[final] ).
cnf(c_0_1604,plain,
( relation_isomorphism(X1,X2,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,esk78_3(X1,X2,X3)),apply(X3,esk79_3(X1,X2,X3))),X2)
| ~ in(esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1) ),
c_0_707,
[final] ).
cnf(c_0_1605,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
c_0_708,
[final] ).
cnf(c_0_1606,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(X4,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
c_0_709,
[final] ).
cnf(c_0_1607,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_710,
[final] ).
cnf(c_0_1608,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_711,
[final] ).
cnf(c_0_1609,plain,
( empty(X2)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_712,
[final] ).
cnf(c_0_1610,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_713,
[final] ).
cnf(c_0_1611,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_714,
[final] ).
cnf(c_0_1612,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_715,
[final] ).
cnf(c_0_1613,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(X3,esk119_2(X2,X1))
| in(esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_716,
[final] ).
cnf(c_0_1614,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_717,
[final] ).
cnf(c_0_1615,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_718,
[final] ).
cnf(c_0_1616,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(ordered_pair(esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5))
| ~ in(X6,esk136_4(X2,X1,X5,X4)) ),
c_0_719,
[final] ).
cnf(c_0_1617,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(ordered_pair(esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5))
| ~ in(X6,esk136_4(X2,X1,X5,X4)) ),
c_0_720,
[final] ).
cnf(c_0_1618,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_721,
[final] ).
cnf(c_0_1619,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_722,
[final] ).
cnf(c_0_1620,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_723,
[final] ).
cnf(c_0_1621,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_724,
[final] ).
cnf(c_0_1622,plain,
( empty(X2)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_725,
[final] ).
cnf(c_0_1623,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_726,
[final] ).
cnf(c_0_1624,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_727,
[final] ).
cnf(c_0_1625,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_728,
[final] ).
cnf(c_0_1626,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_729,
[final] ).
cnf(c_0_1627,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_730,
[final] ).
cnf(c_0_1628,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(ordered_pair(esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4))
| ~ in(X5,esk136_4(X2,X1,X4,X3)) ),
c_0_731,
[final] ).
cnf(c_0_1629,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_732,
[final] ).
cnf(c_0_1630,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_733,
[final] ).
cnf(c_0_1631,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_734,
[final] ).
cnf(c_0_1632,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_735,
[final] ).
cnf(c_0_1633,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1)
| in(ordered_pair(apply(X3,esk78_3(X1,X2,X3)),apply(X3,esk79_3(X1,X2,X3))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
c_0_736,
[final] ).
cnf(c_0_1634,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk84_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk83_3(X1,X2,X3),esk84_3(X1,X2,X3)),X3) ),
c_0_737,
[final] ).
cnf(c_0_1635,plain,
( ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1)) = esk155_3(X3,X2,X1)
| ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_738,
[final] ).
cnf(c_0_1636,plain,
( ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1)) = esk156_3(X3,X2,X1)
| ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_739,
[final] ).
cnf(c_0_1637,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_740,
[final] ).
cnf(c_0_1638,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_741,
[final] ).
cnf(c_0_1639,plain,
( in(ordered_pair(apply(X1,esk157_3(X3,X2,X1)),apply(X1,esk158_3(X3,X2,X1))),X2)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_742,
[final] ).
cnf(c_0_1640,plain,
( in(ordered_pair(apply(X1,esk159_3(X3,X2,X1)),apply(X1,esk160_3(X3,X2,X1))),X2)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_743,
[final] ).
cnf(c_0_1641,plain,
( ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk156_3(X3,X2,X1) != esk155_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_744,
[final] ).
cnf(c_0_1642,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| ordered_pair(esk134_4(X2,X1,X5,X4),esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_745,
[final] ).
cnf(c_0_1643,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| ordered_pair(esk134_4(X2,X1,X5,X4),esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_746,
[final] ).
cnf(c_0_1644,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk135_4(X2,X1,X5,X4),esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_747,
[final] ).
cnf(c_0_1645,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(esk135_4(X2,X1,X5,X4),esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_748,
[final] ).
cnf(c_0_1646,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_749,
[final] ).
cnf(c_0_1647,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| ordered_pair(esk163_4(X3,X2,X1,X4),esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_750,
[final] ).
cnf(c_0_1648,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_751,
[final] ).
cnf(c_0_1649,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_752,
[final] ).
cnf(c_0_1650,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_753,
[final] ).
cnf(c_0_1651,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_754,
[final] ).
cnf(c_0_1652,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_755,
[final] ).
cnf(c_0_1653,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_756,
[final] ).
cnf(c_0_1654,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_757,
[final] ).
cnf(c_0_1655,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_758,
[final] ).
cnf(c_0_1656,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_759,
[final] ).
cnf(c_0_1657,plain,
( empty(X2)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_760,
[final] ).
cnf(c_0_1658,plain,
( empty(X2)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_761,
[final] ).
cnf(c_0_1659,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_762,
[final] ).
cnf(c_0_1660,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_763,
[final] ).
cnf(c_0_1661,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X2 ),
c_0_764,
[final] ).
cnf(c_0_1662,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X3 ),
c_0_765,
[final] ).
cnf(c_0_1663,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X4 ),
c_0_766,
[final] ).
cnf(c_0_1664,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_767,
[final] ).
cnf(c_0_1665,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_768,
[final] ).
cnf(c_0_1666,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_769,
[final] ).
cnf(c_0_1667,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_770,
[final] ).
cnf(c_0_1668,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_771,
[final] ).
cnf(c_0_1669,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| ordered_pair(esk134_4(X2,X1,X4,X3),esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_772,
[final] ).
cnf(c_0_1670,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_773,
[final] ).
cnf(c_0_1671,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_774,
[final] ).
cnf(c_0_1672,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_775,
[final] ).
cnf(c_0_1673,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(esk135_4(X2,X1,X4,X3),esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_776,
[final] ).
cnf(c_0_1674,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_777,
[final] ).
cnf(c_0_1675,plain,
( in(ordered_pair(esk11_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_778,
[final] ).
cnf(c_0_1676,plain,
( ordered_pair(esk45_4(X2,X3,X1,X4),esk46_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_779,
[final] ).
cnf(c_0_1677,plain,
( ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1)) = esk155_3(X3,X2,X1)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_780,
[final] ).
cnf(c_0_1678,plain,
( ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1)) = esk156_3(X3,X2,X1)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_781,
[final] ).
cnf(c_0_1679,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk83_3(X1,X2,X3),esk84_3(X1,X2,X3)),X3)
| in(ordered_pair(esk83_3(X1,X2,X3),esk85_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_782,
[final] ).
cnf(c_0_1680,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk83_3(X1,X2,X3),esk84_3(X1,X2,X3)),X3)
| in(ordered_pair(esk85_3(X1,X2,X3),esk84_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_783,
[final] ).
cnf(c_0_1681,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_784,
[final] ).
cnf(c_0_1682,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_785,
[final] ).
cnf(c_0_1683,plain,
( in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk156_3(X3,X2,X1) != esk155_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_786,
[final] ).
cnf(c_0_1684,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_787,
[final] ).
cnf(c_0_1685,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_788,
[final] ).
cnf(c_0_1686,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_789,
[final] ).
cnf(c_0_1687,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| in(esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_790,
[final] ).
cnf(c_0_1688,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_791,
[final] ).
cnf(c_0_1689,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| in(esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_792,
[final] ).
cnf(c_0_1690,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| esk134_4(X2,X1,X5,X4) = esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_793,
[final] ).
cnf(c_0_1691,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| esk134_4(X2,X1,X5,X4) = esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_794,
[final] ).
cnf(c_0_1692,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_795,
[final] ).
cnf(c_0_1693,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_796,
[final] ).
cnf(c_0_1694,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_797,
[final] ).
cnf(c_0_1695,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_798,
[final] ).
cnf(c_0_1696,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_799,
[final] ).
cnf(c_0_1697,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_800,
[final] ).
cnf(c_0_1698,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_801,
[final] ).
cnf(c_0_1699,plain,
( empty(X2)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_802,
[final] ).
cnf(c_0_1700,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_803,
[final] ).
cnf(c_0_1701,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_804,
[final] ).
cnf(c_0_1702,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_805,
[final] ).
cnf(c_0_1703,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_806,
[final] ).
cnf(c_0_1704,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_807,
[final] ).
cnf(c_0_1705,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_808,
[final] ).
cnf(c_0_1706,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_809,
[final] ).
cnf(c_0_1707,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_810,
[final] ).
cnf(c_0_1708,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_811,
[final] ).
cnf(c_0_1709,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_812,
[final] ).
cnf(c_0_1710,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_813,
[final] ).
cnf(c_0_1711,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_814,
[final] ).
cnf(c_0_1712,plain,
( empty(X2)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_815,
[final] ).
cnf(c_0_1713,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_816,
[final] ).
cnf(c_0_1714,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_817,
[final] ).
cnf(c_0_1715,plain,
( ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1)) = esk155_3(X3,X2,X1)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_818,
[final] ).
cnf(c_0_1716,plain,
( ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1)) = esk156_3(X3,X2,X1)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_819,
[final] ).
cnf(c_0_1717,plain,
( ordered_pair(esk157_3(X3,X2,X1),esk158_3(X3,X2,X1)) = esk155_3(X3,X2,X1)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_820,
[final] ).
cnf(c_0_1718,plain,
( ordered_pair(esk159_3(X3,X2,X1),esk160_3(X3,X2,X1)) = esk156_3(X3,X2,X1)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_821,
[final] ).
cnf(c_0_1719,plain,
( empty(X2)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_822,
[final] ).
cnf(c_0_1720,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_823,
[final] ).
cnf(c_0_1721,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_824,
[final] ).
cnf(c_0_1722,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_825,
[final] ).
cnf(c_0_1723,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_826,
[final] ).
cnf(c_0_1724,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_827,
[final] ).
cnf(c_0_1725,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| in(esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_828,
[final] ).
cnf(c_0_1726,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_829,
[final] ).
cnf(c_0_1727,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_830,
[final] ).
cnf(c_0_1728,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_831,
[final] ).
cnf(c_0_1729,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| esk134_4(X2,X1,X4,X3) = esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_832,
[final] ).
cnf(c_0_1730,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1)
| in(esk78_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
c_0_833,
[final] ).
cnf(c_0_1731,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk78_3(X1,X2,X3),esk79_3(X1,X2,X3)),X1)
| in(esk79_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
c_0_834,
[final] ).
cnf(c_0_1732,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk89_3(X2,X1,X3)),X1)
| ~ in(esk89_3(X2,X1,X3),X3) ),
c_0_835,
[final] ).
cnf(c_0_1733,plain,
( X2 = fiber(X1,X3)
| esk31_3(X1,X3,X2) = X3
| ~ relation(X1)
| ~ in(ordered_pair(esk31_3(X1,X3,X2),X3),X1)
| ~ in(esk31_3(X1,X3,X2),X2) ),
c_0_836,
[final] ).
cnf(c_0_1734,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_837,
[final] ).
cnf(c_0_1735,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_838,
[final] ).
cnf(c_0_1736,plain,
( esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk156_3(X3,X2,X1) != esk155_3(X3,X2,X1)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_839,
[final] ).
cnf(c_0_1737,plain,
( in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk156_3(X3,X2,X1) != esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_840,
[final] ).
cnf(c_0_1738,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_841,
[final] ).
cnf(c_0_1739,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_842,
[final] ).
cnf(c_0_1740,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_843,
[final] ).
cnf(c_0_1741,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_844,
[final] ).
cnf(c_0_1742,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk128_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_845,
[final] ).
cnf(c_0_1743,plain,
( empty(X2)
| in(ordered_pair(esk130_2(X2,X1),X3),X1)
| esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk132_3(X2,X1,X5)) ),
c_0_846,
[final] ).
cnf(c_0_1744,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk57_3(X2,X3,X1),X3)
| ~ in(esk57_3(X2,X3,X1),X2)
| ~ in(esk57_3(X2,X3,X1),X1) ),
c_0_847,
[final] ).
cnf(c_0_1745,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_848,
[final] ).
cnf(c_0_1746,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_849,
[final] ).
cnf(c_0_1747,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk161_3(X3,X2,X1)) ),
c_0_850,
[final] ).
cnf(c_0_1748,plain,
( esk154_3(X3,X2,X1) = esk155_3(X3,X2,X1)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_851,
[final] ).
cnf(c_0_1749,plain,
( esk154_3(X3,X2,X1) = esk156_3(X3,X2,X1)
| in(X4,esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
c_0_852,
[final] ).
cnf(c_0_1750,plain,
( apply(X1,esk5_4(X1,X3,X2,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_853,
[final] ).
cnf(c_0_1751,plain,
( in(esk5_4(X1,X3,X2,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_854,
[final] ).
cnf(c_0_1752,plain,
( in(esk14_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_855,
[final] ).
cnf(c_0_1753,plain,
( in(esk11_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_856,
[final] ).
cnf(c_0_1754,plain,
( in(esk45_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_857,
[final] ).
cnf(c_0_1755,plain,
( in(esk46_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_858,
[final] ).
cnf(c_0_1756,plain,
( empty(X2)
| ordered_pair(esk126_2(X2,X1),esk127_2(X2,X1)) = esk124_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_859,
[final] ).
cnf(c_0_1757,plain,
( empty(X2)
| ordered_pair(esk129_2(X2,X1),esk130_2(X2,X1)) = esk125_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_860,
[final] ).
cnf(c_0_1758,plain,
( X1 = set_difference(X2,X3)
| in(esk67_3(X2,X3,X1),X3)
| ~ in(esk67_3(X2,X3,X1),X2)
| ~ in(esk67_3(X2,X3,X1),X1) ),
c_0_861,
[final] ).
cnf(c_0_1759,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk128_2(X2,X1))
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_862,
[final] ).
cnf(c_0_1760,plain,
( empty(X2)
| in(esk130_2(X2,X1),esk131_2(X2,X1))
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_863,
[final] ).
cnf(c_0_1761,plain,
( empty(X2)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| esk125_2(X2,X1) != esk124_2(X2,X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_864,
[final] ).
cnf(c_0_1762,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk89_3(X2,X1,X3)),X1)
| in(esk89_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_865,
[final] ).
cnf(c_0_1763,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_866,
[final] ).
cnf(c_0_1764,plain,
( empty(X2)
| in(esk129_2(X2,X1),X2)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_867,
[final] ).
cnf(c_0_1765,plain,
( empty(X2)
| esk123_2(X2,X1) = esk124_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_868,
[final] ).
cnf(c_0_1766,plain,
( empty(X2)
| esk126_2(X2,X1) = esk128_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_869,
[final] ).
cnf(c_0_1767,plain,
( empty(X2)
| esk123_2(X2,X1) = esk125_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_870,
[final] ).
cnf(c_0_1768,plain,
( empty(X2)
| esk129_2(X2,X1) = esk131_2(X2,X1)
| esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk132_3(X2,X1,X4)) ),
c_0_871,
[final] ).
cnf(c_0_1769,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk77_2(X1,X2),esk76_2(X1,X2)),X1)
| ~ in(ordered_pair(esk76_2(X1,X2),esk77_2(X1,X2)),X2) ),
c_0_872,
[final] ).
cnf(c_0_1770,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X2)
| ~ in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X1) ),
c_0_873,
[final] ).
cnf(c_0_1771,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1))
| ~ in(X5,esk121_3(X2,X1,X4)) ),
c_0_874,
[final] ).
cnf(c_0_1772,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1))
| ~ in(X5,esk121_3(X2,X1,X4)) ),
c_0_875,
[final] ).
cnf(c_0_1773,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
c_0_876,
[final] ).
cnf(c_0_1774,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| ordered_pair(esk48_3(X2,X3,X1),esk49_3(X2,X3,X1)) = esk47_3(X2,X3,X1) ),
c_0_877,
[final] ).
cnf(c_0_1775,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_878,
[final] ).
cnf(c_0_1776,plain,
( X2 = fiber(X1,X3)
| in(esk31_3(X1,X3,X2),X2)
| in(ordered_pair(esk31_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
c_0_879,
[final] ).
cnf(c_0_1777,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk44_3(X2,X3,X1),X1)
| ~ in(esk44_3(X2,X3,X1),X2) ),
c_0_880,
[final] ).
cnf(c_0_1778,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk44_3(X2,X3,X1),X1)
| ~ in(esk44_3(X2,X3,X1),X3) ),
c_0_881,
[final] ).
cnf(c_0_1779,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_882,
[final] ).
cnf(c_0_1780,plain,
( X1 = set_union2(X2,X3)
| in(esk44_3(X2,X3,X1),X3)
| in(esk44_3(X2,X3,X1),X2)
| in(esk44_3(X2,X3,X1),X1) ),
c_0_883,
[final] ).
cnf(c_0_1781,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_884,
[final] ).
cnf(c_0_1782,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_885,
[final] ).
cnf(c_0_1783,plain,
( X1 = cartesian_product2(X2,X3)
| esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk47_3(X2,X3,X1),X1) ),
c_0_886,
[final] ).
cnf(c_0_1784,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_887,
[final] ).
cnf(c_0_1785,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_888,
[final] ).
cnf(c_0_1786,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| in(X4,esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_889,
[final] ).
cnf(c_0_1787,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_890,
[final] ).
cnf(c_0_1788,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_891,
[final] ).
cnf(c_0_1789,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| in(X4,esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_892,
[final] ).
cnf(c_0_1790,plain,
( X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2
| ~ subset(esk32_2(X2,X1),esk33_2(X2,X1))
| ~ in(ordered_pair(esk32_2(X2,X1),esk33_2(X2,X1)),X1) ),
c_0_893,
[final] ).
cnf(c_0_1791,plain,
( empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_894,
[final] ).
cnf(c_0_1792,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_895,
[final] ).
cnf(c_0_1793,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_896,
[final] ).
cnf(c_0_1794,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_897,
[final] ).
cnf(c_0_1795,plain,
( empty(X2)
| in(ordered_pair(esk115_2(X2,X1),X3),X1)
| esk120_3(X2,X1,X4) = esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk117_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_898,
[final] ).
cnf(c_0_1796,plain,
( empty(X2)
| in(ordered_pair(esk116_2(X2,X1),X3),X1)
| esk120_3(X2,X1,X4) = esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk118_2(X2,X1))
| ~ in(X4,esk119_2(X2,X1)) ),
c_0_899,
[final] ).
cnf(c_0_1797,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_900,
[final] ).
cnf(c_0_1798,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1))
| ~ in(X4,esk121_3(X2,X1,X3)) ),
c_0_901,
[final] ).
cnf(c_0_1799,plain,
( X1 = set_difference(X2,X3)
| in(esk67_3(X2,X3,X1),X1)
| ~ in(esk67_3(X2,X3,X1),X3) ),
c_0_902,
[final] ).
cnf(c_0_1800,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_903,
[final] ).
cnf(c_0_1801,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_904,
[final] ).
cnf(c_0_1802,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_905,
[final] ).
cnf(c_0_1803,plain,
( in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_906,
[final] ).
cnf(c_0_1804,plain,
( in(esk146_1(X1),X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_907,
[final] ).
cnf(c_0_1805,plain,
( in(esk148_1(X1),X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_908,
[final] ).
cnf(c_0_1806,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk55_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
c_0_909,
[final] ).
cnf(c_0_1807,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk77_2(X1,X2),esk76_2(X1,X2)),X1)
| in(ordered_pair(esk76_2(X1,X2),esk77_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_910,
[final] ).
cnf(c_0_1808,plain,
( singleton(esk146_1(X1)) = esk147_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_911,
[final] ).
cnf(c_0_1809,plain,
( singleton(esk148_1(X1)) = esk149_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_912,
[final] ).
cnf(c_0_1810,plain,
( ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| esk145_1(X1) != esk144_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_913,
[final] ).
cnf(c_0_1811,plain,
( X1 = X2
| in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X2)
| in(ordered_pair(esk39_2(X1,X2),esk40_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_914,
[final] ).
cnf(c_0_1812,plain,
( esk143_1(X1) = esk144_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_915,
[final] ).
cnf(c_0_1813,plain,
( esk143_1(X1) = esk145_1(X1)
| ordered_pair(esk152_3(X1,X3,X2),esk153_3(X1,X3,X2)) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_916,
[final] ).
cnf(c_0_1814,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk41_3(X2,X3,X1),X1)
| esk41_3(X2,X3,X1) != X2 ),
c_0_917,
[final] ).
cnf(c_0_1815,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk41_3(X2,X3,X1),X1)
| esk41_3(X2,X3,X1) != X3 ),
c_0_918,
[final] ).
cnf(c_0_1816,plain,
( in(ordered_pair(esk71_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_919,
[final] ).
cnf(c_0_1817,plain,
( in(ordered_pair(X3,esk58_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
c_0_920,
[final] ).
cnf(c_0_1818,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_921,
[final] ).
cnf(c_0_1819,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_922,
[final] ).
cnf(c_0_1820,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_923,
[final] ).
cnf(c_0_1821,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_924,
[final] ).
cnf(c_0_1822,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_925,
[final] ).
cnf(c_0_1823,plain,
( X2 = relation_image(X1,X3)
| in(esk12_3(X1,X3,X2),X2)
| in(esk13_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_926,
[final] ).
cnf(c_0_1824,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_927,
[final] ).
cnf(c_0_1825,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_928,
[final] ).
cnf(c_0_1826,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_929,
[final] ).
cnf(c_0_1827,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_930,
[final] ).
cnf(c_0_1828,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_931,
[final] ).
cnf(c_0_1829,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_932,
[final] ).
cnf(c_0_1830,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_933,
[final] ).
cnf(c_0_1831,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_934,
[final] ).
cnf(c_0_1832,plain,
( X1 = set_difference(X2,X3)
| in(esk67_3(X2,X3,X1),X1)
| in(esk67_3(X2,X3,X1),X2) ),
c_0_935,
[final] ).
cnf(c_0_1833,plain,
( X1 = set_intersection2(X2,X3)
| in(esk57_3(X2,X3,X1),X1)
| in(esk57_3(X2,X3,X1),X2) ),
c_0_936,
[final] ).
cnf(c_0_1834,plain,
( X1 = set_intersection2(X2,X3)
| in(esk57_3(X2,X3,X1),X1)
| in(esk57_3(X2,X3,X1),X3) ),
c_0_937,
[final] ).
cnf(c_0_1835,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk48_3(X2,X3,X1),X2) ),
c_0_938,
[final] ).
cnf(c_0_1836,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk47_3(X2,X3,X1),X1)
| in(esk49_3(X2,X3,X1),X3) ),
c_0_939,
[final] ).
cnf(c_0_1837,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk52_2(X1,X2),esk53_2(X1,X2)),X2) ),
c_0_940,
[final] ).
cnf(c_0_1838,plain,
( empty(X2)
| in(esk115_2(X2,X1),esk117_2(X2,X1))
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_941,
[final] ).
cnf(c_0_1839,plain,
( empty(X2)
| in(esk116_2(X2,X1),esk118_2(X2,X1))
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_942,
[final] ).
cnf(c_0_1840,plain,
( in(esk146_1(X1),X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_943,
[final] ).
cnf(c_0_1841,plain,
( in(esk148_1(X1),X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_944,
[final] ).
cnf(c_0_1842,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk86_2(X1,X2),esk88_2(X1,X2)),X1) ),
c_0_945,
[final] ).
cnf(c_0_1843,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk74_2(X1,X2),esk75_2(X1,X2)),X1) ),
c_0_946,
[final] ).
cnf(c_0_1844,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk75_2(X1,X2),esk74_2(X1,X2)),X1) ),
c_0_947,
[final] ).
cnf(c_0_1845,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk26_2(X1,X2),esk26_2(X1,X2)),X1) ),
c_0_948,
[final] ).
cnf(c_0_1846,plain,
( X1 = unordered_pair(X2,X3)
| esk41_3(X2,X3,X1) = X3
| esk41_3(X2,X3,X1) = X2
| in(esk41_3(X2,X3,X1),X1) ),
c_0_949,
[final] ).
cnf(c_0_1847,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk89_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_950,
[final] ).
cnf(c_0_1848,plain,
( singleton(esk146_1(X1)) = esk147_1(X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_951,
[final] ).
cnf(c_0_1849,plain,
( singleton(esk148_1(X1)) = esk149_1(X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_952,
[final] ).
cnf(c_0_1850,plain,
( in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| esk172_2(X2,X1) != esk171_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_953,
[final] ).
cnf(c_0_1851,plain,
( singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| esk145_1(X1) != esk144_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_954,
[final] ).
cnf(c_0_1852,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_955,
[final] ).
cnf(c_0_1853,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_956,
[final] ).
cnf(c_0_1854,plain,
( empty(X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_957,
[final] ).
cnf(c_0_1855,plain,
( empty(X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_958,
[final] ).
cnf(c_0_1856,plain,
( empty(X2)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_959,
[final] ).
cnf(c_0_1857,plain,
( in(esk173_2(X2,X1),X2)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_960,
[final] ).
cnf(c_0_1858,plain,
( in(esk174_2(X2,X1),X2)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_961,
[final] ).
cnf(c_0_1859,plain,
( esk143_1(X1) = esk144_1(X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_962,
[final] ).
cnf(c_0_1860,plain,
( esk143_1(X1) = esk145_1(X1)
| singleton(esk152_3(X1,X3,X2)) = esk153_3(X1,X3,X2)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_963,
[final] ).
cnf(c_0_1861,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_964,
[final] ).
cnf(c_0_1862,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_965,
[final] ).
cnf(c_0_1863,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_966,
[final] ).
cnf(c_0_1864,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_967,
[final] ).
cnf(c_0_1865,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_968,
[final] ).
cnf(c_0_1866,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_969,
[final] ).
cnf(c_0_1867,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_970,
[final] ).
cnf(c_0_1868,plain,
( in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| esk172_2(X2,X1) != esk171_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_971,
[final] ).
cnf(c_0_1869,plain,
( in(esk173_2(X2,X1),X2)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_972,
[final] ).
cnf(c_0_1870,plain,
( in(esk174_2(X2,X1),X2)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_973,
[final] ).
cnf(c_0_1871,plain,
( X1 = inclusion_relation(X2)
| subset(esk32_2(X2,X1),esk33_2(X2,X1))
| in(ordered_pair(esk32_2(X2,X1),esk33_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
c_0_974,
[final] ).
cnf(c_0_1872,plain,
( in(esk146_1(X1),X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_975,
[final] ).
cnf(c_0_1873,plain,
( in(esk148_1(X1),X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_976,
[final] ).
cnf(c_0_1874,plain,
( X2 = fiber(X1,X3)
| in(esk31_3(X1,X3,X2),X2)
| ~ relation(X1)
| esk31_3(X1,X3,X2) != X3 ),
c_0_977,
[final] ).
cnf(c_0_1875,plain,
( quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| relation_dom_as_subset(X2,X3,X1) != X2 ),
c_0_978,
[final] ).
cnf(c_0_1876,plain,
( relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| ~ quasi_total(X1,X2,X3) ),
c_0_979,
[final] ).
cnf(c_0_1877,plain,
( X3 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) != X2 ),
c_0_980,
[final] ).
cnf(c_0_1878,plain,
( X3 = empty_set
| relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3) ),
c_0_981,
[final] ).
cnf(c_0_1879,plain,
( empty(X2)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| esk116_2(X2,X1) != esk115_2(X2,X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_982,
[final] ).
cnf(c_0_1880,plain,
( ordinal(esk173_2(X2,X1))
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_983,
[final] ).
cnf(c_0_1881,plain,
( ordinal(esk174_2(X2,X1))
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_984,
[final] ).
cnf(c_0_1882,plain,
( ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| esk172_2(X2,X1) != esk171_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_985,
[final] ).
cnf(c_0_1883,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_986,
[final] ).
cnf(c_0_1884,plain,
( esk173_2(X2,X1) = esk171_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_987,
[final] ).
cnf(c_0_1885,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_988,
[final] ).
cnf(c_0_1886,plain,
( esk174_2(X2,X1) = esk172_2(X2,X1)
| in(esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_989,
[final] ).
cnf(c_0_1887,plain,
( singleton(esk146_1(X1)) = esk147_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_990,
[final] ).
cnf(c_0_1888,plain,
( singleton(esk148_1(X1)) = esk149_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_991,
[final] ).
cnf(c_0_1889,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_992,
[final] ).
cnf(c_0_1890,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_993,
[final] ).
cnf(c_0_1891,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_994,
[final] ).
cnf(c_0_1892,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_995,
[final] ).
cnf(c_0_1893,plain,
( empty(X2)
| in(esk114_2(X2,X1),X2)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_996,
[final] ).
cnf(c_0_1894,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_997,
[final] ).
cnf(c_0_1895,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_998,
[final] ).
cnf(c_0_1896,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| in(X3,esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_999,
[final] ).
cnf(c_0_1897,plain,
( in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| esk145_1(X1) != esk144_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1000,
[final] ).
cnf(c_0_1898,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_1001,
[final] ).
cnf(c_0_1899,plain,
( ordinal(esk173_2(X2,X1))
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1002,
[final] ).
cnf(c_0_1900,plain,
( in(esk173_2(X2,X1),X2)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1003,
[final] ).
cnf(c_0_1901,plain,
( ordinal(esk174_2(X2,X1))
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1004,
[final] ).
cnf(c_0_1902,plain,
( in(esk174_2(X2,X1),X2)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1005,
[final] ).
cnf(c_0_1903,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk72_2(X1,X2)),X1)
| ~ in(esk72_2(X1,X2),X2) ),
c_0_1006,
[final] ).
cnf(c_0_1904,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk59_2(X1,X2),X3),X1)
| ~ in(esk59_2(X1,X2),X2) ),
c_0_1007,
[final] ).
cnf(c_0_1905,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1008,
[final] ).
cnf(c_0_1906,plain,
( esk173_2(X2,X1) = esk171_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1009,
[final] ).
cnf(c_0_1907,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1010,
[final] ).
cnf(c_0_1908,plain,
( esk174_2(X2,X1) = esk172_2(X2,X1)
| in(esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1011,
[final] ).
cnf(c_0_1909,plain,
( esk143_1(X1) = esk144_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1012,
[final] ).
cnf(c_0_1910,plain,
( esk143_1(X1) = esk145_1(X1)
| in(esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1013,
[final] ).
cnf(c_0_1911,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1014,
[final] ).
cnf(c_0_1912,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1015,
[final] ).
cnf(c_0_1913,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk27_3(X1,X2,X3)) ),
c_0_1016,
[final] ).
cnf(c_0_1914,plain,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
c_0_1017,
[final] ).
cnf(c_0_1915,plain,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
c_0_1018,
[final] ).
cnf(c_0_1916,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_1019,
[final] ).
cnf(c_0_1917,plain,
( ordinal(esk173_2(X2,X1))
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1020,
[final] ).
cnf(c_0_1918,plain,
( ordinal(esk174_2(X2,X1))
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1021,
[final] ).
cnf(c_0_1919,plain,
( empty(X2)
| esk117_2(X2,X1) = esk114_2(X2,X1)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_1022,
[final] ).
cnf(c_0_1920,plain,
( empty(X2)
| esk114_2(X2,X1) = esk118_2(X2,X1)
| esk120_3(X2,X1,X3) = esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk119_2(X2,X1)) ),
c_0_1023,
[final] ).
cnf(c_0_1921,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1024,
[final] ).
cnf(c_0_1922,plain,
( esk173_2(X2,X1) = esk171_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1025,
[final] ).
cnf(c_0_1923,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1026,
[final] ).
cnf(c_0_1924,plain,
( esk174_2(X2,X1) = esk172_2(X2,X1)
| ordinal(esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1027,
[final] ).
cnf(c_0_1925,plain,
( in(esk146_1(X1),X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1028,
[final] ).
cnf(c_0_1926,plain,
( in(esk148_1(X1),X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1029,
[final] ).
cnf(c_0_1927,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_1030,
[final] ).
cnf(c_0_1928,plain,
( singleton(esk146_1(X1)) = esk147_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1031,
[final] ).
cnf(c_0_1929,plain,
( singleton(esk148_1(X1)) = esk149_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1032,
[final] ).
cnf(c_0_1930,plain,
( in(X4,relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_1033,
[final] ).
cnf(c_0_1931,plain,
( in(X5,relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_1034,
[final] ).
cnf(c_0_1932,plain,
( in(esk152_3(X1,X3,X2),X1)
| esk145_1(X1) != esk144_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1035,
[final] ).
cnf(c_0_1933,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk73_2(X1,X2),esk72_2(X1,X2)),X1)
| in(esk72_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1036,
[final] ).
cnf(c_0_1934,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk59_2(X1,X2),esk60_2(X1,X2)),X1)
| in(esk59_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1037,
[final] ).
cnf(c_0_1935,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_1038,
[final] ).
cnf(c_0_1936,plain,
( esk143_1(X1) = esk144_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1039,
[final] ).
cnf(c_0_1937,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1040,
[final] ).
cnf(c_0_1938,plain,
( esk143_1(X1) = esk145_1(X1)
| in(esk152_3(X1,X3,X2),X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1041,
[final] ).
cnf(c_0_1939,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1042,
[final] ).
cnf(c_0_1940,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_1043,
[final] ).
cnf(c_0_1941,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk56_2(X1,X2))
| ~ in(X3,esk56_2(X1,X2)) ),
c_0_1044,
[final] ).
cnf(c_0_1942,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_1045,
[final] ).
cnf(c_0_1943,plain,
( in(esk146_1(X1),X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1046,
[final] ).
cnf(c_0_1944,plain,
( in(esk148_1(X1),X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1047,
[final] ).
cnf(c_0_1945,plain,
( X2 = empty_set
| X1 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| ~ quasi_total(X1,X2,X3) ),
c_0_1048,
[final] ).
cnf(c_0_1946,plain,
( singleton(esk146_1(X1)) = esk147_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1049,
[final] ).
cnf(c_0_1947,plain,
( singleton(esk148_1(X1)) = esk149_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1050,
[final] ).
cnf(c_0_1948,plain,
( in(X2,esk150_2(X1,X3))
| esk145_1(X1) != esk144_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1051,
[final] ).
cnf(c_0_1949,plain,
( X3 = empty_set
| in(esk55_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
c_0_1052,
[final] ).
cnf(c_0_1950,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk28_2(X1,X2),X2)
| ~ in(esk28_2(X1,X2),esk29_2(X1,X2)) ),
c_0_1053,
[final] ).
cnf(c_0_1951,plain,
( subset(X1,X2)
| in(ordered_pair(esk52_2(X1,X2),esk53_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_1054,
[final] ).
cnf(c_0_1952,plain,
( in(esk68_3(X1,X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_1055,
[final] ).
cnf(c_0_1953,plain,
( esk143_1(X1) = esk144_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1056,
[final] ).
cnf(c_0_1954,plain,
( esk143_1(X1) = esk145_1(X1)
| in(X2,esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1057,
[final] ).
cnf(c_0_1955,plain,
( esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| esk172_2(X2,X1) != esk171_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1058,
[final] ).
cnf(c_0_1956,plain,
( esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| esk172_2(X2,X1) != esk171_2(X2,X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1059,
[final] ).
cnf(c_0_1957,plain,
( apply(X1,esk68_3(X1,X2,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_1060,
[final] ).
cnf(c_0_1958,plain,
( in(esk173_2(X2,X1),X2)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1061,
[final] ).
cnf(c_0_1959,plain,
( in(esk173_2(X2,X1),X2)
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1062,
[final] ).
cnf(c_0_1960,plain,
( in(esk174_2(X2,X1),X2)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1063,
[final] ).
cnf(c_0_1961,plain,
( in(esk174_2(X2,X1),X2)
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1064,
[final] ).
cnf(c_0_1962,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk86_2(X1,X2),esk87_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1065,
[final] ).
cnf(c_0_1963,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk87_2(X1,X2),esk88_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1066,
[final] ).
cnf(c_0_1964,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk61_2(X1,X2),esk62_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1067,
[final] ).
cnf(c_0_1965,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk62_2(X1,X2),esk61_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1068,
[final] ).
cnf(c_0_1966,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_1069,
[final] ).
cnf(c_0_1967,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_1070,
[final] ).
cnf(c_0_1968,plain,
( in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| esk172_2(X2,X1) != esk171_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1071,
[final] ).
cnf(c_0_1969,plain,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| esk69_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(esk69_2(X1,X2),X2) ),
c_0_1072,
[final] ).
cnf(c_0_1970,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_1073,
[final] ).
cnf(c_0_1971,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_1074,
[final] ).
cnf(c_0_1972,plain,
( in(esk173_2(X2,X1),X2)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1075,
[final] ).
cnf(c_0_1973,plain,
( in(esk174_2(X2,X1),X2)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1076,
[final] ).
cnf(c_0_1974,plain,
( ordinal(esk173_2(X2,X1))
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1077,
[final] ).
cnf(c_0_1975,plain,
( ordinal(esk173_2(X2,X1))
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1078,
[final] ).
cnf(c_0_1976,plain,
( ordinal(esk174_2(X2,X1))
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1079,
[final] ).
cnf(c_0_1977,plain,
( ordinal(esk174_2(X2,X1))
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1080,
[final] ).
cnf(c_0_1978,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk64_2(X2,X1),X3)
| ~ in(esk64_2(X2,X1),X1) ),
c_0_1081,
[final] ).
cnf(c_0_1979,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1082,
[final] ).
cnf(c_0_1980,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1083,
[final] ).
cnf(c_0_1981,plain,
( esk173_2(X2,X1) = esk171_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1084,
[final] ).
cnf(c_0_1982,plain,
( esk173_2(X2,X1) = esk171_2(X2,X1)
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1085,
[final] ).
cnf(c_0_1983,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1086,
[final] ).
cnf(c_0_1984,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1087,
[final] ).
cnf(c_0_1985,plain,
( esk174_2(X2,X1) = esk172_2(X2,X1)
| esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1088,
[final] ).
cnf(c_0_1986,plain,
( esk174_2(X2,X1) = esk172_2(X2,X1)
| esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk175_2(X2,X1)) ),
c_0_1089,
[final] ).
cnf(c_0_1987,plain,
( in(X3,esk63_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_1090,
[final] ).
cnf(c_0_1988,plain,
( in(esk63_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_1091,
[final] ).
cnf(c_0_1989,plain,
( ordered_pair(esk146_1(X1),esk147_1(X1)) = esk144_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1092,
[final] ).
cnf(c_0_1990,plain,
( ordered_pair(esk148_1(X1),esk149_1(X1)) = esk145_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1093,
[final] ).
cnf(c_0_1991,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_1094,
[final] ).
cnf(c_0_1992,plain,
( ordinal(esk173_2(X2,X1))
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1095,
[final] ).
cnf(c_0_1993,plain,
( ordinal(esk174_2(X2,X1))
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1096,
[final] ).
cnf(c_0_1994,plain,
( X2 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| X1 != empty_set ),
c_0_1097,
[final] ).
cnf(c_0_1995,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk27_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
c_0_1098,
[final] ).
cnf(c_0_1996,plain,
( esk170_2(X2,X1) = esk171_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1099,
[final] ).
cnf(c_0_1997,plain,
( esk173_2(X2,X1) = esk171_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1100,
[final] ).
cnf(c_0_1998,plain,
( esk170_2(X2,X1) = esk172_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1101,
[final] ).
cnf(c_0_1999,plain,
( esk174_2(X2,X1) = esk172_2(X2,X1)
| in(X3,esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1102,
[final] ).
cnf(c_0_2000,plain,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
c_0_1103,
[final] ).
cnf(c_0_2001,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
c_0_1104,
[final] ).
cnf(c_0_2002,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_1105,
[final] ).
cnf(c_0_2003,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_1106,
[final] ).
cnf(c_0_2004,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_1107,
[final] ).
cnf(c_0_2005,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
c_0_1108,
[final] ).
cnf(c_0_2006,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
c_0_1109,
[final] ).
cnf(c_0_2007,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk42_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
c_0_1110,
[final] ).
cnf(c_0_2008,plain,
( in(esk146_1(X1),X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1111,
[final] ).
cnf(c_0_2009,plain,
( in(esk148_1(X1),X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1112,
[final] ).
cnf(c_0_2010,plain,
( subset(X4,X3)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1113,
[final] ).
cnf(c_0_2011,plain,
( X1 = X2
| ~ in(ordered_pair(X3,X2),X4)
| ~ in(ordered_pair(X3,X1),X4)
| ~ function(X4) ),
c_0_1114,
[final] ).
cnf(c_0_2012,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_1115,
[final] ).
cnf(c_0_2013,plain,
( singleton(esk146_1(X1)) = esk147_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1116,
[final] ).
cnf(c_0_2014,plain,
( singleton(esk148_1(X1)) = esk149_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1117,
[final] ).
cnf(c_0_2015,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_1118,
[final] ).
cnf(c_0_2016,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_1119,
[final] ).
cnf(c_0_2017,plain,
( esk151_3(X1,X3,X2) = X2
| esk145_1(X1) != esk144_1(X1)
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1120,
[final] ).
cnf(c_0_2018,plain,
( X1 = powerset(X2)
| ~ subset(esk35_2(X2,X1),X2)
| ~ in(esk35_2(X2,X1),X1) ),
c_0_1121,
[final] ).
cnf(c_0_2019,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_1122,
[final] ).
cnf(c_0_2020,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
c_0_1123,
[final] ).
cnf(c_0_2021,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_1124,
[final] ).
cnf(c_0_2022,plain,
( X1 = X2
| ~ in(esk178_2(X1,X2),X2)
| ~ in(esk178_2(X1,X2),X1) ),
c_0_1125,
[final] ).
cnf(c_0_2023,plain,
( esk143_1(X1) = esk144_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1126,
[final] ).
cnf(c_0_2024,plain,
( esk143_1(X1) = esk145_1(X1)
| esk151_3(X1,X3,X2) = X2
| ~ in(X2,esk150_2(X1,X3)) ),
c_0_1127,
[final] ).
cnf(c_0_2025,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
c_0_1128,
[final] ).
cnf(c_0_2026,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1129,
[final] ).
cnf(c_0_2027,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
c_0_1130,
[final] ).
cnf(c_0_2028,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1131,
[final] ).
cnf(c_0_2029,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
c_0_1132,
[final] ).
cnf(c_0_2030,plain,
( relation_dom(X3) = relation_field(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
c_0_1133,
[final] ).
cnf(c_0_2031,plain,
( relation_rng(X3) = relation_field(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
c_0_1134,
[final] ).
cnf(c_0_2032,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1135,
[final] ).
cnf(c_0_2033,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
c_0_1136,
[final] ).
cnf(c_0_2034,plain,
( one_to_one(X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
c_0_1137,
[final] ).
cnf(c_0_2035,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
c_0_1138,
[final] ).
cnf(c_0_2036,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
c_0_1139,
[final] ).
cnf(c_0_2037,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk43_1(X1))
| ~ in(X2,esk43_1(X1)) ),
c_0_1140,
[final] ).
cnf(c_0_2038,plain,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
c_0_1141,
[final] ).
cnf(c_0_2039,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_1142,
[final] ).
cnf(c_0_2040,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_1143,
[final] ).
cnf(c_0_2041,plain,
( X2 = relation_rng(X1)
| in(esk69_2(X1,X2),X2)
| apply(X1,esk70_2(X1,X2)) = esk69_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1144,
[final] ).
cnf(c_0_2042,plain,
( X1 = union(X2)
| in(esk64_2(X2,X1),X1)
| in(esk64_2(X2,X1),esk65_2(X2,X1)) ),
c_0_1145,
[final] ).
cnf(c_0_2043,plain,
( in(X4,X2)
| X4 = X3
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1146,
[final] ).
cnf(c_0_2044,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
c_0_1147,
[final] ).
cnf(c_0_2045,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk29_2(X1,X2),X1)
| ~ in(esk28_2(X1,X2),X2) ),
c_0_1148,
[final] ).
cnf(c_0_2046,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk28_2(X1,X2),X3)
| in(esk28_2(X1,X2),X2)
| ~ in(X3,X1) ),
c_0_1149,
[final] ).
cnf(c_0_2047,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1150,
[final] ).
cnf(c_0_2048,plain,
( ~ in(X1,X2)
| ~ in(X3,esk179_2(X1,X2))
| ~ in(X3,X2) ),
c_0_1151,
[final] ).
cnf(c_0_2049,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_1152,
[final] ).
cnf(c_0_2050,plain,
( X2 = relation_rng(X1)
| in(esk69_2(X1,X2),X2)
| in(esk70_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1153,
[final] ).
cnf(c_0_2051,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
c_0_1154,
[final] ).
cnf(c_0_2052,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
c_0_1155,
[final] ).
cnf(c_0_2053,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
c_0_1156,
[final] ).
cnf(c_0_2054,plain,
( in(apply(X1,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1157,
[final] ).
cnf(c_0_2055,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1158,
[final] ).
cnf(c_0_2056,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1159,
[final] ).
cnf(c_0_2057,plain,
( ordered_pair(esk23_2(X2,X1),esk24_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
c_0_1160,
[final] ).
cnf(c_0_2058,plain,
( X4 = pair_second(X1)
| ordered_pair(esk36_2(X1,X4),esk37_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
c_0_1161,
[final] ).
cnf(c_0_2059,plain,
( X4 = pair_first(X1)
| ordered_pair(esk21_2(X1,X4),esk22_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
c_0_1162,
[final] ).
cnf(c_0_2060,plain,
( in(X3,esk181_2(X2,X1))
| ~ in(X1,esk180_1(X2))
| ~ subset(X3,X1) ),
c_0_1163,
[final] ).
cnf(c_0_2061,plain,
( in(esk138_1(X1),X1)
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1164,
[final] ).
cnf(c_0_2062,plain,
( in(esk138_1(X1),X1)
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1165,
[final] ).
cnf(c_0_2063,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
c_0_1166,
[final] ).
cnf(c_0_2064,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1167,
[final] ).
cnf(c_0_2065,plain,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_1168,
[final] ).
cnf(c_0_2066,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1169,
[final] ).
cnf(c_0_2067,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1170,
[final] ).
cnf(c_0_2068,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1171,
[final] ).
cnf(c_0_2069,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1172,
[final] ).
cnf(c_0_2070,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1173,
[final] ).
cnf(c_0_2071,plain,
( in(esk138_1(X1),X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1174,
[final] ).
cnf(c_0_2072,plain,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
c_0_1175,
[final] ).
cnf(c_0_2073,plain,
( X1 = singleton(X2)
| esk30_2(X2,X1) != X2
| ~ in(esk30_2(X2,X1),X1) ),
c_0_1176,
[final] ).
cnf(c_0_2074,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1177,
[final] ).
cnf(c_0_2075,plain,
( singleton(esk138_1(X1)) = esk139_1(X1)
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1178,
[final] ).
cnf(c_0_2076,plain,
( singleton(esk138_1(X1)) = esk140_1(X1)
| in(X2,esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1179,
[final] ).
cnf(c_0_2077,plain,
( X2 = empty_set
| in(esk42_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
c_0_1180,
[final] ).
cnf(c_0_2078,plain,
( in(X2,esk141_1(X1))
| esk140_1(X1) != esk139_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1181,
[final] ).
cnf(c_0_2079,plain,
( singleton(esk138_1(X1)) = esk139_1(X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1182,
[final] ).
cnf(c_0_2080,plain,
( singleton(esk138_1(X1)) = esk139_1(X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1183,
[final] ).
cnf(c_0_2081,plain,
( singleton(esk138_1(X1)) = esk140_1(X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1184,
[final] ).
cnf(c_0_2082,plain,
( singleton(esk138_1(X1)) = esk140_1(X1)
| in(esk142_2(X1,X2),X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1185,
[final] ).
cnf(c_0_2083,plain,
( X1 = union(X2)
| in(esk64_2(X2,X1),X1)
| in(esk65_2(X2,X1),X2) ),
c_0_1186,
[final] ).
cnf(c_0_2084,plain,
( X1 = powerset(X2)
| subset(esk35_2(X2,X1),X2)
| in(esk35_2(X2,X1),X1) ),
c_0_1187,
[final] ).
cnf(c_0_2085,plain,
( in(esk142_2(X1,X2),X1)
| esk140_1(X1) != esk139_1(X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1188,
[final] ).
cnf(c_0_2086,plain,
( in(esk142_2(X1,X2),X1)
| esk140_1(X1) != esk139_1(X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1189,
[final] ).
cnf(c_0_2087,plain,
( in(esk138_1(X1),X1)
| singleton(esk142_2(X1,X2)) = X2
| ~ in(X2,esk141_1(X1)) ),
c_0_1190,
[final] ).
cnf(c_0_2088,plain,
( in(esk138_1(X1),X1)
| singleton(esk142_2(X1,X2)) = X2
| ~ in(X2,esk141_1(X1)) ),
c_0_1191,
[final] ).
cnf(c_0_2089,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_1192,
[final] ).
cnf(c_0_2090,plain,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
c_0_1193,
[final] ).
cnf(c_0_2091,plain,
( X1 = X2
| in(esk178_2(X1,X2),X2)
| in(esk178_2(X1,X2),X1) ),
c_0_1194,
[final] ).
cnf(c_0_2092,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
c_0_1195,
[final] ).
cnf(c_0_2093,plain,
( in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1196,
[final] ).
cnf(c_0_2094,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1197,
[final] ).
cnf(c_0_2095,plain,
relation_of2(esk105_2(X1,X2),X1,X2),
c_0_1198,
[final] ).
cnf(c_0_2096,plain,
relation_of2(esk96_2(X1,X2),X1,X2),
c_0_1199,
[final] ).
cnf(c_0_2097,plain,
quasi_total(esk96_2(X1,X2),X1,X2),
c_0_1200,
[final] ).
cnf(c_0_2098,plain,
relation_of2_as_subset(esk92_2(X1,X2),X1,X2),
c_0_1201,
[final] ).
cnf(c_0_2099,plain,
relation_of2(esk90_2(X1,X2),X1,X2),
c_0_1202,
[final] ).
cnf(c_0_2100,plain,
( in(esk181_2(X2,X1),esk180_1(X2))
| ~ in(X1,esk180_1(X2)) ),
c_0_1203,
[final] ).
cnf(c_0_2101,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_1204,
[final] ).
cnf(c_0_2102,plain,
( singleton(esk138_1(X1)) = esk139_1(X1)
| singleton(esk142_2(X1,X2)) = X2
| ~ in(X2,esk141_1(X1)) ),
c_0_1205,
[final] ).
cnf(c_0_2103,plain,
( singleton(esk138_1(X1)) = esk140_1(X1)
| singleton(esk142_2(X1,X2)) = X2
| ~ in(X2,esk141_1(X1)) ),
c_0_1206,
[final] ).
cnf(c_0_2104,plain,
( subset(X1,X2)
| ~ in(esk54_2(X1,X2),X2) ),
c_0_1207,
[final] ).
cnf(c_0_2105,plain,
( singleton(esk142_2(X1,X2)) = X2
| esk140_1(X1) != esk139_1(X1)
| ~ in(X2,esk141_1(X1)) ),
c_0_1208,
[final] ).
cnf(c_0_2106,plain,
( ordinal(esk166_0)
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
c_0_1209,
[final] ).
cnf(c_0_2107,plain,
( ordinal(esk167_0)
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
c_0_1210,
[final] ).
cnf(c_0_2108,plain,
( in(X1,esk180_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk180_1(X2)) ),
c_0_1211,
[final] ).
cnf(c_0_2109,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_1212,
[final] ).
cnf(c_0_2110,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_1213,
[final] ).
cnf(c_0_2111,plain,
( in(esk169_2(X2,X1),X2)
| esk167_0 != esk166_0
| ~ in(X1,esk168_1(X2)) ),
c_0_1214,
[final] ).
cnf(c_0_2112,plain,
( in(X1,esk180_1(X2))
| are_equipotent(X1,esk180_1(X2))
| ~ subset(X1,esk180_1(X2)) ),
c_0_1215,
[final] ).
cnf(c_0_2113,plain,
( esk165_0 = esk166_0
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
c_0_1216,
[final] ).
cnf(c_0_2114,plain,
( esk165_0 = esk167_0
| in(esk169_2(X2,X1),X2)
| ~ in(X1,esk168_1(X2)) ),
c_0_1217,
[final] ).
cnf(c_0_2115,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
c_0_1218,
[final] ).
cnf(c_0_2116,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
c_0_1219,
[final] ).
cnf(c_0_2117,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1220,
[final] ).
cnf(c_0_2118,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1221,
[final] ).
cnf(c_0_2119,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
c_0_1222,
[final] ).
cnf(c_0_2120,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_1223,
[final] ).
cnf(c_0_2121,plain,
( function(X1)
| in(ordered_pair(esk18_1(X1),esk19_1(X1)),X1) ),
c_0_1224,
[final] ).
cnf(c_0_2122,plain,
( function(X1)
| in(ordered_pair(esk18_1(X1),esk20_1(X1)),X1) ),
c_0_1225,
[final] ).
cnf(c_0_2123,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_1226,
[final] ).
cnf(c_0_2124,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| esk74_2(X1,X2) != esk75_2(X1,X2) ),
c_0_1227,
[final] ).
cnf(c_0_2125,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| esk62_2(X1,X2) != esk61_2(X1,X2) ),
c_0_1228,
[final] ).
cnf(c_0_2126,plain,
( in(esk179_2(X1,X2),X2)
| ~ in(X1,X2) ),
c_0_1229,
[final] ).
cnf(c_0_2127,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_1230,
[final] ).
cnf(c_0_2128,plain,
( is_transitive_in(X1,X2)
| in(esk86_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1231,
[final] ).
cnf(c_0_2129,plain,
( is_transitive_in(X1,X2)
| in(esk87_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1232,
[final] ).
cnf(c_0_2130,plain,
( is_transitive_in(X1,X2)
| in(esk88_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1233,
[final] ).
cnf(c_0_2131,plain,
( is_connected_in(X1,X2)
| in(esk74_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1234,
[final] ).
cnf(c_0_2132,plain,
( is_connected_in(X1,X2)
| in(esk75_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1235,
[final] ).
cnf(c_0_2133,plain,
( is_antisymmetric_in(X1,X2)
| in(esk61_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1236,
[final] ).
cnf(c_0_2134,plain,
( is_antisymmetric_in(X1,X2)
| in(esk62_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1237,
[final] ).
cnf(c_0_2135,plain,
( is_well_founded_in(X1,X2)
| subset(esk56_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1238,
[final] ).
cnf(c_0_2136,plain,
( is_reflexive_in(X1,X2)
| in(esk26_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1239,
[final] ).
cnf(c_0_2137,plain,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_1240,
[final] ).
cnf(c_0_2138,plain,
( X1 = inclusion_relation(X2)
| in(esk32_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
c_0_1241,
[final] ).
cnf(c_0_2139,plain,
( X1 = inclusion_relation(X2)
| in(esk33_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
c_0_1242,
[final] ).
cnf(c_0_2140,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_1243,
[final] ).
cnf(c_0_2141,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_1244,
[final] ).
cnf(c_0_2142,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_1245,
[final] ).
cnf(c_0_2143,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_1246,
[final] ).
cnf(c_0_2144,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_1247,
[final] ).
cnf(c_0_2145,plain,
( X1 = singleton(X2)
| esk30_2(X2,X1) = X2
| in(esk30_2(X2,X1),X1) ),
c_0_1248,
[final] ).
cnf(c_0_2146,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
c_0_1249,
[final] ).
cnf(c_0_2147,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
c_0_1250,
[final] ).
cnf(c_0_2148,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_1251,
[final] ).
cnf(c_0_2149,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_1252,
[final] ).
cnf(c_0_2150,plain,
( one_to_one(X1)
| apply(X1,esk81_1(X1)) = apply(X1,esk80_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1253,
[final] ).
cnf(c_0_2151,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_1254,
[final] ).
cnf(c_0_2152,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_1255,
[final] ).
cnf(c_0_2153,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X6,X5)
| X4 != pair_second(X1) ),
c_0_1256,
[final] ).
cnf(c_0_2154,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X5,X6)
| X4 != pair_first(X1) ),
c_0_1257,
[final] ).
cnf(c_0_2155,plain,
( ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2)
| X4 != X3 ),
c_0_1258,
[final] ).
cnf(c_0_2156,plain,
( ordinal(esk166_0)
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1259,
[final] ).
cnf(c_0_2157,plain,
( ordinal(esk167_0)
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1260,
[final] ).
cnf(c_0_2158,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
c_0_1261,
[final] ).
cnf(c_0_2159,plain,
( in(X1,esk168_1(X2))
| esk167_0 != esk166_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1262,
[final] ).
cnf(c_0_2160,plain,
( esk165_0 = esk166_0
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1263,
[final] ).
cnf(c_0_2161,plain,
( esk165_0 = esk167_0
| in(X1,esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1264,
[final] ).
cnf(c_0_2162,plain,
( subset(X1,X2)
| in(esk54_2(X1,X2),X1) ),
c_0_1265,
[final] ).
cnf(c_0_2163,plain,
( relation_dom(esk66_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
c_0_1266,
[final] ).
cnf(c_0_2164,plain,
( relation_rng(esk66_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
c_0_1267,
[final] ).
cnf(c_0_2165,plain,
( relation(esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
c_0_1268,
[final] ).
cnf(c_0_2166,plain,
( function(esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
c_0_1269,
[final] ).
cnf(c_0_2167,plain,
( one_to_one(esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
c_0_1270,
[final] ).
cnf(c_0_2168,plain,
( X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3)
| esk37_2(X1,X4) != X4 ),
c_0_1271,
[final] ).
cnf(c_0_2169,plain,
( X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3)
| esk21_2(X1,X4) != X4 ),
c_0_1272,
[final] ).
cnf(c_0_2170,plain,
( equipotent(X1,X2)
| relation_rng(X3) != X2
| relation_dom(X3) != X1
| ~ one_to_one(X3)
| ~ function(X3)
| ~ relation(X3) ),
c_0_1273,
[final] ).
cnf(c_0_2171,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
c_0_1274,
[final] ).
cnf(c_0_2172,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_1275,
[final] ).
cnf(c_0_2173,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_1276,
[final] ).
cnf(c_0_2174,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
c_0_1277,
[final] ).
cnf(c_0_2175,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
c_0_1278,
[final] ).
cnf(c_0_2176,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_1279,
[final] ).
cnf(c_0_2177,plain,
( ordinal(esk166_0)
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
c_0_1280,
[final] ).
cnf(c_0_2178,plain,
( ordinal(esk167_0)
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
c_0_1281,
[final] ).
cnf(c_0_2179,plain,
( esk169_2(X2,X1) = X1
| esk167_0 != esk166_0
| ~ in(X1,esk168_1(X2)) ),
c_0_1282,
[final] ).
cnf(c_0_2180,plain,
( esk165_0 = esk166_0
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
c_0_1283,
[final] ).
cnf(c_0_2181,plain,
( esk165_0 = esk167_0
| esk169_2(X2,X1) = X1
| ~ in(X1,esk168_1(X2)) ),
c_0_1284,
[final] ).
cnf(c_0_2182,plain,
~ empty(unordered_pair(X1,X2)),
c_0_1285,
[final] ).
cnf(c_0_2183,plain,
~ empty(ordered_pair(X1,X2)),
c_0_1286,
[final] ).
cnf(c_0_2184,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_1287,
[final] ).
cnf(c_0_2185,plain,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
c_0_1288,
[final] ).
cnf(c_0_2186,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
c_0_1289,
[final] ).
cnf(c_0_2187,plain,
( epsilon_connected(X1)
| ~ in(esk50_1(X1),esk51_1(X1)) ),
c_0_1290,
[final] ).
cnf(c_0_2188,plain,
( epsilon_connected(X1)
| ~ in(esk51_1(X1),esk50_1(X1)) ),
c_0_1291,
[final] ).
cnf(c_0_2189,plain,
( one_to_one(X1)
| in(esk80_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1292,
[final] ).
cnf(c_0_2190,plain,
( one_to_one(X1)
| in(esk81_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1293,
[final] ).
cnf(c_0_2191,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_1294,
[final] ).
cnf(c_0_2192,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_1295,
[final] ).
cnf(c_0_2193,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_1296,
[final] ).
cnf(c_0_2194,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_1297,
[final] ).
cnf(c_0_2195,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1298,
[final] ).
cnf(c_0_2196,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1299,
[final] ).
cnf(c_0_2197,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1300,
[final] ).
cnf(c_0_2198,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1301,
[final] ).
cnf(c_0_2199,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1302,
[final] ).
cnf(c_0_2200,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1303,
[final] ).
cnf(c_0_2201,plain,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1304,
[final] ).
cnf(c_0_2202,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1305,
[final] ).
cnf(c_0_2203,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1306,
[final] ).
cnf(c_0_2204,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_1307,
[final] ).
cnf(c_0_2205,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_1308,
[final] ).
cnf(c_0_2206,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1309,
[final] ).
cnf(c_0_2207,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1310,
[final] ).
cnf(c_0_2208,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1311,
[final] ).
cnf(c_0_2209,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1312,
[final] ).
cnf(c_0_2210,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1313,
[final] ).
cnf(c_0_2211,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1314,
[final] ).
cnf(c_0_2212,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1315,
[final] ).
cnf(c_0_2213,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1316,
[final] ).
cnf(c_0_2214,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk56_2(X1,X2) != empty_set ),
c_0_1317,
[final] ).
cnf(c_0_2215,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
c_0_1318,
[final] ).
cnf(c_0_2216,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
c_0_1319,
[final] ).
cnf(c_0_2217,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
c_0_1320,
[final] ).
cnf(c_0_2218,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
c_0_1321,
[final] ).
cnf(c_0_2219,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
c_0_1322,
[final] ).
cnf(c_0_2220,plain,
( finite(X1)
| ~ element(X1,powerset(X2))
| ~ finite(X2) ),
c_0_1323,
[final] ).
cnf(c_0_2221,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
c_0_1324,
[final] ).
cnf(c_0_2222,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
c_0_1325,
[final] ).
cnf(c_0_2223,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_1326,
[final] ).
cnf(c_0_2224,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_1327,
[final] ).
cnf(c_0_2225,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
c_0_1328,
[final] ).
cnf(c_0_2226,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_1329,
[final] ).
cnf(c_0_2227,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_1330,
[final] ).
cnf(c_0_2228,plain,
( ordinal(esk166_0)
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
c_0_1331,
[final] ).
cnf(c_0_2229,plain,
( ordinal(esk167_0)
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
c_0_1332,
[final] ).
cnf(c_0_2230,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_1333,
[final] ).
cnf(c_0_2231,plain,
( well_founded_relation(X1)
| subset(esk43_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1334,
[final] ).
cnf(c_0_2232,plain,
( ordinal(X1)
| esk167_0 != esk166_0
| ~ in(X1,esk168_1(X2)) ),
c_0_1335,
[final] ).
cnf(c_0_2233,plain,
( esk165_0 = esk166_0
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
c_0_1336,
[final] ).
cnf(c_0_2234,plain,
( esk165_0 = esk167_0
| ordinal(X1)
| ~ in(X1,esk168_1(X2)) ),
c_0_1337,
[final] ).
cnf(c_0_2235,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
c_0_1338,
[final] ).
cnf(c_0_2236,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X2) ),
c_0_1339,
[final] ).
cnf(c_0_2237,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
c_0_1340,
[final] ).
cnf(c_0_2238,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
c_0_1341,
[final] ).
cnf(c_0_2239,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
c_0_1342,
[final] ).
cnf(c_0_2240,plain,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
c_0_1343,
[final] ).
cnf(c_0_2241,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
c_0_1344,
[final] ).
cnf(c_0_2242,plain,
( equipotent(X1,X2)
| ~ equipotent(X2,X1) ),
c_0_1345,
[final] ).
cnf(c_0_2243,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_1346,
[final] ).
cnf(c_0_2244,plain,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
c_0_1347,
[final] ).
cnf(c_0_2245,plain,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
c_0_1348,
[final] ).
cnf(c_0_2246,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_1349,
[final] ).
cnf(c_0_2247,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_1350,
[final] ).
cnf(c_0_2248,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_1351,
[final] ).
cnf(c_0_2249,plain,
( epsilon_transitive(X1)
| ~ subset(esk38_1(X1),X1) ),
c_0_1352,
[final] ).
cnf(c_0_2250,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
c_0_1353,
[final] ).
cnf(c_0_2251,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
c_0_1354,
[final] ).
cnf(c_0_2252,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
c_0_1355,
[final] ).
cnf(c_0_2253,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
c_0_1356,
[final] ).
cnf(c_0_2254,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_1357,
[final] ).
cnf(c_0_2255,plain,
( epsilon_transitive(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
c_0_1358,
[final] ).
cnf(c_0_2256,plain,
( epsilon_connected(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
c_0_1359,
[final] ).
cnf(c_0_2257,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
c_0_1360,
[final] ).
cnf(c_0_2258,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_1361,
[final] ).
cnf(c_0_2259,plain,
( relation(X1)
| esk25_1(X1) != ordered_pair(X2,X3) ),
c_0_1362,
[final] ).
cnf(c_0_2260,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1363,
[final] ).
cnf(c_0_2261,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1364,
[final] ).
cnf(c_0_2262,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk81_1(X1) != esk80_1(X1) ),
c_0_1365,
[final] ).
cnf(c_0_2263,plain,
( empty(X1)
| element(esk109_1(X1),powerset(X1)) ),
c_0_1366,
[final] ).
cnf(c_0_2264,plain,
( empty(X1)
| element(esk100_1(X1),powerset(X1)) ),
c_0_1367,
[final] ).
cnf(c_0_2265,plain,
relation(esk105_2(X1,X2)),
c_0_1368,
[final] ).
cnf(c_0_2266,plain,
function(esk105_2(X1,X2)),
c_0_1369,
[final] ).
cnf(c_0_2267,plain,
relation(esk96_2(X1,X2)),
c_0_1370,
[final] ).
cnf(c_0_2268,plain,
function(esk96_2(X1,X2)),
c_0_1371,
[final] ).
cnf(c_0_2269,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_1372,
[final] ).
cnf(c_0_2270,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1373,
[final] ).
cnf(c_0_2271,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
c_0_1374,
[final] ).
cnf(c_0_2272,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_1375,
[final] ).
cnf(c_0_2273,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
c_0_1376,
[final] ).
cnf(c_0_2274,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
c_0_1377,
[final] ).
cnf(c_0_2275,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_1378,
[final] ).
cnf(c_0_2276,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_1379,
[final] ).
cnf(c_0_2277,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_1380,
[final] ).
cnf(c_0_2278,plain,
element(esk107_1(X1),powerset(X1)),
c_0_1381,
[final] ).
cnf(c_0_2279,plain,
element(esk102_1(X1),powerset(X1)),
c_0_1382,
[final] ).
cnf(c_0_2280,plain,
element(cast_to_subset(X1),powerset(X1)),
c_0_1383,
[final] ).
cnf(c_0_2281,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_1384,
[final] ).
cnf(c_0_2282,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_1385,
[final] ).
cnf(c_0_2283,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_1386,
[final] ).
cnf(c_0_2284,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_1387,
[final] ).
cnf(c_0_2285,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_1388,
[final] ).
cnf(c_0_2286,plain,
( epsilon_connected(X1)
| in(esk50_1(X1),X1) ),
c_0_1389,
[final] ).
cnf(c_0_2287,plain,
( epsilon_connected(X1)
| in(esk51_1(X1),X1) ),
c_0_1390,
[final] ).
cnf(c_0_2288,plain,
( epsilon_transitive(X1)
| in(esk38_1(X1),X1) ),
c_0_1391,
[final] ).
cnf(c_0_2289,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_1392,
[final] ).
cnf(c_0_2290,plain,
( relation(X1)
| in(esk25_1(X1),X1) ),
c_0_1393,
[final] ).
cnf(c_0_2291,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1394,
[final] ).
cnf(c_0_2292,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1395,
[final] ).
cnf(c_0_2293,plain,
set_union2(X1,singleton(X1)) = succ(X1),
c_0_1396,
[final] ).
cnf(c_0_2294,plain,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
c_0_1397,
[final] ).
cnf(c_0_2295,plain,
~ proper_subset(X1,X1),
c_0_1398,
[final] ).
cnf(c_0_2296,plain,
( X1 = empty_set
| in(esk34_1(X1),X1) ),
c_0_1399,
[final] ).
cnf(c_0_2297,plain,
( empty(X1)
| ~ empty(esk109_1(X1)) ),
c_0_1400,
[final] ).
cnf(c_0_2298,plain,
( empty(X1)
| ~ empty(esk100_1(X1)) ),
c_0_1401,
[final] ).
cnf(c_0_2299,plain,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
c_0_1402,
[final] ).
cnf(c_0_2300,plain,
in(X1,esk180_1(X1)),
c_0_1403,
[final] ).
cnf(c_0_2301,plain,
element(esk91_1(X1),X1),
c_0_1404,
[final] ).
cnf(c_0_2302,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1405,
[final] ).
cnf(c_0_2303,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1406,
[final] ).
cnf(c_0_2304,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1407,
[final] ).
cnf(c_0_2305,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1408,
[final] ).
cnf(c_0_2306,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1409,
[final] ).
cnf(c_0_2307,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_1410,
[final] ).
cnf(c_0_2308,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk43_1(X1) != empty_set ),
c_0_1411,
[final] ).
cnf(c_0_2309,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_1412,
[final] ).
cnf(c_0_2310,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1413,
[final] ).
cnf(c_0_2311,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1414,
[final] ).
cnf(c_0_2312,plain,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1415,
[final] ).
cnf(c_0_2313,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1416,
[final] ).
cnf(c_0_2314,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
c_0_1417,
[final] ).
cnf(c_0_2315,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_1418,
[final] ).
cnf(c_0_2316,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_1419,
[final] ).
cnf(c_0_2317,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
c_0_1420,
[final] ).
cnf(c_0_2318,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
c_0_1421,
[final] ).
cnf(c_0_2319,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
c_0_1422,
[final] ).
cnf(c_0_2320,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
c_0_1423,
[final] ).
cnf(c_0_2321,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
c_0_1424,
[final] ).
cnf(c_0_2322,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
c_0_1425,
[final] ).
cnf(c_0_2323,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
c_0_1426,
[final] ).
cnf(c_0_2324,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
c_0_1427,
[final] ).
cnf(c_0_2325,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
c_0_1428,
[final] ).
cnf(c_0_2326,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
c_0_1429,
[final] ).
cnf(c_0_2327,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
c_0_1430,
[final] ).
cnf(c_0_2328,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
c_0_1431,
[final] ).
cnf(c_0_2329,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
c_0_1432,
[final] ).
cnf(c_0_2330,plain,
( epsilon_connected(X1)
| esk50_1(X1) != esk51_1(X1) ),
c_0_1433,
[final] ).
cnf(c_0_2331,plain,
( function(X1)
| esk20_1(X1) != esk19_1(X1) ),
c_0_1434,
[final] ).
cnf(c_0_2332,plain,
~ empty(singleton(X1)),
c_0_1435,
[final] ).
cnf(c_0_2333,plain,
~ empty(powerset(X1)),
c_0_1436,
[final] ).
cnf(c_0_2334,plain,
~ empty(succ(X1)),
c_0_1437,
[final] ).
cnf(c_0_2335,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_1438,
[final] ).
cnf(c_0_2336,plain,
( empty(X1)
| finite(esk109_1(X1)) ),
c_0_1439,
[final] ).
cnf(c_0_2337,plain,
set_intersection2(X1,X1) = X1,
c_0_1440,
[final] ).
cnf(c_0_2338,plain,
set_union2(X1,X1) = X1,
c_0_1441,
[final] ).
cnf(c_0_2339,plain,
equipotent(X1,X1),
c_0_1442,
[final] ).
cnf(c_0_2340,plain,
subset(X1,X1),
c_0_1443,
[final] ).
cnf(c_0_2341,plain,
set_difference(X1,empty_set) = X1,
c_0_1444,
[final] ).
cnf(c_0_2342,plain,
set_union2(X1,empty_set) = X1,
c_0_1445,
[final] ).
cnf(c_0_2343,plain,
set_difference(empty_set,X1) = empty_set,
c_0_1446,
[final] ).
cnf(c_0_2344,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_1447,
[final] ).
cnf(c_0_2345,plain,
( being_limit_ordinal(X1)
| union(X1) != X1 ),
c_0_1448,
[final] ).
cnf(c_0_2346,plain,
( union(X1) = X1
| ~ being_limit_ordinal(X1) ),
c_0_1449,
[final] ).
cnf(c_0_2347,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
c_0_1450,
[final] ).
cnf(c_0_2348,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_1451,
[final] ).
cnf(c_0_2349,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_1452,
[final] ).
cnf(c_0_2350,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
c_0_1453,
[final] ).
cnf(c_0_2351,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
c_0_1454,
[final] ).
cnf(c_0_2352,plain,
( ordinal(X1)
| ~ empty(X1) ),
c_0_1455,
[final] ).
cnf(c_0_2353,plain,
( relation(X1)
| ~ empty(X1) ),
c_0_1456,
[final] ).
cnf(c_0_2354,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_1457,
[final] ).
cnf(c_0_2355,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_1458,
[final] ).
cnf(c_0_2356,plain,
( function(X1)
| ~ empty(X1) ),
c_0_1459,
[final] ).
cnf(c_0_2357,plain,
( finite(X1)
| ~ empty(X1) ),
c_0_1460,
[final] ).
cnf(c_0_2358,plain,
empty(esk107_1(X1)),
c_0_1461,
[final] ).
cnf(c_0_2359,plain,
empty(esk102_1(X1)),
c_0_1462,
[final] ).
cnf(c_0_2360,plain,
relation(esk102_1(X1)),
c_0_1463,
[final] ).
cnf(c_0_2361,plain,
function(esk102_1(X1)),
c_0_1464,
[final] ).
cnf(c_0_2362,plain,
one_to_one(esk102_1(X1)),
c_0_1465,
[final] ).
cnf(c_0_2363,plain,
epsilon_transitive(esk102_1(X1)),
c_0_1466,
[final] ).
cnf(c_0_2364,plain,
epsilon_connected(esk102_1(X1)),
c_0_1467,
[final] ).
cnf(c_0_2365,plain,
ordinal(esk102_1(X1)),
c_0_1468,
[final] ).
cnf(c_0_2366,plain,
natural(esk102_1(X1)),
c_0_1469,
[final] ).
cnf(c_0_2367,plain,
finite(esk102_1(X1)),
c_0_1470,
[final] ).
cnf(c_0_2368,plain,
relation(identity_relation(X1)),
c_0_1471,
[final] ).
cnf(c_0_2369,plain,
function(identity_relation(X1)),
c_0_1472,
[final] ).
cnf(c_0_2370,plain,
relation(identity_relation(X1)),
c_0_1473,
[final] ).
cnf(c_0_2371,plain,
relation(inclusion_relation(X1)),
c_0_1474,
[final] ).
cnf(c_0_2372,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
c_0_1475,
[final] ).
cnf(c_0_2373,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_1476,
[final] ).
cnf(c_0_2374,plain,
cast_to_subset(X1) = X1,
c_0_1477,
[final] ).
cnf(c_0_2375,plain,
~ empty(esk111_0),
c_0_1478,
[final] ).
cnf(c_0_2376,plain,
~ empty(esk108_0),
c_0_1479,
[final] ).
cnf(c_0_2377,plain,
~ empty(esk106_0),
c_0_1480,
[final] ).
cnf(c_0_2378,plain,
~ empty(esk94_0),
c_0_1481,
[final] ).
cnf(c_0_2379,plain,
~ empty(esk93_0),
c_0_1482,
[final] ).
cnf(c_0_2380,plain,
relation(esk113_0),
c_0_1483,
[final] ).
cnf(c_0_2381,plain,
relation_empty_yielding(esk113_0),
c_0_1484,
[final] ).
cnf(c_0_2382,plain,
function(esk113_0),
c_0_1485,
[final] ).
cnf(c_0_2383,plain,
relation(esk112_0),
c_0_1486,
[final] ).
cnf(c_0_2384,plain,
relation_empty_yielding(esk112_0),
c_0_1487,
[final] ).
cnf(c_0_2385,plain,
epsilon_transitive(esk111_0),
c_0_1488,
[final] ).
cnf(c_0_2386,plain,
epsilon_connected(esk111_0),
c_0_1489,
[final] ).
cnf(c_0_2387,plain,
ordinal(esk111_0),
c_0_1490,
[final] ).
cnf(c_0_2388,plain,
relation(esk110_0),
c_0_1491,
[final] ).
cnf(c_0_2389,plain,
function(esk110_0),
c_0_1492,
[final] ).
cnf(c_0_2390,plain,
one_to_one(esk110_0),
c_0_1493,
[final] ).
cnf(c_0_2391,plain,
relation(esk106_0),
c_0_1494,
[final] ).
cnf(c_0_2392,plain,
relation(esk104_0),
c_0_1495,
[final] ).
cnf(c_0_2393,plain,
function(esk104_0),
c_0_1496,
[final] ).
cnf(c_0_2394,plain,
one_to_one(esk104_0),
c_0_1497,
[final] ).
cnf(c_0_2395,plain,
empty(esk104_0),
c_0_1498,
[final] ).
cnf(c_0_2396,plain,
epsilon_transitive(esk104_0),
c_0_1499,
[final] ).
cnf(c_0_2397,plain,
epsilon_connected(esk104_0),
c_0_1500,
[final] ).
cnf(c_0_2398,plain,
ordinal(esk104_0),
c_0_1501,
[final] ).
cnf(c_0_2399,plain,
relation(esk103_0),
c_0_1502,
[final] ).
cnf(c_0_2400,plain,
empty(esk103_0),
c_0_1503,
[final] ).
cnf(c_0_2401,plain,
function(esk103_0),
c_0_1504,
[final] ).
cnf(c_0_2402,plain,
empty(esk101_0),
c_0_1505,
[final] ).
cnf(c_0_2403,plain,
empty(esk99_0),
c_0_1506,
[final] ).
cnf(c_0_2404,plain,
relation(esk99_0),
c_0_1507,
[final] ).
cnf(c_0_2405,plain,
relation(esk98_0),
c_0_1508,
[final] ).
cnf(c_0_2406,plain,
function(esk98_0),
c_0_1509,
[final] ).
cnf(c_0_2407,plain,
one_to_one(esk98_0),
c_0_1510,
[final] ).
cnf(c_0_2408,plain,
empty(esk98_0),
c_0_1511,
[final] ).
cnf(c_0_2409,plain,
epsilon_transitive(esk97_0),
c_0_1512,
[final] ).
cnf(c_0_2410,plain,
epsilon_connected(esk97_0),
c_0_1513,
[final] ).
cnf(c_0_2411,plain,
ordinal(esk97_0),
c_0_1514,
[final] ).
cnf(c_0_2412,plain,
relation(esk95_0),
c_0_1515,
[final] ).
cnf(c_0_2413,plain,
function(esk95_0),
c_0_1516,
[final] ).
cnf(c_0_2414,plain,
finite(esk94_0),
c_0_1517,
[final] ).
cnf(c_0_2415,plain,
epsilon_transitive(esk93_0),
c_0_1518,
[final] ).
cnf(c_0_2416,plain,
epsilon_connected(esk93_0),
c_0_1519,
[final] ).
cnf(c_0_2417,plain,
ordinal(esk93_0),
c_0_1520,
[final] ).
cnf(c_0_2418,plain,
natural(esk93_0),
c_0_1521,
[final] ).
cnf(c_0_2419,plain,
empty(empty_set),
c_0_1522,
[final] ).
cnf(c_0_2420,plain,
relation(empty_set),
c_0_1523,
[final] ).
cnf(c_0_2421,plain,
relation(empty_set),
c_0_1524,
[final] ).
cnf(c_0_2422,plain,
relation_empty_yielding(empty_set),
c_0_1525,
[final] ).
cnf(c_0_2423,plain,
function(empty_set),
c_0_1526,
[final] ).
cnf(c_0_2424,plain,
one_to_one(empty_set),
c_0_1527,
[final] ).
cnf(c_0_2425,plain,
empty(empty_set),
c_0_1528,
[final] ).
cnf(c_0_2426,plain,
epsilon_transitive(empty_set),
c_0_1529,
[final] ).
cnf(c_0_2427,plain,
epsilon_connected(empty_set),
c_0_1530,
[final] ).
cnf(c_0_2428,plain,
ordinal(empty_set),
c_0_1531,
[final] ).
cnf(c_0_2429,plain,
empty(empty_set),
c_0_1532,
[final] ).
cnf(c_0_2430,plain,
empty(empty_set),
c_0_1533,
[final] ).
cnf(c_0_2431,plain,
relation(empty_set),
c_0_1534,
[final] ).
cnf(c_0_2432,plain,
relation_empty_yielding(empty_set),
c_0_1535,
[final] ).
cnf(c_0_2433,plain,
$true,
c_0_1536,
[final] ).
cnf(c_0_2434,plain,
$true,
c_0_1537,
[final] ).
cnf(c_0_2435,plain,
$true,
c_0_1538,
[final] ).
cnf(c_0_2436,plain,
$true,
c_0_1539,
[final] ).
cnf(c_0_2437,plain,
$true,
c_0_1540,
[final] ).
cnf(c_0_2438,plain,
$true,
c_0_1541,
[final] ).
cnf(c_0_2439,plain,
$true,
c_0_1542,
[final] ).
cnf(c_0_2440,plain,
$true,
c_0_1543,
[final] ).
cnf(c_0_2441,plain,
$true,
c_0_1544,
[final] ).
cnf(c_0_2442,plain,
$true,
c_0_1545,
[final] ).
cnf(c_0_2443,plain,
$true,
c_0_1546,
[final] ).
cnf(c_0_2444,plain,
$true,
c_0_1547,
[final] ).
cnf(c_0_2445,plain,
$true,
c_0_1548,
[final] ).
cnf(c_0_2446,plain,
$true,
c_0_1549,
[final] ).
cnf(c_0_2447,plain,
$true,
c_0_1550,
[final] ).
cnf(c_0_2448,plain,
$true,
c_0_1551,
[final] ).
cnf(c_0_2449,plain,
$true,
c_0_1552,
[final] ).
cnf(c_0_2450,plain,
$true,
c_0_1553,
[final] ).
cnf(c_0_2451,plain,
$true,
c_0_1554,
[final] ).
cnf(c_0_2452,plain,
$true,
c_0_1555,
[final] ).
cnf(c_0_2453,plain,
$true,
c_0_1556,
[final] ).
cnf(c_0_2454,plain,
$true,
c_0_1557,
[final] ).
cnf(c_0_2455,plain,
$true,
c_0_1558,
[final] ).
cnf(c_0_2456,plain,
$true,
c_0_1559,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1560_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_2,axiom,
( in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_5,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_6,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_7,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_8,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_9,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_10,axiom,
( ~ in(X8,X9)
| X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_11,axiom,
( ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1)
| ~ in(X8,X9)
| X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1561_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk132_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_2,axiom,
( in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_5,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_6,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_7,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_8,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_9,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_10,axiom,
( ~ in(X8,X9)
| X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_11,axiom,
( ~ in(ordered_pair(X8,sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1)
| ~ in(X8,X9)
| X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1562_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1563_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1563_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1564_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1565_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1566_0,axiom,
( empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_1,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_2,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1567_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1568_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1569_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1570_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1571_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1572_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1)
| ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1573_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_2,axiom,
( in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_3,axiom,
( in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_5,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_6,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_7,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_8,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_9,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_10,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1573_11,axiom,
( ~ in(X8,X9)
| X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1574_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_2,axiom,
( in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_3,axiom,
( in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_5,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,cartesian_product2(X2,X5))
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_6,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| X6 != X4
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_7,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(X7,X8) != X4
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_8,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_9,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_10,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_11,axiom,
( ~ in(X8,X9)
| X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk132_3(X2,X1,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1575_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1576_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1577_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1577_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1578_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1578_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1579_0,axiom,
( empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_1,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_2,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_3,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_4,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1580_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1581_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1582_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1583_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1583_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1584_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1585_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk132_3(X2,X1,X4))
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_2,axiom,
( in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_3,axiom,
( in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_4,axiom,
( ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X5,cartesian_product2(X2,X4))
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| X5 != X3
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk137_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1586_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| in(X4,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_2,axiom,
( in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_4,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_5,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_6,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_7,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_8,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_9,axiom,
( ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1)
| ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1587_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| in(X4,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_2,axiom,
( in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_4,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_5,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_6,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_7,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_8,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_9,axiom,
( ~ in(ordered_pair(X4,sk1_esk122_5(X2,X1,X4,X5,X6)),X1)
| ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1588_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1589_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1590_0,axiom,
( empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_1,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_2,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_3,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_4,axiom,
( ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1591_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1591_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1592_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1593_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1594_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk122_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1595_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1595_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1596_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1596_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1597_0,axiom,
( in(ordered_pair(X4,sk1_esk82_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_1597]) ).
cnf(c_0_1597_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk82_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_1597]) ).
cnf(c_0_1597_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk82_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_1597]) ).
cnf(c_0_1597_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk82_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_1597]) ).
cnf(c_0_1597_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk82_5(X1,X2,X3,X4,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1597_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk82_5(X1,X2,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1598_0,axiom,
( in(ordered_pair(sk1_esk82_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_1598]) ).
cnf(c_0_1598_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk82_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_1598]) ).
cnf(c_0_1598_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk82_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_1598]) ).
cnf(c_0_1598_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk82_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_1598]) ).
cnf(c_0_1598_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk82_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1598_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk82_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1599_0,axiom,
( ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1600_0,axiom,
( ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1600_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1601_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_1,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_4,axiom,
( sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1601_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1602_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1603_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk163_4(X3,X2,X1,X4)),apply(X1,sk1_esk164_4(X3,X2,X1,X4))),X2)
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1604_0,axiom,
( relation_isomorphism(X1,X2,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_1,axiom,
( ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_5,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_6,axiom,
( relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_7,axiom,
( ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_8,axiom,
( ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_9,axiom,
( ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_10,axiom,
( ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_11,axiom,
( ~ in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| ~ in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1605_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_2,axiom,
( in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_3,axiom,
( in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_5,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_6,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_7,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_8,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_9,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1606_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| in(X4,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_2,axiom,
( in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_3,axiom,
( in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_5,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_6,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_7,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_8,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_9,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk119_2(X2,X1))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1607_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_3,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1608_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_3,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1609_0,axiom,
( empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_1,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_2,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_3,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_4,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_5,axiom,
( ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1610_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_3,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1611_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_3,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1612_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_3,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1613_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk119_2(X2,X1))
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_2,axiom,
( in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_3,axiom,
( in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_4,axiom,
( ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk122_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk119_2(X2,X1))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1614_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_1,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1615_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_1,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1616_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_6,axiom,
( ~ in(X6,sk1_esk136_4(X2,X1,X5,X4))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1617_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,sk1_esk136_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_6,axiom,
( ~ in(X6,sk1_esk136_4(X2,X1,X5,X4))
| ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1618_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1619_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1620_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1621_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1622_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_1,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1623_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1623_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1624_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1625_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1626_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1627_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1628_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_2,axiom,
( in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk136_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_5,axiom,
( ~ in(X5,sk1_esk136_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk135_4(X2,X1,X4,X3),X5),X1)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1629_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_1,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_2,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1630_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_1,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_2,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1630_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1631_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_1631]) ).
cnf(c_0_1631_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_1631]) ).
cnf(c_0_1631_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_1631]) ).
cnf(c_0_1631_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_1631]) ).
cnf(c_0_1631_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_1631]) ).
cnf(c_0_1631_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_1631]) ).
cnf(c_0_1632_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_1632]) ).
cnf(c_0_1632_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_1632]) ).
cnf(c_0_1632_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_1632]) ).
cnf(c_0_1632_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_1632]) ).
cnf(c_0_1632_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_1632]) ).
cnf(c_0_1632_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_1632]) ).
cnf(c_0_1633_0,axiom,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_1,axiom,
( in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_2,axiom,
( in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_3,axiom,
( ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_5,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_6,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_7,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_8,axiom,
( relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_9,axiom,
( ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk78_3(X1,X2,X3)),apply(X3,sk1_esk79_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1634_0,axiom,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_1,axiom,
( ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_4,axiom,
( ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_5,axiom,
( ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1634_6,axiom,
( ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(sk1_esk83_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk84_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1635_0,axiom,
( ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_1,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1635_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1636_0,axiom,
( ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_1,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1637_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_1,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_2,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1638_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_1,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_2,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1639_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_1,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk157_3(X3,X2,X1)),apply(X1,sk1_esk158_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1640_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_1,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1640_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk159_3(X3,X2,X1)),apply(X1,sk1_esk160_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1641_0,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_1,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_4,axiom,
( sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1642_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1642_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1643_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X5,X4),sk1_esk135_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1644_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_2,axiom,
( in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1645_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_2,axiom,
( in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X5,X4),sk1_esk136_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1646_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_1,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1647_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_1,axiom,
( ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk163_4(X3,X2,X1,X4),sk1_esk164_4(X3,X2,X1,X4)) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1648_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_1648]) ).
cnf(c_0_1648_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_1648]) ).
cnf(c_0_1648_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_1648]) ).
cnf(c_0_1648_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_1648]) ).
cnf(c_0_1648_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_1648]) ).
cnf(c_0_1649_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1650_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1651_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1651_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1652_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1653_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1654_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1655_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1656_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1657_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_1,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_2,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1658_0,axiom,
( empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_1,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_2,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1659_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1660_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1660_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1661_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_1661]) ).
cnf(c_0_1661_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_1661]) ).
cnf(c_0_1661_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_1661]) ).
cnf(c_0_1662_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_1662]) ).
cnf(c_0_1662_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_1662]) ).
cnf(c_0_1662_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_1662]) ).
cnf(c_0_1663_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_1663]) ).
cnf(c_0_1663_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_1663]) ).
cnf(c_0_1663_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_1663]) ).
cnf(c_0_1664_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1664_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1665_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1665_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1666_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1667_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1668_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1668_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1669_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_2,axiom,
( ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk134_4(X2,X1,X4,X3),sk1_esk135_4(X2,X1,X4,X3)) = X3
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1670_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1671_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1672_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1673_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_2,axiom,
( in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_3,axiom,
( ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk135_4(X2,X1,X4,X3),sk1_esk136_4(X2,X1,X4,X3))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1674_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_1674]) ).
cnf(c_0_1674_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_1674]) ).
cnf(c_0_1674_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_1674]) ).
cnf(c_0_1674_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_1674]) ).
cnf(c_0_1675_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_1675]) ).
cnf(c_0_1675_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_1675]) ).
cnf(c_0_1675_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_1675]) ).
cnf(c_0_1675_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_1675]) ).
cnf(c_0_1676_0,axiom,
( ordered_pair(sk1_esk45_4(X2,X3,X1,X4),sk1_esk46_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk45_4(X2,X3,X1,X4),sk1_esk46_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk45_4(X2,X3,X1,X4),sk1_esk46_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1677_0,axiom,
( ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_1,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_2,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1678_0,axiom,
( ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_1,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_2,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1679_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk85_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_1,axiom,
( in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk85_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_2,axiom,
( in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk85_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk85_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk85_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1679_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk85_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1680_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk85_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_1,axiom,
( in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk85_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_2,axiom,
( in(ordered_pair(sk1_esk85_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk85_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk85_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk85_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk83_3(X1,X2,X3),sk1_esk84_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1681_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_1681]) ).
cnf(c_0_1681_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_1681]) ).
cnf(c_0_1681_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_1681]) ).
cnf(c_0_1681_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_1681]) ).
cnf(c_0_1681_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_1681]) ).
cnf(c_0_1682_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_1682]) ).
cnf(c_0_1682_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_1682]) ).
cnf(c_0_1682_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_1682]) ).
cnf(c_0_1682_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_1682]) ).
cnf(c_0_1682_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_1682]) ).
cnf(c_0_1683_0,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_1,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_4,axiom,
( sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1684_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_2,axiom,
( in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1685_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_2,axiom,
( in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1686_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_2,axiom,
( in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1687_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_2,axiom,
( in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1688_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_1,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_2,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1689_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_1,axiom,
( in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_2,axiom,
( ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk162_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1690_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_2,axiom,
( sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1691_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_2,axiom,
( sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X5,X4) = sk1_esk136_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1692_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_1692]) ).
cnf(c_0_1693_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1693_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1694_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1695_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1696_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1697_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1698_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1699_0,axiom,
( empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_1,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_2,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1700_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1701_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1702_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1703_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1704_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1706_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1708_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1709_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1710_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_2,axiom,
( in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_3,axiom,
( ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk133_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_0,axiom,
( empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_1,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_2,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1713_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1715_0,axiom,
( ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_1,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_2,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1716_0,axiom,
( ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_1,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_2,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1717_0,axiom,
( ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_1,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk157_3(X3,X2,X1),sk1_esk158_3(X3,X2,X1)) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1718_0,axiom,
( ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_1,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ordered_pair(sk1_esk159_3(X3,X2,X1),sk1_esk160_3(X3,X2,X1)) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1719_0,axiom,
( empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_1,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_2,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1720_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1721_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1722_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1723_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1724_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1725_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_2,axiom,
( in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk134_4(X2,X1,X4,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1727_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1728_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1729_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_2,axiom,
( sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_3,axiom,
( ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk134_4(X2,X1,X4,X3) = sk1_esk136_4(X2,X1,X4,X3)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_2,axiom,
( in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_3,axiom,
( ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_5,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_6,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_7,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_8,axiom,
( relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_9,axiom,
( ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk78_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_0,axiom,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_1,axiom,
( in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_2,axiom,
( in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_3,axiom,
( ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ function(X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_5,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_6,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_7,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_8,axiom,
( relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_9,axiom,
( ~ one_to_one(X3)
| relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk79_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk78_3(X1,X2,X3),sk1_esk79_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1732_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| ~ in(sk1_esk89_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| ~ in(sk1_esk89_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| ~ in(sk1_esk89_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_3,axiom,
( ~ in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(sk1_esk89_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_4,axiom,
( ~ in(sk1_esk89_3(X2,X1,X3),X3)
| ~ in(subset_complement(X2,sk1_esk89_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_1732]) ).
cnf(c_0_1733_0,axiom,
( X2 = fiber(X1,X3)
| sk1_esk31_3(X1,X3,X2) = X3
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ in(sk1_esk31_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_1,axiom,
( sk1_esk31_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ in(sk1_esk31_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_2,axiom,
( ~ relation(X1)
| sk1_esk31_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3)
| ~ in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ in(sk1_esk31_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_3,axiom,
( ~ in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ relation(X1)
| sk1_esk31_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3)
| ~ in(sk1_esk31_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_4,axiom,
( ~ in(sk1_esk31_3(X1,X3,X2),X2)
| ~ in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ relation(X1)
| sk1_esk31_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1734_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_1734]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1735_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_1735]) ).
cnf(c_0_1736_0,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_1,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_4,axiom,
( sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1737_0,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_1,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_4,axiom,
( sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk156_3(X3,X2,X1) != sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1738_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_1738]) ).
cnf(c_0_1738_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_1738]) ).
cnf(c_0_1738_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_1738]) ).
cnf(c_0_1738_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_1738]) ).
cnf(c_0_1738_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_1738]) ).
cnf(c_0_1739_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_1739]) ).
cnf(c_0_1739_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_1739]) ).
cnf(c_0_1739_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_1739]) ).
cnf(c_0_1739_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_1739]) ).
cnf(c_0_1739_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_1739]) ).
cnf(c_0_1740_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_1740]) ).
cnf(c_0_1740_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_1740]) ).
cnf(c_0_1740_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_1740]) ).
cnf(c_0_1740_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_1740]) ).
cnf(c_0_1741_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_1741]) ).
cnf(c_0_1741_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_1741]) ).
cnf(c_0_1741_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_1741]) ).
cnf(c_0_1741_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_1741]) ).
cnf(c_0_1742_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_2,axiom,
( sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_4,axiom,
( ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk128_2(X2,X1))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1743_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_1,axiom,
( in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_2,axiom,
( sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk132_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_5,axiom,
( ~ in(X4,sk1_esk132_3(X2,X1,X5))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk130_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1744_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk57_3(X2,X3,X1),X3)
| ~ in(sk1_esk57_3(X2,X3,X1),X2)
| ~ in(sk1_esk57_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_1,axiom,
( ~ in(sk1_esk57_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk57_3(X2,X3,X1),X2)
| ~ in(sk1_esk57_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_2,axiom,
( ~ in(sk1_esk57_3(X2,X3,X1),X2)
| ~ in(sk1_esk57_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk57_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_3,axiom,
( ~ in(sk1_esk57_3(X2,X3,X1),X1)
| ~ in(sk1_esk57_3(X2,X3,X1),X2)
| ~ in(sk1_esk57_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1745_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_1745]) ).
cnf(c_0_1745_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_1745]) ).
cnf(c_0_1745_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_1745]) ).
cnf(c_0_1745_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_1745]) ).
cnf(c_0_1745_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_1745]) ).
cnf(c_0_1746_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_1,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_2,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1747_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_1,axiom,
( sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_2,axiom,
( ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ in(X4,sk1_esk161_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_5,axiom,
( ~ in(X4,sk1_esk161_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk162_4(X3,X2,X1,X4) = X4
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1748_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_1,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk155_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1749_0,axiom,
( sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_1,axiom,
( in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_8,axiom,
( ~ in(X7,cartesian_product2(X3,X3))
| X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk161_3(X3,X2,X1))
| sk1_esk154_3(X3,X2,X1) = sk1_esk156_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1750_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_1750]) ).
cnf(c_0_1750_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_1750]) ).
cnf(c_0_1750_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_1750]) ).
cnf(c_0_1750_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_1750]) ).
cnf(c_0_1750_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_1750]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1751_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_1751]) ).
cnf(c_0_1752_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_1752]) ).
cnf(c_0_1752_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_1752]) ).
cnf(c_0_1752_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_1752]) ).
cnf(c_0_1752_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_1752]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1753_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_1753]) ).
cnf(c_0_1754_0,axiom,
( in(sk1_esk45_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk45_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk45_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1755_0,axiom,
( in(sk1_esk46_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk46_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk46_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1756_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_1,axiom,
( ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk126_2(X2,X1),sk1_esk127_2(X2,X1)) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1757_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_1,axiom,
( ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk129_2(X2,X1),sk1_esk130_2(X2,X1)) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1758_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk67_3(X2,X3,X1),X3)
| ~ in(sk1_esk67_3(X2,X3,X1),X2)
| ~ in(sk1_esk67_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_1,axiom,
( in(sk1_esk67_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk67_3(X2,X3,X1),X2)
| ~ in(sk1_esk67_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_2,axiom,
( ~ in(sk1_esk67_3(X2,X3,X1),X2)
| in(sk1_esk67_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk67_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_3,axiom,
( ~ in(sk1_esk67_3(X2,X3,X1),X1)
| ~ in(sk1_esk67_3(X2,X3,X1),X2)
| in(sk1_esk67_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1759_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk127_2(X2,X1),sk1_esk128_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1760_0,axiom,
( empty(X2)
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_1,axiom,
( in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk130_2(X2,X1),sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1761_0,axiom,
( empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_1,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| empty(X2)
| ~ relation(X1)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_2,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| empty(X2)
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_3,axiom,
( sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| sk1_esk125_2(X2,X1) != sk1_esk124_2(X2,X1)
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1762_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| in(sk1_esk89_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_1,axiom,
( in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| in(sk1_esk89_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_2,axiom,
( in(sk1_esk89_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk89_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_1762]) ).
cnf(c_0_1762_3,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk89_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_4,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk89_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk89_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1763_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1764_0,axiom,
( empty(X2)
| in(sk1_esk129_2(X2,X1),X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_1,axiom,
( in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| in(sk1_esk129_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1765_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk123_2(X2,X1) = sk1_esk124_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1766_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk126_2(X2,X1) = sk1_esk128_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1767_0,axiom,
( empty(X2)
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_1,axiom,
( sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk123_2(X2,X1) = sk1_esk125_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1768_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_2,axiom,
( sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_3,axiom,
( ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk132_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_4,axiom,
( ~ in(X3,sk1_esk132_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk133_4(X2,X1,X4,X3) = X3
| sk1_esk129_2(X2,X1) = sk1_esk131_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1769_0,axiom,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_3,axiom,
( ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_4,axiom,
( ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1770_0,axiom,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_1,axiom,
( ~ relation(X1)
| X1 = X2
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_3,axiom,
( ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_4,axiom,
( ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1771_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_2,axiom,
( in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_4,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_6,axiom,
( ~ in(X5,sk1_esk121_3(X2,X1,X4))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1772_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_2,axiom,
( in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_4,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,sk1_esk121_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_6,axiom,
( ~ in(X5,sk1_esk121_3(X2,X1,X4))
| ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1773_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_6,axiom,
( ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(X5,relation_field(X1))
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_7,axiom,
( ~ in(X5,relation_field(X1))
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_8,axiom,
( ~ in(X4,relation_field(X1))
| ~ in(X5,relation_field(X1))
| ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1774_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk48_3(X2,X3,X1),sk1_esk49_3(X2,X3,X1)) = sk1_esk47_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_1,axiom,
( in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk48_3(X2,X3,X1),sk1_esk49_3(X2,X3,X1)) = sk1_esk47_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_2,axiom,
( ordered_pair(sk1_esk48_3(X2,X3,X1),sk1_esk49_3(X2,X3,X1)) = sk1_esk47_3(X2,X3,X1)
| in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1775_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_1775]) ).
cnf(c_0_1776_0,axiom,
( X2 = fiber(X1,X3)
| in(sk1_esk31_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_1,axiom,
( in(sk1_esk31_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_2,axiom,
( in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| in(sk1_esk31_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk31_3(X1,X3,X2),X3),X1)
| in(sk1_esk31_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1777_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk44_3(X2,X3,X1),X1)
| ~ in(sk1_esk44_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_1,axiom,
( ~ in(sk1_esk44_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk44_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_2,axiom,
( ~ in(sk1_esk44_3(X2,X3,X1),X2)
| ~ in(sk1_esk44_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1778_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk44_3(X2,X3,X1),X1)
| ~ in(sk1_esk44_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_1,axiom,
( ~ in(sk1_esk44_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk44_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_2,axiom,
( ~ in(sk1_esk44_3(X2,X3,X1),X3)
| ~ in(sk1_esk44_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1779_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_1779]) ).
cnf(c_0_1780_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk44_3(X2,X3,X1),X3)
| in(sk1_esk44_3(X2,X3,X1),X2)
| in(sk1_esk44_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_1,axiom,
( in(sk1_esk44_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk44_3(X2,X3,X1),X2)
| in(sk1_esk44_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_2,axiom,
( in(sk1_esk44_3(X2,X3,X1),X2)
| in(sk1_esk44_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk44_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_3,axiom,
( in(sk1_esk44_3(X2,X3,X1),X1)
| in(sk1_esk44_3(X2,X3,X1),X2)
| in(sk1_esk44_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1781_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1782_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1783_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_1,axiom,
( sk1_esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_2,axiom,
( ~ in(X5,X3)
| sk1_esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk47_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_4,axiom,
( ~ in(sk1_esk47_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk47_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1784_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_2,axiom,
( in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_4,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1785_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_2,axiom,
( in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_4,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1786_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_2,axiom,
( in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_4,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1787_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_2,axiom,
( in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_4,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1788_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_2,axiom,
( in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_4,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1789_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk121_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_2,axiom,
( in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_4,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk121_3(X2,X1,X4))
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1790_0,axiom,
( X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2
| ~ subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| ~ in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_1,axiom,
( ~ relation(X1)
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2
| ~ subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| ~ in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_2,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| X1 = inclusion_relation(X2)
| ~ subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| ~ in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_3,axiom,
( ~ subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| relation_field(X1) != X2
| ~ relation(X1)
| X1 = inclusion_relation(X2)
| ~ in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_4,axiom,
( ~ in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1)
| ~ subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| relation_field(X1) != X2
| ~ relation(X1)
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1791_0,axiom,
( empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_1,axiom,
( in(ordered_pair(X3,X4),X1)
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_2,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_3,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1792_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_1792]) ).
cnf(c_0_1793_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1794_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1795_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_1,axiom,
( in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_2,axiom,
( sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_4,axiom,
( ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk117_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk115_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1796_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_1,axiom,
( in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_2,axiom,
( sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_4,axiom,
( ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_5,axiom,
( ~ in(X4,sk1_esk119_2(X2,X1))
| ~ in(X3,sk1_esk118_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X4) = sk1_esk121_3(X2,X1,X4)
| in(ordered_pair(sk1_esk116_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1797_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_2,axiom,
( in(ordered_pair(X3,X4),X1)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1798_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_2,axiom,
( in(ordered_pair(X3,X4),X1)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X4,sk1_esk121_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_5,axiom,
( ~ in(X4,sk1_esk121_3(X2,X1,X3))
| ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1799_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk67_3(X2,X3,X1),X1)
| ~ in(sk1_esk67_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_1,axiom,
( in(sk1_esk67_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk67_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_2,axiom,
( ~ in(sk1_esk67_3(X2,X3,X1),X3)
| in(sk1_esk67_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1800_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_1800]) ).
cnf(c_0_1800_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_1800]) ).
cnf(c_0_1800_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_1800]) ).
cnf(c_0_1800_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_1800]) ).
cnf(c_0_1800_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_1800]) ).
cnf(c_0_1801_0,axiom,
( ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1802_0,axiom,
( ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1803_0,axiom,
( in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_1,axiom,
( ~ relation(X1)
| in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_6,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1804_0,axiom,
( in(sk1_esk146_1(X1),X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| in(sk1_esk146_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| in(sk1_esk146_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1805_0,axiom,
( in(sk1_esk148_1(X1),X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| in(sk1_esk148_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| in(sk1_esk148_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1806_0,axiom,
( X3 = empty_set
| disjoint(fiber(X1,sk1_esk55_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_1,axiom,
( disjoint(fiber(X1,sk1_esk55_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_1806]) ).
cnf(c_0_1806_2,axiom,
( ~ relation(X1)
| disjoint(fiber(X1,sk1_esk55_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_3,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk55_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_4,axiom,
( ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk55_3(X1,X2,X3)),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1807_0,axiom,
( X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_1,axiom,
( in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_2,axiom,
( in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1808_0,axiom,
( singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1808_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1808_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1809_0,axiom,
( singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1809_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1809_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1810_0,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_1,axiom,
( sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1811_0,axiom,
( X1 = X2
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_1,axiom,
( in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| X1 = X2
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_2,axiom,
( in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk39_2(X1,X2),sk1_esk40_2(X1,X2)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1812_0,axiom,
( sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| sk1_esk143_1(X1) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1813_0,axiom,
( sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_1,axiom,
( ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk152_3(X1,X3,X2),sk1_esk153_3(X1,X3,X2)) = X2
| sk1_esk143_1(X1) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1814_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk41_3(X2,X3,X1),X1)
| sk1_esk41_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_1,axiom,
( ~ in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk41_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_2,axiom,
( sk1_esk41_3(X2,X3,X1) != X2
| ~ in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1815_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk41_3(X2,X3,X1),X1)
| sk1_esk41_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_1,axiom,
( ~ in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk41_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_2,axiom,
( sk1_esk41_3(X2,X3,X1) != X3
| ~ in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1816_0,axiom,
( in(ordered_pair(sk1_esk71_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk71_3(X1,X2,X3),X3),X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk71_3(X1,X2,X3),X3),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_3,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk71_3(X1,X2,X3),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( in(ordered_pair(X3,sk1_esk58_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,sk1_esk58_3(X1,X2,X3)),X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk58_3(X1,X2,X3)),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_3,axiom,
( ~ in(X3,X2)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk58_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1818_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_1818]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1819_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_1819]) ).
cnf(c_0_1820_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_1820]) ).
cnf(c_0_1820_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_1820]) ).
cnf(c_0_1820_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_1820]) ).
cnf(c_0_1820_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_1820]) ).
cnf(c_0_1820_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_1820]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1821_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_1821]) ).
cnf(c_0_1822_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_1822]) ).
cnf(c_0_1822_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_1822]) ).
cnf(c_0_1822_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_1822]) ).
cnf(c_0_1822_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_1822]) ).
cnf(c_0_1823_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_1823]) ).
cnf(c_0_1823_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_1823]) ).
cnf(c_0_1823_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_1823]) ).
cnf(c_0_1823_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_1823]) ).
cnf(c_0_1824_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1826_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_2,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1827_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_2,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1830_0,axiom,
( ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1831_0,axiom,
( ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1832_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk67_3(X2,X3,X1),X1)
| in(sk1_esk67_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_1,axiom,
( in(sk1_esk67_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk67_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_2,axiom,
( in(sk1_esk67_3(X2,X3,X1),X2)
| in(sk1_esk67_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1833_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk57_3(X2,X3,X1),X1)
| in(sk1_esk57_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_1,axiom,
( in(sk1_esk57_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk57_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_2,axiom,
( in(sk1_esk57_3(X2,X3,X1),X2)
| in(sk1_esk57_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk57_3(X2,X3,X1),X1)
| in(sk1_esk57_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_1,axiom,
( in(sk1_esk57_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk57_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_2,axiom,
( in(sk1_esk57_3(X2,X3,X1),X3)
| in(sk1_esk57_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1835_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| in(sk1_esk48_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_1,axiom,
( in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk48_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_2,axiom,
( in(sk1_esk48_3(X2,X3,X1),X2)
| in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1836_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| in(sk1_esk49_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_1,axiom,
( in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk49_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_2,axiom,
( in(sk1_esk49_3(X2,X3,X1),X3)
| in(sk1_esk47_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_1,axiom,
( ~ relation(X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2)
| ~ in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_3,axiom,
( ~ in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1838_0,axiom,
( empty(X2)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_2,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk115_2(X2,X1),sk1_esk117_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,axiom,
( empty(X2)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_1,axiom,
( in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_2,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk116_2(X2,X1),sk1_esk118_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1840_0,axiom,
( in(sk1_esk146_1(X1),X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| in(sk1_esk146_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| in(sk1_esk146_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
( in(sk1_esk148_1(X1),X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| in(sk1_esk148_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| in(sk1_esk148_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk86_2(X1,X2),sk1_esk88_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,X2)
| ~ in(ordered_pair(sk1_esk86_2(X1,X2),sk1_esk88_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_2,axiom,
( ~ in(ordered_pair(sk1_esk86_2(X1,X2),sk1_esk88_2(X1,X2)),X1)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk74_2(X1,X2),sk1_esk75_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ in(ordered_pair(sk1_esk74_2(X1,X2),sk1_esk75_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_2,axiom,
( ~ in(ordered_pair(sk1_esk74_2(X1,X2),sk1_esk75_2(X1,X2)),X1)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1844_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_2,axiom,
( ~ in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk26_2(X1,X2),sk1_esk26_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,X2)
| ~ in(ordered_pair(sk1_esk26_2(X1,X2),sk1_esk26_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_2,axiom,
( ~ in(ordered_pair(sk1_esk26_2(X1,X2),sk1_esk26_2(X1,X2)),X1)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk41_3(X2,X3,X1) = X3
| sk1_esk41_3(X2,X3,X1) = X2
| in(sk1_esk41_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( sk1_esk41_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk41_3(X2,X3,X1) = X2
| in(sk1_esk41_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_2,axiom,
( sk1_esk41_3(X2,X3,X1) = X2
| sk1_esk41_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk41_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_3,axiom,
( in(sk1_esk41_3(X2,X3,X1),X1)
| sk1_esk41_3(X2,X3,X1) = X2
| sk1_esk41_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| element(sk1_esk89_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_1,axiom,
( element(sk1_esk89_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_1847]) ).
cnf(c_0_1847_2,axiom,
( ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk89_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_3,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk89_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1848_0,axiom,
( singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_2,axiom,
( sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_0,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( sk1_esk145_1(X1) != sk1_esk144_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1853_0,axiom,
( ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_0,axiom,
( empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_1,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_2,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_3,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1855_0,axiom,
( empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_1,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_2,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_3,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
( empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_1,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_2,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_3,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1857_0,axiom,
( in(sk1_esk173_2(X2,X1),X2)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| in(sk1_esk173_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1858_0,axiom,
( in(sk1_esk174_2(X2,X1),X2)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| in(sk1_esk174_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1859_0,axiom,
( sk1_esk143_1(X1) = sk1_esk144_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| sk1_esk143_1(X1) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( sk1_esk143_1(X1) = sk1_esk145_1(X1)
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk152_3(X1,X3,X2)) = sk1_esk153_3(X1,X3,X2)
| sk1_esk143_1(X1) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_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_1861]) ).
cnf(c_0_1861_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_1861]) ).
cnf(c_0_1861_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_1861]) ).
cnf(c_0_1861_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_1861]) ).
cnf(c_0_1861_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_1861]) ).
cnf(c_0_1861_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_1861]) ).
cnf(c_0_1862_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_2,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1865_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1866_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_2,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_1,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_2,axiom,
( sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
( in(sk1_esk173_2(X2,X1),X2)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| in(sk1_esk173_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1870_0,axiom,
( in(sk1_esk174_2(X2,X1),X2)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| in(sk1_esk174_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1871_0,axiom,
( X1 = inclusion_relation(X2)
| subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_1,axiom,
( subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| X1 = inclusion_relation(X2)
| in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_2,axiom,
( in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1)
| subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1)
| subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_4,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| in(ordered_pair(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1)),X1)
| subset(sk1_esk32_2(X2,X1),sk1_esk33_2(X2,X1))
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1872_0,axiom,
( in(sk1_esk146_1(X1),X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1872_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk146_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1872_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk146_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1873_0,axiom,
( in(sk1_esk148_1(X1),X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk148_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk148_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
( X2 = fiber(X1,X3)
| in(sk1_esk31_3(X1,X3,X2),X2)
| ~ relation(X1)
| sk1_esk31_3(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_1,axiom,
( in(sk1_esk31_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| ~ relation(X1)
| sk1_esk31_3(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_2,axiom,
( ~ relation(X1)
| in(sk1_esk31_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| sk1_esk31_3(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_3,axiom,
( sk1_esk31_3(X1,X3,X2) != X3
| ~ relation(X1)
| in(sk1_esk31_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
( quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_1,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| X2 != empty_set
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_2,axiom,
( X2 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_3,axiom,
( relation_dom_as_subset(X2,X3,X1) != X2
| X2 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_0,axiom,
( relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_1,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = X2
| X2 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_2,axiom,
( X2 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = X2
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_3,axiom,
( ~ quasi_total(X1,X2,X3)
| X2 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1877_0,axiom,
( X3 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_1,axiom,
( quasi_total(X1,X2,X3)
| X3 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_2,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| X3 = empty_set
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_3,axiom,
( relation_dom_as_subset(X2,X3,X1) != X2
| ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
( X3 = empty_set
| relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_1,axiom,
( relation_dom_as_subset(X2,X3,X1) = X2
| X3 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_2,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = X2
| X3 = empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_3,axiom,
( ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = X2
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
( empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_1,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| empty(X2)
| ~ relation(X1)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_2,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| empty(X2)
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_3,axiom,
( sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| sk1_esk116_2(X2,X1) != sk1_esk115_2(X2,X1)
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
( ordinal(sk1_esk173_2(X2,X1))
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk173_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
( ordinal(sk1_esk174_2(X2,X1))
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk174_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1882_1,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1882_2,axiom,
( sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1882_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_0,axiom,
( sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1885_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
( sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_1,axiom,
( in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk176_3(X2,X1,X3),succ(X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1887_0,axiom,
( singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
( singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_2,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_2,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1893_0,axiom,
( empty(X2)
| in(sk1_esk114_2(X2,X1),X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_1,axiom,
( in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_2,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| in(sk1_esk114_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1894_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(sk1_esk120_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_2,axiom,
( in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_3,axiom,
( ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk120_3(X2,X1,X3),X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1896_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk121_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_2,axiom,
( in(X3,sk1_esk121_3(X2,X1,X3))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk121_3(X2,X1,X3))
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1897_0,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_1,axiom,
( sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1898_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_1898]) ).
cnf(c_0_1899_0,axiom,
( ordinal(sk1_esk173_2(X2,X1))
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ordinal(sk1_esk173_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1900_0,axiom,
( in(sk1_esk173_2(X2,X1),X2)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| in(sk1_esk173_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1901_0,axiom,
( ordinal(sk1_esk174_2(X2,X1))
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ordinal(sk1_esk174_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1902_0,axiom,
( in(sk1_esk174_2(X2,X1),X2)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| in(sk1_esk174_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1903_0,axiom,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sk1_esk72_2(X1,X2)),X1)
| ~ in(sk1_esk72_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(ordered_pair(X3,sk1_esk72_2(X1,X2)),X1)
| ~ in(sk1_esk72_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_2,axiom,
( ~ in(ordered_pair(X3,sk1_esk72_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk72_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_3,axiom,
( ~ in(sk1_esk72_2(X1,X2),X2)
| ~ in(ordered_pair(X3,sk1_esk72_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk59_2(X1,X2),X3),X1)
| ~ in(sk1_esk59_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(ordered_pair(sk1_esk59_2(X1,X2),X3),X1)
| ~ in(sk1_esk59_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_2,axiom,
( ~ in(ordered_pair(sk1_esk59_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(sk1_esk59_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_3,axiom,
( ~ in(sk1_esk59_2(X1,X2),X2)
| ~ in(ordered_pair(sk1_esk59_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1906_0,axiom,
( sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1907_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1908_0,axiom,
( sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk177_3(X2,X1,X3),X2)
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( sk1_esk143_1(X1) = sk1_esk144_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( sk1_esk143_1(X1) = sk1_esk145_1(X1)
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk151_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
( ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1913_0,axiom,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk27_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_1,axiom,
( in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk27_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_2,axiom,
( X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set
| ~ in(X3,sk1_esk27_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_3,axiom,
( ~ in(X3,sk1_esk27_3(X1,X2,X3))
| X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1914_0,axiom,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_1,axiom,
( ~ relation_of2(X3,X1,X2)
| element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_0,axiom,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_1,axiom,
( ~ relation_of2(X3,X1,X2)
| element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1916_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_1916]) ).
cnf(c_0_1917_0,axiom,
( ordinal(sk1_esk173_2(X2,X1))
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ordinal(sk1_esk173_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_0,axiom,
( ordinal(sk1_esk174_2(X2,X1))
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ordinal(sk1_esk174_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1919_0,axiom,
( empty(X2)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_1,axiom,
( sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_2,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| sk1_esk117_2(X2,X1) = sk1_esk114_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
( empty(X2)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_1,axiom,
( sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_2,axiom,
( sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_3,axiom,
( ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk119_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_4,axiom,
( ~ in(X3,sk1_esk119_2(X2,X1))
| ~ relation(X1)
| sk1_esk120_3(X2,X1,X3) = sk1_esk121_3(X2,X1,X3)
| sk1_esk114_2(X2,X1) = sk1_esk118_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1922_0,axiom,
( sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1923_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
( sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_1,axiom,
( ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk177_3(X2,X1,X3))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
( in(sk1_esk146_1(X1),X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| in(sk1_esk146_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| in(sk1_esk146_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
( in(sk1_esk148_1(X1),X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| in(sk1_esk148_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| in(sk1_esk148_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1927_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_1927]) ).
cnf(c_0_1928_0,axiom,
( singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( in(X4,relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( ~ relation(X1)
| in(X4,relation_field(X1))
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X4,relation_field(X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,relation_field(X1))
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,relation_field(X1))
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,relation_field(X1))
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_6,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1931_0,axiom,
( in(X5,relation_field(X1))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_1,axiom,
( ~ relation(X1)
| in(X5,relation_field(X1))
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X5,relation_field(X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,relation_field(X1))
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,relation_field(X1))
| ~ relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,relation_field(X1))
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_6,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1932_0,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( X2 = relation_rng(X1)
| in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk72_2(X1,X2)),X1)
| in(sk1_esk72_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk72_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| in(sk1_esk72_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_2,axiom,
( in(sk1_esk72_2(X1,X2),X2)
| in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk72_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_3,axiom,
( ~ relation(X1)
| in(sk1_esk72_2(X1,X2),X2)
| in(ordered_pair(sk1_esk73_2(X1,X2),sk1_esk72_2(X1,X2)),X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( X2 = relation_dom(X1)
| in(ordered_pair(sk1_esk59_2(X1,X2),sk1_esk60_2(X1,X2)),X1)
| in(sk1_esk59_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( in(ordered_pair(sk1_esk59_2(X1,X2),sk1_esk60_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| in(sk1_esk59_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_2,axiom,
( in(sk1_esk59_2(X1,X2),X2)
| in(ordered_pair(sk1_esk59_2(X1,X2),sk1_esk60_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_3,axiom,
( ~ relation(X1)
| in(sk1_esk59_2(X1,X2),X2)
| in(ordered_pair(sk1_esk59_2(X1,X2),sk1_esk60_2(X1,X2)),X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1935_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_1935]) ).
cnf(c_0_1935_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_1935]) ).
cnf(c_0_1935_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_1935]) ).
cnf(c_0_1935_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_1935]) ).
cnf(c_0_1936_0,axiom,
( sk1_esk143_1(X1) = sk1_esk144_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| sk1_esk143_1(X1) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1937_0,axiom,
( ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1938_0,axiom,
( sk1_esk143_1(X1) = sk1_esk145_1(X1)
| in(sk1_esk152_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_1,axiom,
( in(sk1_esk152_3(X1,X3,X2),X1)
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk152_3(X1,X3,X2),X1)
| sk1_esk143_1(X1) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1939_0,axiom,
( ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1940_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_1940]) ).
cnf(c_0_1940_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_1940]) ).
cnf(c_0_1940_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_1940]) ).
cnf(c_0_1941_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),sk1_esk56_2(X1,X2))
| ~ in(X3,sk1_esk56_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ disjoint(fiber(X1,X3),sk1_esk56_2(X1,X2))
| ~ in(X3,sk1_esk56_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_2,axiom,
( ~ disjoint(fiber(X1,X3),sk1_esk56_2(X1,X2))
| ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ in(X3,sk1_esk56_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_3,axiom,
( ~ in(X3,sk1_esk56_2(X1,X2))
| ~ disjoint(fiber(X1,X3),sk1_esk56_2(X1,X2))
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_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_1942]) ).
cnf(c_0_1942_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_1942]) ).
cnf(c_0_1942_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_1942]) ).
cnf(c_0_1942_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_1942]) ).
cnf(c_0_1943_0,axiom,
( in(sk1_esk146_1(X1),X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk146_1(X1),X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk146_1(X1),X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk146_1(X1),X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk146_1(X1),X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk146_1(X1),X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk146_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1944_0,axiom,
( in(sk1_esk148_1(X1),X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk148_1(X1),X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk148_1(X1),X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk148_1(X1),X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk148_1(X1),X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk148_1(X1),X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| in(sk1_esk148_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1945_0,axiom,
( X2 = empty_set
| X1 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_1,axiom,
( X1 = empty_set
| X2 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_2,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| X1 = empty_set
| X2 = empty_set
| X3 != empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_3,axiom,
( X3 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X1 = empty_set
| X2 = empty_set
| ~ quasi_total(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_4,axiom,
( ~ quasi_total(X1,X2,X3)
| X3 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X1 = empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1946_0,axiom,
( singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1947_0,axiom,
( singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1948_0,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_1,axiom,
( sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_2,axiom,
( X4 != singleton(X5)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1949_0,axiom,
( X3 = empty_set
| in(sk1_esk55_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_1,axiom,
( in(sk1_esk55_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_1949]) ).
cnf(c_0_1949_2,axiom,
( ~ relation(X1)
| in(sk1_esk55_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_3,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| in(sk1_esk55_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_4,axiom,
( ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| in(sk1_esk55_3(X1,X2,X3),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1950_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(sk1_esk28_2(X1,X2),X2)
| ~ in(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk28_2(X1,X2),X2)
| ~ in(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_2,axiom,
( ~ in(sk1_esk28_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_3,axiom,
( ~ in(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2))
| ~ in(sk1_esk28_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1951_0,axiom,
( subset(X1,X2)
| in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk52_2(X1,X2),sk1_esk53_2(X1,X2)),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_0,axiom,
( in(sk1_esk68_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_1952]) ).
cnf(c_0_1952_1,axiom,
( ~ function(X1)
| in(sk1_esk68_3(X1,X2,X3),relation_dom(X1))
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk68_3(X1,X2,X3),relation_dom(X1))
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk68_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_4,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk68_3(X1,X2,X3),relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1953_0,axiom,
( sk1_esk143_1(X1) = sk1_esk144_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1954_0,axiom,
( sk1_esk143_1(X1) = sk1_esk145_1(X1)
| in(X2,sk1_esk150_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_1,axiom,
( in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk150_2(X1,X3))
| sk1_esk143_1(X1) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1955_0,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_1,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_2,axiom,
( sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1956_0,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_1,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_2,axiom,
( sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1957_0,axiom,
( apply(X1,sk1_esk68_3(X1,X2,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_1,axiom,
( ~ function(X1)
| apply(X1,sk1_esk68_3(X1,X2,X3)) = X3
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk68_3(X1,X2,X3)) = X3
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk68_3(X1,X2,X3)) = X3
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_4,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk68_3(X1,X2,X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1958_0,axiom,
( in(sk1_esk173_2(X2,X1),X2)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| in(sk1_esk173_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
( in(sk1_esk173_2(X2,X1),X2)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| in(sk1_esk173_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1960_0,axiom,
( in(sk1_esk174_2(X2,X1),X2)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| in(sk1_esk174_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1961_0,axiom,
( in(sk1_esk174_2(X2,X1),X2)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| in(sk1_esk174_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1962_0,axiom,
( is_transitive_in(X1,X2)
| in(ordered_pair(sk1_esk86_2(X1,X2),sk1_esk87_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_1,axiom,
( in(ordered_pair(sk1_esk86_2(X1,X2),sk1_esk87_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk86_2(X1,X2),sk1_esk87_2(X1,X2)),X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1963_0,axiom,
( is_transitive_in(X1,X2)
| in(ordered_pair(sk1_esk87_2(X1,X2),sk1_esk88_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_1,axiom,
( in(ordered_pair(sk1_esk87_2(X1,X2),sk1_esk88_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk87_2(X1,X2),sk1_esk88_2(X1,X2)),X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1964_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(sk1_esk61_2(X1,X2),sk1_esk62_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_1,axiom,
( in(ordered_pair(sk1_esk61_2(X1,X2),sk1_esk62_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk61_2(X1,X2),sk1_esk62_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1965_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_1,axiom,
( in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1966_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_1966]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1967_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_1967]) ).
cnf(c_0_1968_0,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_1,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_2,axiom,
( sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_3,axiom,
( ~ in(X4,X2)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| sk1_esk172_2(X2,X1) != sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1969_0,axiom,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk69_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk69_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_1,axiom,
( ~ function(X1)
| X2 = relation_rng(X1)
| ~ relation(X1)
| sk1_esk69_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk69_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| sk1_esk69_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk69_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_3,axiom,
( sk1_esk69_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk69_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_4,axiom,
( ~ in(X3,relation_dom(X1))
| sk1_esk69_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk69_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_5,axiom,
( ~ in(sk1_esk69_2(X1,X2),X2)
| ~ in(X3,relation_dom(X1))
| sk1_esk69_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1970_0,axiom,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_1,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1971_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_1971]) ).
cnf(c_0_1972_0,axiom,
( in(sk1_esk173_2(X2,X1),X2)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk173_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
( in(sk1_esk174_2(X2,X1),X2)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| in(sk1_esk174_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
( ordinal(sk1_esk173_2(X2,X1))
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ordinal(sk1_esk173_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1975_0,axiom,
( ordinal(sk1_esk173_2(X2,X1))
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ordinal(sk1_esk173_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1976_0,axiom,
( ordinal(sk1_esk174_2(X2,X1))
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ordinal(sk1_esk174_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1977_0,axiom,
( ordinal(sk1_esk174_2(X2,X1))
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ordinal(sk1_esk174_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1978_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk64_2(X2,X1),X3)
| ~ in(sk1_esk64_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk64_2(X2,X1),X3)
| ~ in(sk1_esk64_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_2,axiom,
( ~ in(sk1_esk64_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk64_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_3,axiom,
( ~ in(sk1_esk64_2(X2,X1),X1)
| ~ in(sk1_esk64_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1979_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1979_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1979_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1979_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1980_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
( sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1982_0,axiom,
( sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1982_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1982_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1982_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1983_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
( sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| sk1_esk176_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_1,axiom,
( sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_2,axiom,
( ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk176_3(X2,X1,X3) = X3
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
( sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| sk1_esk177_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_1,axiom,
( sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_2,axiom,
( ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X3,sk1_esk175_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_3,axiom,
( ~ in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk177_3(X2,X1,X3) = X3
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_0,axiom,
( in(X3,sk1_esk63_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk63_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk63_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
( in(sk1_esk63_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_1,axiom,
( X1 != union(X2)
| in(sk1_esk63_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk63_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
( ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk146_1(X1),sk1_esk147_1(X1)) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1990_0,axiom,
( ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk148_1(X1),sk1_esk149_1(X1)) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1991_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_1991]) ).
cnf(c_0_1992_0,axiom,
( ordinal(sk1_esk173_2(X2,X1))
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1))
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1))
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1))
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1))
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk173_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( ordinal(sk1_esk174_2(X2,X1))
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1))
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1))
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1))
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1))
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| ordinal(sk1_esk174_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( X2 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| X1 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( quasi_total(X1,X2,X3)
| X2 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| X1 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_2,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| X2 = empty_set
| X3 != empty_set
| X1 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_3,axiom,
( X3 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| X2 = empty_set
| X1 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_4,axiom,
( X1 != empty_set
| X3 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| quasi_total(X1,X2,X3)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_0,axiom,
( X1 = empty_set
| in(X3,X2)
| in(sk1_esk27_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_1,axiom,
( in(X3,X2)
| X1 = empty_set
| in(sk1_esk27_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_2,axiom,
( in(sk1_esk27_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_3,axiom,
( X2 != set_meet(X1)
| in(sk1_esk27_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1996_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
( sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk173_2(X2,X1) = sk1_esk171_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
( sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk170_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| in(X3,sk1_esk175_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk175_2(X2,X1))
| sk1_esk174_2(X2,X1) = sk1_esk172_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( ~ relation_of2(X3,X1,X2)
| relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_1,axiom,
( ~ relation_of2(X3,X1,X2)
| relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2002_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_2002]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2003_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_2003]) ).
cnf(c_0_2004_0,axiom,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( ~ relation_of2(X1,X2,X3)
| relation_of2_as_subset(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2006_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_2006]) ).
cnf(c_0_2007_0,axiom,
( X2 = empty_set
| disjoint(fiber(X1,sk1_esk42_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_1,axiom,
( disjoint(fiber(X1,sk1_esk42_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_2007]) ).
cnf(c_0_2007_2,axiom,
( ~ relation(X1)
| disjoint(fiber(X1,sk1_esk42_2(X1,X2)),X2)
| X2 = empty_set
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_3,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk42_2(X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_4,axiom,
( ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk42_2(X1,X2)),X2)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
( in(sk1_esk146_1(X1),X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| in(sk1_esk146_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| in(sk1_esk146_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( in(sk1_esk148_1(X1),X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| in(sk1_esk148_1(X1),X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| in(sk1_esk148_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( subset(X4,X3)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( ~ relation(X1)
| subset(X4,X3)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_2,axiom,
( X1 != inclusion_relation(X2)
| ~ relation(X1)
| subset(X4,X3)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_3,axiom,
( ~ in(X3,X2)
| X1 != inclusion_relation(X2)
| ~ relation(X1)
| subset(X4,X3)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_4,axiom,
( ~ in(X4,X2)
| ~ in(X3,X2)
| X1 != inclusion_relation(X2)
| ~ relation(X1)
| subset(X4,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_5,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| X1 != inclusion_relation(X2)
| ~ relation(X1)
| subset(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( X1 = X2
| ~ in(ordered_pair(X3,X2),X4)
| ~ in(ordered_pair(X3,X1),X4)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( ~ in(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ in(ordered_pair(X3,X1),X4)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_2,axiom,
( ~ in(ordered_pair(X3,X1),X4)
| ~ in(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_3,axiom,
( ~ function(X4)
| ~ in(ordered_pair(X3,X1),X4)
| ~ in(ordered_pair(X3,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2012_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_2012]) ).
cnf(c_0_2013_0,axiom,
( singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| singleton(sk1_esk146_1(X1)) = sk1_esk147_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| singleton(sk1_esk148_1(X1)) = sk1_esk149_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_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_2015]) ).
cnf(c_0_2015_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_2015]) ).
cnf(c_0_2015_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_2015]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2016_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_2016]) ).
cnf(c_0_2017_0,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( sk1_esk145_1(X1) != sk1_esk144_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk145_1(X1) != sk1_esk144_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk35_2(X2,X1),X2)
| ~ in(sk1_esk35_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( ~ subset(sk1_esk35_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk35_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_2,axiom,
( ~ in(sk1_esk35_2(X2,X1),X1)
| ~ subset(sk1_esk35_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_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_2019]) ).
cnf(c_0_2019_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_2019]) ).
cnf(c_0_2019_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_2019]) ).
cnf(c_0_2019_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_2019]) ).
cnf(c_0_2019_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_2019]) ).
cnf(c_0_2020_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_2020]) ).
cnf(c_0_2020_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_2020]) ).
cnf(c_0_2020_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_2020]) ).
cnf(c_0_2020_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_2020]) ).
cnf(c_0_2020_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_2020]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2021_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_2021]) ).
cnf(c_0_2022_0,axiom,
( X1 = X2
| ~ in(sk1_esk178_2(X1,X2),X2)
| ~ in(sk1_esk178_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ in(sk1_esk178_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk178_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_2,axiom,
( ~ in(sk1_esk178_2(X1,X2),X1)
| ~ in(sk1_esk178_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( sk1_esk143_1(X1) = sk1_esk144_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| sk1_esk143_1(X1) = sk1_esk144_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| sk1_esk143_1(X1) = sk1_esk144_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( sk1_esk143_1(X1) = sk1_esk145_1(X1)
| sk1_esk151_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( sk1_esk151_3(X1,X3,X2) = X2
| sk1_esk143_1(X1) = sk1_esk145_1(X1)
| ~ in(X2,sk1_esk150_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_2,axiom,
( ~ in(X2,sk1_esk150_2(X1,X3))
| sk1_esk151_3(X1,X3,X2) = X2
| sk1_esk143_1(X1) = sk1_esk145_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2025_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_2025]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2027_0,axiom,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( ~ relation_of2(X1,X2,X3)
| subset(X1,cartesian_product2(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2028_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_2028]) ).
cnf(c_0_2029_0,axiom,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_2,axiom,
( X1 != inclusion_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_3,axiom,
( ~ in(X3,X2)
| X1 != inclusion_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_4,axiom,
( ~ in(X4,X2)
| ~ in(X3,X2)
| X1 != inclusion_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| ~ subset(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_5,axiom,
( ~ subset(X4,X3)
| ~ in(X4,X2)
| ~ in(X3,X2)
| X1 != inclusion_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
( relation_dom(X3) = relation_field(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( ~ relation(X1)
| relation_dom(X3) = relation_field(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| relation_dom(X3) = relation_field(X1)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_dom(X3) = relation_field(X1)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_dom(X3) = relation_field(X1)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_dom(X3) = relation_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
( relation_rng(X3) = relation_field(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_1,axiom,
( ~ relation(X1)
| relation_rng(X3) = relation_field(X2)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| relation_rng(X3) = relation_field(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_rng(X3) = relation_field(X2)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_rng(X3) = relation_field(X2)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| relation_rng(X3) = relation_field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2034_0,axiom,
( one_to_one(X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_1,axiom,
( ~ relation(X1)
| one_to_one(X3)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| one_to_one(X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_3,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| one_to_one(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_4,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| one_to_one(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_5,axiom,
( ~ relation_isomorphism(X1,X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2035_0,axiom,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_1,axiom,
( ~ subset(X1,cartesian_product2(X2,X3))
| relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2036_0,axiom,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_1,axiom,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2037_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),sk1_esk43_1(X1))
| ~ in(X2,sk1_esk43_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ disjoint(fiber(X1,X2),sk1_esk43_1(X1))
| ~ in(X2,sk1_esk43_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_2,axiom,
( ~ disjoint(fiber(X1,X2),sk1_esk43_1(X1))
| ~ relation(X1)
| well_founded_relation(X1)
| ~ in(X2,sk1_esk43_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_3,axiom,
( ~ in(X2,sk1_esk43_1(X1))
| ~ disjoint(fiber(X1,X2),sk1_esk43_1(X1))
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2038_0,axiom,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_1,axiom,
( X5 = X3
| X5 = X4
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_2,axiom,
( X5 = X2
| X5 = X3
| X5 = X4
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_3,axiom,
( X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_4,axiom,
( ~ in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2040_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_2040]) ).
cnf(c_0_2040_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_2040]) ).
cnf(c_0_2040_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_2040]) ).
cnf(c_0_2040_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_2040]) ).
cnf(c_0_2040_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_2040]) ).
cnf(c_0_2041_0,axiom,
( X2 = relation_rng(X1)
| in(sk1_esk69_2(X1,X2),X2)
| apply(X1,sk1_esk70_2(X1,X2)) = sk1_esk69_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_1,axiom,
( in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1)
| apply(X1,sk1_esk70_2(X1,X2)) = sk1_esk69_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_2,axiom,
( apply(X1,sk1_esk70_2(X1,X2)) = sk1_esk69_2(X1,X2)
| in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_3,axiom,
( ~ function(X1)
| apply(X1,sk1_esk70_2(X1,X2)) = sk1_esk69_2(X1,X2)
| in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk70_2(X1,X2)) = sk1_esk69_2(X1,X2)
| in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2042_0,axiom,
( X1 = union(X2)
| in(sk1_esk64_2(X2,X1),X1)
| in(sk1_esk64_2(X2,X1),sk1_esk65_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_1,axiom,
( in(sk1_esk64_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk64_2(X2,X1),sk1_esk65_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_2,axiom,
( in(sk1_esk64_2(X2,X1),sk1_esk65_2(X2,X1))
| in(sk1_esk64_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2043_0,axiom,
( in(X4,X2)
| X4 = X3
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_1,axiom,
( X4 = X3
| in(X4,X2)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_2,axiom,
( ~ relation(X1)
| X4 = X3
| in(X4,X2)
| X2 != fiber(X1,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_3,axiom,
( X2 != fiber(X1,X3)
| ~ relation(X1)
| X4 = X3
| in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_4,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != fiber(X1,X3)
| ~ relation(X1)
| X4 = X3
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2045_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk29_2(X1,X2),X1)
| ~ in(sk1_esk28_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk29_2(X1,X2),X1)
| ~ in(sk1_esk28_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_2,axiom,
( in(sk1_esk29_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk28_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_3,axiom,
( ~ in(sk1_esk28_2(X1,X2),X2)
| in(sk1_esk29_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2046_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk28_2(X1,X2),X3)
| in(sk1_esk28_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk28_2(X1,X2),X3)
| in(sk1_esk28_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_2,axiom,
( in(sk1_esk28_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk28_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_3,axiom,
( in(sk1_esk28_2(X1,X2),X2)
| in(sk1_esk28_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_4,axiom,
( ~ in(X3,X1)
| in(sk1_esk28_2(X1,X2),X2)
| in(sk1_esk28_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2047_0,axiom,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2048_0,axiom,
( ~ in(X1,X2)
| ~ in(X3,sk1_esk179_2(X1,X2))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_1,axiom,
( ~ in(X3,sk1_esk179_2(X1,X2))
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_2,axiom,
( ~ in(X3,X2)
| ~ in(X3,sk1_esk179_2(X1,X2))
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2050_0,axiom,
( X2 = relation_rng(X1)
| in(sk1_esk69_2(X1,X2),X2)
| in(sk1_esk70_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_1,axiom,
( in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1)
| in(sk1_esk70_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_2,axiom,
( in(sk1_esk70_2(X1,X2),relation_dom(X1))
| in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_3,axiom,
( ~ function(X1)
| in(sk1_esk70_2(X1,X2),relation_dom(X1))
| in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk70_2(X1,X2),relation_dom(X1))
| in(sk1_esk69_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2051_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_2,axiom,
( X5 != X2
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2052_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_2,axiom,
( X5 != X3
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2053_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_2,axiom,
( X5 != X4
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2054_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_2054]) ).
cnf(c_0_2055_0,axiom,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2056_0,axiom,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(union_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2057_0,axiom,
( ordered_pair(sk1_esk23_2(X2,X1),sk1_esk24_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_1,axiom,
( ~ in(X1,X2)
| ordered_pair(sk1_esk23_2(X2,X1),sk1_esk24_2(X2,X1)) = X1
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_2,axiom,
( ~ relation(X2)
| ~ in(X1,X2)
| ordered_pair(sk1_esk23_2(X2,X1),sk1_esk24_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2058_0,axiom,
( X4 = pair_second(X1)
| ordered_pair(sk1_esk36_2(X1,X4),sk1_esk37_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( ordered_pair(sk1_esk36_2(X1,X4),sk1_esk37_2(X1,X4)) = X1
| X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_2,axiom,
( X1 != ordered_pair(X2,X3)
| ordered_pair(sk1_esk36_2(X1,X4),sk1_esk37_2(X1,X4)) = X1
| X4 = pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2059_0,axiom,
( X4 = pair_first(X1)
| ordered_pair(sk1_esk21_2(X1,X4),sk1_esk22_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_1,axiom,
( ordered_pair(sk1_esk21_2(X1,X4),sk1_esk22_2(X1,X4)) = X1
| X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_2,axiom,
( X1 != ordered_pair(X2,X3)
| ordered_pair(sk1_esk21_2(X1,X4),sk1_esk22_2(X1,X4)) = X1
| X4 = pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2060_0,axiom,
( in(X3,sk1_esk181_2(X2,X1))
| ~ in(X1,sk1_esk180_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_1,axiom,
( ~ in(X1,sk1_esk180_1(X2))
| in(X3,sk1_esk181_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk180_1(X2))
| in(X3,sk1_esk181_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2061_0,axiom,
( in(sk1_esk138_1(X1),X1)
| in(X2,sk1_esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_1,axiom,
( in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2062_0,axiom,
( in(sk1_esk138_1(X1),X1)
| in(X2,sk1_esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_1,axiom,
( in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_2,axiom,
( X2 != fiber(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_3,axiom,
( ~ in(X4,X2)
| X2 != fiber(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2064_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_3,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2066_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2066_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2066_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2066_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2067_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2067_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2067_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2067_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2068_0,axiom,
( in(sk1_esk138_1(X1),X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2068_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2068_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2069_0,axiom,
( in(sk1_esk138_1(X1),X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2070_0,axiom,
( in(sk1_esk138_1(X1),X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2071_0,axiom,
( in(sk1_esk138_1(X1),X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2073_0,axiom,
( X1 = singleton(X2)
| sk1_esk30_2(X2,X1) != X2
| ~ in(sk1_esk30_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_1,axiom,
( sk1_esk30_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk30_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_2,axiom,
( ~ in(sk1_esk30_2(X2,X1),X1)
| sk1_esk30_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2074_0,axiom,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2075_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| in(X2,sk1_esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_1,axiom,
( in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2076_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| in(X2,sk1_esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_1,axiom,
( in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( X2 = empty_set
| in(sk1_esk42_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_1,axiom,
( in(sk1_esk42_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_2077]) ).
cnf(c_0_2077_2,axiom,
( ~ relation(X1)
| in(sk1_esk42_2(X1,X2),X2)
| X2 = empty_set
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_3,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| in(sk1_esk42_2(X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_4,axiom,
( ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1)
| in(sk1_esk42_2(X1,X2),X2)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2078_0,axiom,
( in(X2,sk1_esk141_1(X1))
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_1,axiom,
( sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(X2,sk1_esk141_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_2,axiom,
( X2 != singleton(X3)
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(X2,sk1_esk141_1(X1))
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(X2,sk1_esk141_1(X1))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2079_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2080_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2081_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_1,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| in(sk1_esk142_2(X1,X2),X1)
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( X1 = union(X2)
| in(sk1_esk64_2(X2,X1),X1)
| in(sk1_esk65_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_1,axiom,
( in(sk1_esk64_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk65_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_2,axiom,
( in(sk1_esk65_2(X2,X1),X2)
| in(sk1_esk64_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk35_2(X2,X1),X2)
| in(sk1_esk35_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_1,axiom,
( subset(sk1_esk35_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk35_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_2,axiom,
( in(sk1_esk35_2(X2,X1),X1)
| subset(sk1_esk35_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2085_0,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2085_1,axiom,
( sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2085_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(sk1_esk142_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2086_0,axiom,
( in(sk1_esk142_2(X1,X2),X1)
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_1,axiom,
( sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(sk1_esk142_2(X1,X2),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| in(sk1_esk142_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2087_0,axiom,
( in(sk1_esk138_1(X1),X1)
| singleton(sk1_esk142_2(X1,X2)) = X2
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_1,axiom,
( singleton(sk1_esk142_2(X1,X2)) = X2
| in(sk1_esk138_1(X1),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk142_2(X1,X2)) = X2
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2088_0,axiom,
( in(sk1_esk138_1(X1),X1)
| singleton(sk1_esk142_2(X1,X2)) = X2
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_1,axiom,
( singleton(sk1_esk142_2(X1,X2)) = X2
| in(sk1_esk138_1(X1),X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk142_2(X1,X2)) = X2
| in(sk1_esk138_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2089_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2090_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_2090]) ).
cnf(c_0_2090_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_2090]) ).
cnf(c_0_2090_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_2090]) ).
cnf(c_0_2090_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_2090]) ).
cnf(c_0_2090_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_2090]) ).
cnf(c_0_2090_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_2090]) ).
cnf(c_0_2091_0,axiom,
( X1 = X2
| in(sk1_esk178_2(X1,X2),X2)
| in(sk1_esk178_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_1,axiom,
( in(sk1_esk178_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk178_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_2,axiom,
( in(sk1_esk178_2(X1,X2),X1)
| in(sk1_esk178_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2092_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_2092]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2093_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_2093]) ).
cnf(c_0_2094_0,axiom,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_1,axiom,
( ~ relation(X1)
| X3 = X4
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2100_0,axiom,
( in(sk1_esk181_2(X2,X1),sk1_esk180_1(X2))
| ~ in(X1,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_1,axiom,
( ~ in(X1,sk1_esk180_1(X2))
| in(sk1_esk181_2(X2,X1),sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2101_0,axiom,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_1,axiom,
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2102_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| singleton(sk1_esk142_2(X1,X2)) = X2
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_1,axiom,
( singleton(sk1_esk142_2(X1,X2)) = X2
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk142_2(X1,X2)) = X2
| singleton(sk1_esk138_1(X1)) = sk1_esk139_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2103_0,axiom,
( singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| singleton(sk1_esk142_2(X1,X2)) = X2
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_1,axiom,
( singleton(sk1_esk142_2(X1,X2)) = X2
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| singleton(sk1_esk142_2(X1,X2)) = X2
| singleton(sk1_esk138_1(X1)) = sk1_esk140_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2104_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk54_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_1,axiom,
( ~ in(sk1_esk54_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2105_0,axiom,
( singleton(sk1_esk142_2(X1,X2)) = X2
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( sk1_esk140_1(X1) != sk1_esk139_1(X1)
| singleton(sk1_esk142_2(X1,X2)) = X2
| ~ in(X2,sk1_esk141_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_2,axiom,
( ~ in(X2,sk1_esk141_1(X1))
| sk1_esk140_1(X1) != sk1_esk139_1(X1)
| singleton(sk1_esk142_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_0,axiom,
( ordinal(sk1_esk166_0)
| in(sk1_esk169_2(X2,X1),X2)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_1,axiom,
( in(sk1_esk169_2(X2,X1),X2)
| ordinal(sk1_esk166_0)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| in(sk1_esk169_2(X2,X1),X2)
| ordinal(sk1_esk166_0) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2107_0,axiom,
( ordinal(sk1_esk167_0)
| in(sk1_esk169_2(X2,X1),X2)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( in(sk1_esk169_2(X2,X1),X2)
| ordinal(sk1_esk167_0)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| in(sk1_esk169_2(X2,X1),X2)
| ordinal(sk1_esk167_0) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_0,axiom,
( in(X1,sk1_esk180_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk180_1(X2))
| ~ in(X3,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_2,axiom,
( ~ in(X3,sk1_esk180_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2109_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2110_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_0,axiom,
( in(sk1_esk169_2(X2,X1),X2)
| sk1_esk167_0 != sk1_esk166_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_1,axiom,
( sk1_esk167_0 != sk1_esk166_0
| in(sk1_esk169_2(X2,X1),X2)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk167_0 != sk1_esk166_0
| in(sk1_esk169_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2112_0,axiom,
( in(X1,sk1_esk180_1(X2))
| are_equipotent(X1,sk1_esk180_1(X2))
| ~ subset(X1,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2112_1,axiom,
( are_equipotent(X1,sk1_esk180_1(X2))
| in(X1,sk1_esk180_1(X2))
| ~ subset(X1,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2112_2,axiom,
( ~ subset(X1,sk1_esk180_1(X2))
| are_equipotent(X1,sk1_esk180_1(X2))
| in(X1,sk1_esk180_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2113_0,axiom,
( sk1_esk165_0 = sk1_esk166_0
| in(sk1_esk169_2(X2,X1),X2)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_1,axiom,
( in(sk1_esk169_2(X2,X1),X2)
| sk1_esk165_0 = sk1_esk166_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| in(sk1_esk169_2(X2,X1),X2)
| sk1_esk165_0 = sk1_esk166_0 ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2114_0,axiom,
( sk1_esk165_0 = sk1_esk167_0
| in(sk1_esk169_2(X2,X1),X2)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_1,axiom,
( in(sk1_esk169_2(X2,X1),X2)
| sk1_esk165_0 = sk1_esk167_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| in(sk1_esk169_2(X2,X1),X2)
| sk1_esk165_0 = sk1_esk167_0 ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2115_0,axiom,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_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_2116]) ).
cnf(c_0_2116_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_2116]) ).
cnf(c_0_2116_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_2116]) ).
cnf(c_0_2116_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_2116]) ).
cnf(c_0_2116_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_2116]) ).
cnf(c_0_2117_0,axiom,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| meet_of_subsets(X1,X2) = set_meet(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2118_0,axiom,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| union_of_subsets(X1,X2) = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2119_0,axiom,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_1,axiom,
( ~ element(X3,powerset(X2))
| element(X1,X2)
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_2,axiom,
( ~ in(X1,X3)
| ~ element(X3,powerset(X2))
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2120_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2120_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2120_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2120]) ).
cnf(c_0_2121_0,axiom,
( function(X1)
| in(ordered_pair(sk1_esk18_1(X1),sk1_esk19_1(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2121_1,axiom,
( in(ordered_pair(sk1_esk18_1(X1),sk1_esk19_1(X1)),X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2122_0,axiom,
( function(X1)
| in(ordered_pair(sk1_esk18_1(X1),sk1_esk20_1(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_1,axiom,
( in(ordered_pair(sk1_esk18_1(X1),sk1_esk20_1(X1)),X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2123_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2124_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| sk1_esk74_2(X1,X2) != sk1_esk75_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| sk1_esk74_2(X1,X2) != sk1_esk75_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_2,axiom,
( sk1_esk74_2(X1,X2) != sk1_esk75_2(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2125_0,axiom,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| sk1_esk62_2(X1,X2) != sk1_esk61_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,X2)
| sk1_esk62_2(X1,X2) != sk1_esk61_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_2,axiom,
( sk1_esk62_2(X1,X2) != sk1_esk61_2(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2126_0,axiom,
( in(sk1_esk179_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_1,axiom,
( ~ in(X1,X2)
| in(sk1_esk179_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2127_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2128_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk86_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_1,axiom,
( in(sk1_esk86_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_2,axiom,
( ~ relation(X1)
| in(sk1_esk86_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2129_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk87_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_1,axiom,
( in(sk1_esk87_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_2,axiom,
( ~ relation(X1)
| in(sk1_esk87_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2130_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk88_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_1,axiom,
( in(sk1_esk88_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_2,axiom,
( ~ relation(X1)
| in(sk1_esk88_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2131_0,axiom,
( is_connected_in(X1,X2)
| in(sk1_esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_1,axiom,
( in(sk1_esk74_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_2,axiom,
( ~ relation(X1)
| in(sk1_esk74_2(X1,X2),X2)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2132_0,axiom,
( is_connected_in(X1,X2)
| in(sk1_esk75_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_1,axiom,
( in(sk1_esk75_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_2,axiom,
( ~ relation(X1)
| in(sk1_esk75_2(X1,X2),X2)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2133_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(sk1_esk61_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_1,axiom,
( in(sk1_esk61_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_2,axiom,
( ~ relation(X1)
| in(sk1_esk61_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2134_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(sk1_esk62_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_1,axiom,
( in(sk1_esk62_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_2,axiom,
( ~ relation(X1)
| in(sk1_esk62_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2135_0,axiom,
( is_well_founded_in(X1,X2)
| subset(sk1_esk56_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_1,axiom,
( subset(sk1_esk56_2(X1,X2),X2)
| is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_2,axiom,
( ~ relation(X1)
| subset(sk1_esk56_2(X1,X2),X2)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2136_0,axiom,
( is_reflexive_in(X1,X2)
| in(sk1_esk26_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_1,axiom,
( in(sk1_esk26_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_2,axiom,
( ~ relation(X1)
| in(sk1_esk26_2(X1,X2),X2)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2137_0,axiom,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_1,axiom,
( ~ relation(X1)
| set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2138_0,axiom,
( X1 = inclusion_relation(X2)
| in(sk1_esk32_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_1,axiom,
( in(sk1_esk32_2(X2,X1),X2)
| X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_2,axiom,
( ~ relation(X1)
| in(sk1_esk32_2(X2,X1),X2)
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_3,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| in(sk1_esk32_2(X2,X1),X2)
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2139_0,axiom,
( X1 = inclusion_relation(X2)
| in(sk1_esk33_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( in(sk1_esk33_2(X2,X1),X2)
| X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_2,axiom,
( ~ relation(X1)
| in(sk1_esk33_2(X2,X1),X2)
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_3,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| in(sk1_esk33_2(X2,X1),X2)
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2141_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2142_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2144_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2145_0,axiom,
( X1 = singleton(X2)
| sk1_esk30_2(X2,X1) = X2
| in(sk1_esk30_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_1,axiom,
( sk1_esk30_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk30_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_2,axiom,
( in(sk1_esk30_2(X2,X1),X1)
| sk1_esk30_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2146_0,axiom,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2149_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_0,axiom,
( one_to_one(X1)
| apply(X1,sk1_esk81_1(X1)) = apply(X1,sk1_esk80_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_1,axiom,
( apply(X1,sk1_esk81_1(X1)) = apply(X1,sk1_esk80_1(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_2,axiom,
( ~ function(X1)
| apply(X1,sk1_esk81_1(X1)) = apply(X1,sk1_esk80_1(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk81_1(X1)) = apply(X1,sk1_esk80_1(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2151_0,axiom,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_1,axiom,
( ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2152_0,axiom,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_1,axiom,
( ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2153_0,axiom,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X6,X5)
| X4 != pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_1,axiom,
( X1 != ordered_pair(X2,X3)
| X4 = X5
| X1 != ordered_pair(X6,X5)
| X4 != pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_2,axiom,
( X1 != ordered_pair(X6,X5)
| X1 != ordered_pair(X2,X3)
| X4 = X5
| X4 != pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_3,axiom,
( X4 != pair_second(X1)
| X1 != ordered_pair(X6,X5)
| X1 != ordered_pair(X2,X3)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2154_0,axiom,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X5,X6)
| X4 != pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_1,axiom,
( X1 != ordered_pair(X2,X3)
| X4 = X5
| X1 != ordered_pair(X5,X6)
| X4 != pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_2,axiom,
( X1 != ordered_pair(X5,X6)
| X1 != ordered_pair(X2,X3)
| X4 = X5
| X4 != pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_3,axiom,
( X4 != pair_first(X1)
| X1 != ordered_pair(X5,X6)
| X1 != ordered_pair(X2,X3)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2155_0,axiom,
( ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_1,axiom,
( X2 != fiber(X1,X3)
| ~ relation(X1)
| ~ in(X4,X2)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_2,axiom,
( ~ in(X4,X2)
| X2 != fiber(X1,X3)
| ~ relation(X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_3,axiom,
( X4 != X3
| ~ in(X4,X2)
| X2 != fiber(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2156_0,axiom,
( ordinal(sk1_esk166_0)
| in(X1,sk1_esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_1,axiom,
( in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk166_0)
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk166_0)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk166_0)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk166_0) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2157_0,axiom,
( ordinal(sk1_esk167_0)
| in(X1,sk1_esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_1,axiom,
( in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk167_0)
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk167_0)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk167_0)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| ordinal(sk1_esk167_0) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2158_0,axiom,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_1,axiom,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_2,axiom,
( ~ empty(cartesian_product2(X1,X2))
| empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2159_0,axiom,
( in(X1,sk1_esk168_1(X2))
| sk1_esk167_0 != sk1_esk166_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_1,axiom,
( sk1_esk167_0 != sk1_esk166_0
| in(X1,sk1_esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_2,axiom,
( ~ ordinal(X1)
| sk1_esk167_0 != sk1_esk166_0
| in(X1,sk1_esk168_1(X2))
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| sk1_esk167_0 != sk1_esk166_0
| in(X1,sk1_esk168_1(X2))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| sk1_esk167_0 != sk1_esk166_0
| in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2160_0,axiom,
( sk1_esk165_0 = sk1_esk166_0
| in(X1,sk1_esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_1,axiom,
( in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk166_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk166_0
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk166_0
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk166_0 ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2161_0,axiom,
( sk1_esk165_0 = sk1_esk167_0
| in(X1,sk1_esk168_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_1,axiom,
( in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk167_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk167_0
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk167_0
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk168_1(X2))
| sk1_esk165_0 = sk1_esk167_0 ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2162_0,axiom,
( subset(X1,X2)
| in(sk1_esk54_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_1,axiom,
( in(sk1_esk54_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2163_0,axiom,
( relation_dom(sk1_esk66_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_1,axiom,
( ~ equipotent(X1,X2)
| relation_dom(sk1_esk66_2(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2164_0,axiom,
( relation_rng(sk1_esk66_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_1,axiom,
( ~ equipotent(X1,X2)
| relation_rng(sk1_esk66_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2165_0,axiom,
( relation(sk1_esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_1,axiom,
( ~ equipotent(X1,X2)
| relation(sk1_esk66_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2166_0,axiom,
( function(sk1_esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_1,axiom,
( ~ equipotent(X1,X2)
| function(sk1_esk66_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2167_0,axiom,
( one_to_one(sk1_esk66_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_1,axiom,
( ~ equipotent(X1,X2)
| one_to_one(sk1_esk66_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2168_0,axiom,
( X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3)
| sk1_esk37_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_1,axiom,
( X1 != ordered_pair(X2,X3)
| X4 = pair_second(X1)
| sk1_esk37_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_2,axiom,
( sk1_esk37_2(X1,X4) != X4
| X1 != ordered_pair(X2,X3)
| X4 = pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2169_0,axiom,
( X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3)
| sk1_esk21_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_1,axiom,
( X1 != ordered_pair(X2,X3)
| X4 = pair_first(X1)
| sk1_esk21_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_2,axiom,
( sk1_esk21_2(X1,X4) != X4
| X1 != ordered_pair(X2,X3)
| X4 = pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2170_0,axiom,
( equipotent(X1,X2)
| relation_rng(X3) != X2
| relation_dom(X3) != X1
| ~ one_to_one(X3)
| ~ function(X3)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_1,axiom,
( relation_rng(X3) != X2
| equipotent(X1,X2)
| relation_dom(X3) != X1
| ~ one_to_one(X3)
| ~ function(X3)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_2,axiom,
( relation_dom(X3) != X1
| relation_rng(X3) != X2
| equipotent(X1,X2)
| ~ one_to_one(X3)
| ~ function(X3)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_3,axiom,
( ~ one_to_one(X3)
| relation_dom(X3) != X1
| relation_rng(X3) != X2
| equipotent(X1,X2)
| ~ function(X3)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_4,axiom,
( ~ function(X3)
| ~ one_to_one(X3)
| relation_dom(X3) != X1
| relation_rng(X3) != X2
| equipotent(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_5,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ one_to_one(X3)
| relation_dom(X3) != X1
| relation_rng(X3) != X2
| equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2172_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2173_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2174_0,axiom,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_1,axiom,
( ~ ordinal(X1)
| subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_2,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| subset(X2,X1)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_3,axiom,
( ~ ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2175_0,axiom,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_1,axiom,
( ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_2,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_3,axiom,
( ~ subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2176_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2177_0,axiom,
( ordinal(sk1_esk166_0)
| sk1_esk169_2(X2,X1) = X1
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( sk1_esk169_2(X2,X1) = X1
| ordinal(sk1_esk166_0)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk169_2(X2,X1) = X1
| ordinal(sk1_esk166_0) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2178_0,axiom,
( ordinal(sk1_esk167_0)
| sk1_esk169_2(X2,X1) = X1
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_1,axiom,
( sk1_esk169_2(X2,X1) = X1
| ordinal(sk1_esk167_0)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk169_2(X2,X1) = X1
| ordinal(sk1_esk167_0) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2179_0,axiom,
( sk1_esk169_2(X2,X1) = X1
| sk1_esk167_0 != sk1_esk166_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_1,axiom,
( sk1_esk167_0 != sk1_esk166_0
| sk1_esk169_2(X2,X1) = X1
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk167_0 != sk1_esk166_0
| sk1_esk169_2(X2,X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
( sk1_esk165_0 = sk1_esk166_0
| sk1_esk169_2(X2,X1) = X1
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_1,axiom,
( sk1_esk169_2(X2,X1) = X1
| sk1_esk165_0 = sk1_esk166_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk169_2(X2,X1) = X1
| sk1_esk165_0 = sk1_esk166_0 ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2181_0,axiom,
( sk1_esk165_0 = sk1_esk167_0
| sk1_esk169_2(X2,X1) = X1
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_1,axiom,
( sk1_esk169_2(X2,X1) = X1
| sk1_esk165_0 = sk1_esk167_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2181_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk169_2(X2,X1) = X1
| sk1_esk165_0 = sk1_esk167_0 ),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2184_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2186_0,axiom,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_1,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2187_0,axiom,
( epsilon_connected(X1)
| ~ in(sk1_esk50_1(X1),sk1_esk51_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_1,axiom,
( ~ in(sk1_esk50_1(X1),sk1_esk51_1(X1))
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
( epsilon_connected(X1)
| ~ in(sk1_esk51_1(X1),sk1_esk50_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( ~ in(sk1_esk51_1(X1),sk1_esk50_1(X1))
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( one_to_one(X1)
| in(sk1_esk80_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( in(sk1_esk80_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_2,axiom,
( ~ function(X1)
| in(sk1_esk80_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk80_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
( one_to_one(X1)
| in(sk1_esk81_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_1,axiom,
( in(sk1_esk81_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_2,axiom,
( ~ function(X1)
| in(sk1_esk81_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2190_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk81_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2191_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2192_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2194_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2195_0,axiom,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_0,axiom,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_1,axiom,
( ~ function(X1)
| relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_rng_restriction(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2198_0,axiom,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_1,axiom,
( ~ function(X1)
| function(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_rng_restriction(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_1,axiom,
( ~ function(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_1,axiom,
( ~ function(X1)
| function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2201_0,axiom,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2201_1,axiom,
( ~ relation(X2)
| relation(set_difference(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2201_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_difference(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2202_0,axiom,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_1,axiom,
( ~ relation(X2)
| relation(set_union2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2203_0,axiom,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_1,axiom,
( ~ relation(X2)
| relation(set_intersection2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2204_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_0,axiom,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_1,axiom,
( ~ relation(X2)
| relation(relation_composition(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2209_0,axiom,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| sk1_esk56_2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| sk1_esk56_2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_2,axiom,
( sk1_esk56_2(X1,X2) != empty_set
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_0,axiom,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_1,axiom,
( ~ in(X1,X2)
| subset(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_2,axiom,
( ~ epsilon_transitive(X2)
| ~ in(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_0,axiom,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_2,axiom,
( ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_2,axiom,
( ~ is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_0,axiom,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_1,axiom,
( ~ relation(X1)
| connected(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_2,axiom,
( ~ is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2219_0,axiom,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_1,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_2,axiom,
( ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
( finite(X1)
| ~ element(X1,powerset(X2))
| ~ finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_1,axiom,
( ~ element(X1,powerset(X2))
| finite(X1)
| ~ finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_2,axiom,
( ~ finite(X2)
| ~ element(X1,powerset(X2))
| finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_1,axiom,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_1,axiom,
( ordinal_subset(X2,X1)
| ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_2,axiom,
( ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ordinal_subset(X1,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_3,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ordinal_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_2,axiom,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
( ordinal(sk1_esk166_0)
| ordinal(X1)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( ordinal(X1)
| ordinal(sk1_esk166_0)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| ordinal(X1)
| ordinal(sk1_esk166_0) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( ordinal(sk1_esk167_0)
| ordinal(X1)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( ordinal(X1)
| ordinal(sk1_esk167_0)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| ordinal(X1)
| ordinal(sk1_esk167_0) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
( well_founded_relation(X1)
| subset(sk1_esk43_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_1,axiom,
( subset(sk1_esk43_1(X1),relation_field(X1))
| well_founded_relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_2,axiom,
( ~ relation(X1)
| subset(sk1_esk43_1(X1),relation_field(X1))
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
( ordinal(X1)
| sk1_esk167_0 != sk1_esk166_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( sk1_esk167_0 != sk1_esk166_0
| ordinal(X1)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| sk1_esk167_0 != sk1_esk166_0
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2233_0,axiom,
( sk1_esk165_0 = sk1_esk166_0
| ordinal(X1)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( ordinal(X1)
| sk1_esk165_0 = sk1_esk166_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| ordinal(X1)
| sk1_esk165_0 = sk1_esk166_0 ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_0,axiom,
( sk1_esk165_0 = sk1_esk167_0
| ordinal(X1)
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( ordinal(X1)
| sk1_esk165_0 = sk1_esk167_0
| ~ in(X1,sk1_esk168_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_2,axiom,
( ~ in(X1,sk1_esk168_1(X2))
| ordinal(X1)
| sk1_esk165_0 = sk1_esk167_0 ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( ~ finite(X1)
| finite(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( finite(set_intersection2(X1,X2))
| ~ finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( ~ finite(X2)
| finite(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_0,axiom,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_1,axiom,
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2240_0,axiom,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_1,axiom,
( ~ relation(X1)
| set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2241_0,axiom,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_1,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2242_0,axiom,
( equipotent(X1,X2)
| ~ equipotent(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_1,axiom,
( ~ equipotent(X2,X1)
| equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2243_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_0,axiom,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( ~ equipotent(X1,X2)
| are_equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2245_0,axiom,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_1,axiom,
( ~ are_equipotent(X1,X2)
| equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2246_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_0,axiom,
( epsilon_transitive(X1)
| ~ subset(sk1_esk38_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( ~ subset(sk1_esk38_1(X1),X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_2,axiom,
( ~ reflexive(X1)
| ~ relation(X1)
| is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,relation_field(X1))
| ~ transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_2,axiom,
( ~ transitive(X1)
| ~ relation(X1)
| is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2252_0,axiom,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,relation_field(X1))
| ~ connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_2,axiom,
( ~ connected(X1)
| ~ relation(X1)
| is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,relation_field(X1))
| ~ antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_2,axiom,
( ~ antisymmetric(X1)
| ~ relation(X1)
| is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2254_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( epsilon_transitive(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_2,axiom,
( ~ element(X2,X1)
| ~ ordinal(X1)
| epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( epsilon_connected(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_2,axiom,
( ~ element(X2,X1)
| ~ ordinal(X1)
| epsilon_connected(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( ordinal(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( ~ ordinal(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_2,axiom,
( ~ element(X2,X1)
| ~ ordinal(X1)
| ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_0,axiom,
( relation(X1)
| sk1_esk25_1(X1) != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_1,axiom,
( sk1_esk25_1(X1) != ordered_pair(X2,X3)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_1,axiom,
( ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_0,axiom,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_1,axiom,
( ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2262_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk81_1(X1) != sk1_esk80_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ relation(X1)
| sk1_esk81_1(X1) != sk1_esk80_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| one_to_one(X1)
| sk1_esk81_1(X1) != sk1_esk80_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_3,axiom,
( sk1_esk81_1(X1) != sk1_esk80_1(X1)
| ~ relation(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
( empty(X1)
| element(sk1_esk109_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( element(sk1_esk109_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( empty(X1)
| element(sk1_esk100_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( element(sk1_esk100_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2269_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( ~ ordinal(X2)
| ordinal_subset(X1,X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_2,axiom,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( ~ empty(relation_rng(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_2,axiom,
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_0,axiom,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( ~ empty(relation_dom(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_2,axiom,
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2281_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2282_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2283_0,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2285_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2286_0,axiom,
( epsilon_connected(X1)
| in(sk1_esk50_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( in(sk1_esk50_1(X1),X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2287_0,axiom,
( epsilon_connected(X1)
| in(sk1_esk51_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_1,axiom,
( in(sk1_esk51_1(X1),X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2288_0,axiom,
( epsilon_transitive(X1)
| in(sk1_esk38_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( in(sk1_esk38_1(X1),X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2290_0,axiom,
( relation(X1)
| in(sk1_esk25_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_1,axiom,
( in(sk1_esk25_1(X1),X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2291_0,axiom,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_1,axiom,
( ~ function(X1)
| relation(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2292_0,axiom,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_1,axiom,
( ~ function(X1)
| function(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2294_0,axiom,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_1,axiom,
( ~ empty(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2296_0,axiom,
( X1 = empty_set
| in(sk1_esk34_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( in(sk1_esk34_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( empty(X1)
| ~ empty(sk1_esk109_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( ~ empty(sk1_esk109_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( empty(X1)
| ~ empty(sk1_esk100_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( ~ empty(sk1_esk100_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( ~ relation(X1)
| relation_field(X1) = X2
| X1 != inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_2,axiom,
( X1 != inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2302_0,axiom,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2305_0,axiom,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_1,axiom,
( ~ relation(X1)
| connected(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2306_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2307_1,axiom,
( ~ epsilon_connected(X1)
| ordinal(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2307_2,axiom,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2308_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| sk1_esk43_1(X1) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2308_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| sk1_esk43_1(X1) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2308_2,axiom,
( sk1_esk43_1(X1) != empty_set
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2309_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_1,axiom,
( ~ epsilon_connected(X1)
| ordinal(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_2,axiom,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2310_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2312_0,axiom,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_1,axiom,
( ~ ordinal(X1)
| ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2312_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2313_0,axiom,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_1,axiom,
( ~ ordinal(X1)
| natural(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| natural(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_1,axiom,
( ~ relation(X1)
| relation_inverse(relation_inverse(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2315_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2316_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2317_0,axiom,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2317_1,axiom,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2318_0,axiom,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_1,axiom,
( ~ empty(X1)
| relation(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_1,axiom,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2320_0,axiom,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_1,axiom,
( ~ empty(X1)
| relation(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2321_0,axiom,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2322_0,axiom,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2323_0,axiom,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_1,axiom,
( ~ ordinal(X1)
| ordinal(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2324_0,axiom,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2325_0,axiom,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2326_0,axiom,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_1,axiom,
( ~ ordinal(X1)
| ordinal(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2327_0,axiom,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( ~ empty(X1)
| empty(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2328_0,axiom,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_1,axiom,
( ~ empty(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2329_0,axiom,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_1,axiom,
( ~ relation(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2330_0,axiom,
( epsilon_connected(X1)
| sk1_esk50_1(X1) != sk1_esk51_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( sk1_esk50_1(X1) != sk1_esk51_1(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_0,axiom,
( function(X1)
| sk1_esk20_1(X1) != sk1_esk19_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( sk1_esk20_1(X1) != sk1_esk19_1(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2335_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2336_0,axiom,
( empty(X1)
| finite(sk1_esk109_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( finite(sk1_esk109_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2345_0,axiom,
( being_limit_ordinal(X1)
| union(X1) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_1,axiom,
( union(X1) != X1
| being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2346_0,axiom,
( union(X1) = X1
| ~ being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_1,axiom,
( ~ being_limit_ordinal(X1)
| union(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2347_0,axiom,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_1,axiom,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_2,axiom,
( X2 != set_meet(X1)
| X1 != empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2348_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2349_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2350_0,axiom,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_1,axiom,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_1,axiom,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2352_0,axiom,
( ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( ~ empty(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( relation(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2354_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2355_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2356_0,axiom,
( function(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_1,axiom,
( ~ empty(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2357_0,axiom,
( finite(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_1,axiom,
( ~ empty(X1)
| finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2372_0,axiom,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_1,axiom,
( X1 != empty_set
| X2 = set_meet(X1)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_2,axiom,
( X2 != empty_set
| X1 != empty_set
| X2 = set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2373_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2182_0,axiom,
~ empty(unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2183_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2295_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2332_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2333_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2334_0,axiom,
~ empty(succ(X1)),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2375_0,axiom,
~ empty(sk1_esk111_0),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2376_0,axiom,
~ empty(sk1_esk108_0),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2377_0,axiom,
~ empty(sk1_esk106_0),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2378_0,axiom,
~ empty(sk1_esk94_0),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2379_0,axiom,
~ empty(sk1_esk93_0),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2095_0,axiom,
relation_of2(sk1_esk105_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2096_0,axiom,
relation_of2(sk1_esk96_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2097_0,axiom,
quasi_total(sk1_esk96_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2098_0,axiom,
relation_of2_as_subset(sk1_esk92_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2099_0,axiom,
relation_of2(sk1_esk90_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2148_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2265_0,axiom,
relation(sk1_esk105_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2266_0,axiom,
function(sk1_esk105_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
relation(sk1_esk96_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2268_0,axiom,
function(sk1_esk96_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2275_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2277_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2278_0,axiom,
element(sk1_esk107_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
element(sk1_esk102_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
element(cast_to_subset(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2293_0,axiom,
set_union2(X1,singleton(X1)) = succ(X1),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2300_0,axiom,
in(X1,sk1_esk180_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2301_0,axiom,
element(sk1_esk91_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2337_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2338_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
equipotent(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2341_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2342_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2344_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2358_0,axiom,
empty(sk1_esk107_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2359_0,axiom,
empty(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2360_0,axiom,
relation(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2361_0,axiom,
function(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
one_to_one(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2363_0,axiom,
epsilon_transitive(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2364_0,axiom,
epsilon_connected(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2365_0,axiom,
ordinal(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2366_0,axiom,
natural(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2367_0,axiom,
finite(sk1_esk102_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2369_0,axiom,
function(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2370_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2371_0,axiom,
relation(inclusion_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2374_0,axiom,
cast_to_subset(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2380_0,axiom,
relation(sk1_esk113_0),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2381_0,axiom,
relation_empty_yielding(sk1_esk113_0),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2382_0,axiom,
function(sk1_esk113_0),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2383_0,axiom,
relation(sk1_esk112_0),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2384_0,axiom,
relation_empty_yielding(sk1_esk112_0),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2385_0,axiom,
epsilon_transitive(sk1_esk111_0),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2386_0,axiom,
epsilon_connected(sk1_esk111_0),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2387_0,axiom,
ordinal(sk1_esk111_0),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2388_0,axiom,
relation(sk1_esk110_0),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2389_0,axiom,
function(sk1_esk110_0),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2390_0,axiom,
one_to_one(sk1_esk110_0),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2391_0,axiom,
relation(sk1_esk106_0),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2392_0,axiom,
relation(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2393_0,axiom,
function(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2394_0,axiom,
one_to_one(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2395_0,axiom,
empty(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2396_0,axiom,
epsilon_transitive(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2397_0,axiom,
epsilon_connected(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2398_0,axiom,
ordinal(sk1_esk104_0),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2399_0,axiom,
relation(sk1_esk103_0),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2400_0,axiom,
empty(sk1_esk103_0),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2401_0,axiom,
function(sk1_esk103_0),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2402_0,axiom,
empty(sk1_esk101_0),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2403_0,axiom,
empty(sk1_esk99_0),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2404_0,axiom,
relation(sk1_esk99_0),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2405_0,axiom,
relation(sk1_esk98_0),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2406_0,axiom,
function(sk1_esk98_0),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2407_0,axiom,
one_to_one(sk1_esk98_0),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2408_0,axiom,
empty(sk1_esk98_0),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2409_0,axiom,
epsilon_transitive(sk1_esk97_0),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2410_0,axiom,
epsilon_connected(sk1_esk97_0),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2411_0,axiom,
ordinal(sk1_esk97_0),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2412_0,axiom,
relation(sk1_esk95_0),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2413_0,axiom,
function(sk1_esk95_0),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2414_0,axiom,
finite(sk1_esk94_0),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2415_0,axiom,
epsilon_transitive(sk1_esk93_0),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2416_0,axiom,
epsilon_connected(sk1_esk93_0),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2417_0,axiom,
ordinal(sk1_esk93_0),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2418_0,axiom,
natural(sk1_esk93_0),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2419_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2420_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2421_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2422_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2423_0,axiom,
function(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2424_0,axiom,
one_to_one(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2425_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2426_0,axiom,
epsilon_transitive(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2427_0,axiom,
epsilon_connected(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2428_0,axiom,
ordinal(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2429_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2430_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2431_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2432_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2433_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2434_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2435_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2436_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2437_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2438_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2439_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2440_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2441_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2442_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2446_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2448_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2449_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2450_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2451_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2452_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2453_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2454_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2455_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2456_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,lemma,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(X1,X3))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X5
& in(X6,X1)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X7,X9),X2) ) ) ) ) ) ),
file('<stdin>',s1_xboole_0__e10_24__wellord2__1) ).
fof(c_0_1_002,lemma,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& in(X3,X1)
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
=> ? [X3] :
( relation(X3)
& function(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X1)
& in(X4,X1)
& ? [X10] :
( X4 = X10
& in(X5,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X5,X11),X2) ) ) ) ) ) ) ),
file('<stdin>',s1_funct_1__e10_24__wellord2__1) ).
fof(c_0_2_003,lemma,
! [X1,X2,X3] :
( ( relation(X2)
& relation(X3)
& function(X3) )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(X1,X1))
& ? [X6,X7] :
( X5 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ),
file('<stdin>',s1_xboole_0__e6_21__wellord2__1) ).
fof(c_0_3_004,lemma,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
& ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
~ ? [X10] :
( X3 = X10
& in(X4,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X4,X11),X2) ) ) ) )
=> ? [X3] :
( relation(X3)
& function(X3)
& relation_dom(X3) = X1
& ! [X4] :
( in(X4,X1)
=> ? [X12] :
( X4 = X12
& in(apply(X3,X4),X12)
& ! [X13] :
( in(X13,X12)
=> in(ordered_pair(apply(X3,X4),X13),X2) ) ) ) ) ) ),
file('<stdin>',s2_funct_1__e10_24__wellord2) ).
fof(c_0_4_005,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X5,X4),X3) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
file('<stdin>',t23_relset_1) ).
fof(c_0_5_006,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
file('<stdin>',t22_relset_1) ).
fof(c_0_6_007,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_7_008,lemma,
! [X1,X2,X3] :
( ( relation(X2)
& relation(X3)
& function(X3) )
=> ? [X4] :
( relation(X4)
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( in(X5,X1)
& in(X6,X1)
& in(ordered_pair(apply(X3,X5),apply(X3,X6)),X2) ) ) ) ),
file('<stdin>',s1_relat_1__e6_21__wellord2) ).
fof(c_0_8_009,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_9_010,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_10_011,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_11_012,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( X2 != empty_set
=> ! [X5] :
( in(X5,relation_inverse_image(X4,X3))
<=> ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
file('<stdin>',t46_funct_2) ).
fof(c_0_12_013,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
file('<stdin>',t21_funct_2) ).
fof(c_0_13_014,lemma,
! [X1,X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& X6 = singleton(X5) ) ) ),
file('<stdin>',s1_xboole_0__e16_22__wellord2__1) ).
fof(c_0_14_015,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
file('<stdin>',t9_funct_2) ).
fof(c_0_15_016,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
file('<stdin>',t6_funct_2) ).
fof(c_0_16_017,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_17_018,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_18_019,lemma,
! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,succ(X2))
& ? [X5] :
( ordinal(X5)
& X4 = X5
& in(X5,X1) ) ) ) ),
file('<stdin>',s1_xboole_0__e8_6__wellord2__1) ).
fof(c_0_19_020,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_20_021,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_21_022,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_22_023,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_23_024,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> relation_isomorphism(X2,X1,function_inverse(X3)) ) ) ) ),
file('<stdin>',t49_wellord1) ).
fof(c_0_24_025,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('<stdin>',t14_relset_1) ).
fof(c_0_25_026,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_26_027,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(X1,X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('<stdin>',t16_relset_1) ).
fof(c_0_27_028,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_28_029,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_29_030,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_30_031,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_31_032,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_32_033,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
file('<stdin>',t19_wellord1) ).
fof(c_0_33_034,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_34_035,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_35_036,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_36_037,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_37_038,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> ( ( reflexive(X1)
=> reflexive(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( connected(X1)
=> connected(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( well_founded_relation(X1)
=> well_founded_relation(X2) ) ) ) ) ) ),
file('<stdin>',t53_wellord1) ).
fof(c_0_38_039,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( well_ordering(X1)
& relation_isomorphism(X1,X2,X3) )
=> well_ordering(X2) ) ) ) ),
file('<stdin>',t54_wellord1) ).
fof(c_0_39_040,lemma,
! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
file('<stdin>',t21_wellord1) ).
fof(c_0_40_041,lemma,
! [X1] :
( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& in(X2,X1)
& X4 = singleton(X2) )
=> X3 = X4 )
=> ? [X2] :
( relation(X2)
& function(X2)
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(X3,X1)
& X4 = singleton(X3) ) ) ) ),
file('<stdin>',s1_funct_1__e16_22__wellord2__1) ).
fof(c_0_41_042,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_42_043,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_43_044,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_44_045,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_45_046,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_46_047,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_47_048,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_48_049,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_49_050,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_50_051,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('<stdin>',t12_relset_1) ).
fof(c_0_51_052,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_52_053,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_53_054,lemma,
! [X1] :
( ~ empty(X1)
=> ~ ( ! [X2] :
~ ( in(X2,X1)
& X2 = empty_set )
& ! [X2] :
( ( relation(X2)
& function(X2) )
=> ~ ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> in(apply(X2,X3),X3) ) ) ) ) ),
file('<stdin>',t28_wellord2) ).
fof(c_0_54_055,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_55_056,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_56_057,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_57_058,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_58_059,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_59_060,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_60_061,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_61_062,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_62_063,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_63_064,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_64_065,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_65_066,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_66_067,lemma,
! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
file('<stdin>',s2_funct_1__e16_22__wellord2__1) ).
fof(c_0_67_068,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_68_069,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_69_070,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( well_ordering(X2)
& equipotent(X1,relation_field(X2))
& ! [X3] :
( relation(X3)
=> ~ well_orders(X3,X1) ) ) ),
file('<stdin>',l30_wellord2) ).
fof(c_0_70_071,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_71_072,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_72_073,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_73_074,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_74_075,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('<stdin>',t99_relat_1) ).
fof(c_0_75_076,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
& subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
file('<stdin>',t20_wellord1) ).
fof(c_0_76_077,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('<stdin>',t118_relat_1) ).
fof(c_0_77_078,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
file('<stdin>',l29_wellord1) ).
fof(c_0_78_079,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('<stdin>',l71_subset_1) ).
fof(c_0_79_080,lemma,
! [X1] :
( ? [X2] :
( ordinal(X2)
& in(X2,X1) )
=> ? [X2] :
( ordinal(X2)
& in(X2,X1)
& ! [X3] :
( ordinal(X3)
=> ( in(X3,X1)
=> ordinal_subset(X2,X3) ) ) ) ),
file('<stdin>',s1_ordinal1__e8_6__wellord2) ).
fof(c_0_80_081,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('<stdin>',t116_relat_1) ).
fof(c_0_81_082,lemma,
! [X1,X2] :
( relation(X2)
=> ( ( well_ordering(X2)
& subset(X1,relation_field(X2)) )
=> relation_field(relation_restriction(X2,X1)) = X1 ) ),
file('<stdin>',t39_wellord1) ).
fof(c_0_82_083,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_83_084,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_84_085,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('<stdin>',t56_relat_1) ).
fof(c_0_85_086,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_86_087,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('<stdin>',t21_relat_1) ).
fof(c_0_87_088,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_88_089,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_89_090,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
file('<stdin>',t3_ordinal1) ).
fof(c_0_90_091,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_91_092,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_92_093,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_93_094,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_94_095,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_95_096,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_96_097,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_97_098,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('<stdin>',t33_ordinal1) ).
fof(c_0_98_099,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_orders(X2,X1)
=> ( relation_field(relation_restriction(X2,X1)) = X1
& well_ordering(relation_restriction(X2,X1)) ) ) ),
file('<stdin>',t25_wellord2) ).
fof(c_0_99_100,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_100_101,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_101_102,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_102_103,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_103_104,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_104_105,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_105_106,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_106_107,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_107_108,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_108_109,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('<stdin>',t31_ordinal1) ).
fof(c_0_109_110,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('<stdin>',t167_relat_1) ).
fof(c_0_110_111,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('<stdin>',t144_relat_1) ).
fof(c_0_111_112,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('<stdin>',t21_ordinal1) ).
fof(c_0_112_113,lemma,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
file('<stdin>',s1_xboole_0__e6_22__wellord2) ).
fof(c_0_113_114,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_114_115,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('<stdin>',t88_relat_1) ).
fof(c_0_115_116,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('<stdin>',t117_relat_1) ).
fof(c_0_116_117,lemma,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
file('<stdin>',s3_funct_1__e16_22__wellord2) ).
fof(c_0_117_118,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_118_119,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_119_120,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_120_121,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('<stdin>',t24_ordinal1) ).
fof(c_0_121_122,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_122_123,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
file('<stdin>',t32_wellord1) ).
fof(c_0_123_124,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
file('<stdin>',t31_wellord1) ).
fof(c_0_124_125,lemma,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('<stdin>',t25_wellord1) ).
fof(c_0_125_126,lemma,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
file('<stdin>',t24_wellord1) ).
fof(c_0_126_127,lemma,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
file('<stdin>',t23_wellord1) ).
fof(c_0_127_128,lemma,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
file('<stdin>',t22_wellord1) ).
fof(c_0_128_129,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_129_130,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('<stdin>',t8_wellord1) ).
fof(c_0_130_131,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('<stdin>',t5_wellord1) ).
fof(c_0_131_132,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_132_133,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('<stdin>',t35_funct_1) ).
fof(c_0_133_134,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_134_135,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_135_136,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_136_137,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('<stdin>',t94_relat_1) ).
fof(c_0_137_138,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_138_139,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_139_140,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_140_141,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_141_142,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_142_143,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_143_144,conjecture,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('<stdin>',t15_finset_1) ).
fof(c_0_144_145,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_145_146,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_146_147,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_147_148,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_148_149,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_149_150,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_150_151,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('<stdin>',t23_ordinal1) ).
fof(c_0_151_152,lemma,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('<stdin>',t13_finset_1) ).
fof(c_0_152_153,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('<stdin>',t62_funct_1) ).
fof(c_0_153_154,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('<stdin>',t146_relat_1) ).
fof(c_0_154_155,lemma,
! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
file('<stdin>',t7_mcart_1) ).
fof(c_0_155_156,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_156_157,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_157_158,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_158_159,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_159_160,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_160_161,lemma,
! [X1] :
? [X2] :
( relation(X2)
& well_orders(X2,X1) ),
file('<stdin>',t26_wellord2) ).
fof(c_0_161_162,lemma,
! [X1] : in(X1,succ(X1)),
file('<stdin>',t10_ordinal1) ).
fof(c_0_162_163,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('<stdin>',t65_relat_1) ).
fof(c_0_163_164,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_164_165,lemma,
! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
file('<stdin>',t7_wellord2) ).
fof(c_0_165_166,lemma,
! [X1] :
( ordinal(X1)
=> well_founded_relation(inclusion_relation(X1)) ),
file('<stdin>',t6_wellord2) ).
fof(c_0_166_167,lemma,
! [X1] :
( ordinal(X1)
=> connected(inclusion_relation(X1)) ),
file('<stdin>',t4_wellord2) ).
fof(c_0_167_168,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_168_169,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_169_170,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_170_171,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('<stdin>',t71_relat_1) ).
fof(c_0_171_172,lemma,
! [X1] : antisymmetric(inclusion_relation(X1)),
file('<stdin>',t5_wellord2) ).
fof(c_0_172_173,lemma,
! [X1] : transitive(inclusion_relation(X1)),
file('<stdin>',t3_wellord2) ).
fof(c_0_173_174,lemma,
! [X1] : reflexive(inclusion_relation(X1)),
file('<stdin>',t2_wellord2) ).
fof(c_0_174_175,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_175_176,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_176_177,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('<stdin>',t60_relat_1) ).
fof(c_0_177_178,plain,
! [X1,X2] :
( epred1_2(X2,X1)
<=> ( ( reflexive(X1)
=> reflexive(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( connected(X1)
=> connected(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( well_founded_relation(X1)
=> well_founded_relation(X2) ) ) ),
introduced(definition) ).
fof(c_0_178_179,lemma,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(X1,X3))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X5
& in(X6,X1)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X7,X9),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_179_180,lemma,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& in(X3,X1)
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
=> ? [X3] :
( relation(X3)
& function(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X1)
& in(X4,X1)
& ? [X10] :
( X4 = X10
& in(X5,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X5,X11),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_180_181,lemma,
! [X1,X2,X3] :
( ( relation(X2)
& relation(X3)
& function(X3) )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(X1,X1))
& ? [X6,X7] :
( X5 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ),
c_0_2 ).
fof(c_0_181_182,lemma,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
& ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
~ ? [X10] :
( X3 = X10
& in(X4,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X4,X11),X2) ) ) ) )
=> ? [X3] :
( relation(X3)
& function(X3)
& relation_dom(X3) = X1
& ! [X4] :
( in(X4,X1)
=> ? [X12] :
( X4 = X12
& in(apply(X3,X4),X12)
& ! [X13] :
( in(X13,X12)
=> in(ordered_pair(apply(X3,X4),X13),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_182_183,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X5,X4),X3) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_183_184,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_184_185,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_6 ).
fof(c_0_185_186,lemma,
! [X1,X2,X3] :
( ( relation(X2)
& relation(X3)
& function(X3) )
=> ? [X4] :
( relation(X4)
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( in(X5,X1)
& in(X6,X1)
& in(ordered_pair(apply(X3,X5),apply(X3,X6)),X2) ) ) ) ),
c_0_7 ).
fof(c_0_186_187,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_8 ).
fof(c_0_187_188,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_9 ).
fof(c_0_188_189,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_10 ).
fof(c_0_189_190,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( X2 != empty_set
=> ! [X5] :
( in(X5,relation_inverse_image(X4,X3))
<=> ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
c_0_11 ).
fof(c_0_190_191,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
c_0_12 ).
fof(c_0_191_192,lemma,
! [X1,X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& X6 = singleton(X5) ) ) ),
c_0_13 ).
fof(c_0_192_193,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
c_0_14 ).
fof(c_0_193_194,lemma,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
c_0_15 ).
fof(c_0_194_195,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_16 ).
fof(c_0_195_196,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_17 ).
fof(c_0_196_197,lemma,
! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,succ(X2))
& ? [X5] :
( ordinal(X5)
& X4 = X5
& in(X5,X1) ) ) ) ),
c_0_18 ).
fof(c_0_197_198,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_19 ).
fof(c_0_198_199,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_20 ).
fof(c_0_199_200,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_21 ).
fof(c_0_200_201,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_22 ).
fof(c_0_201_202,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> relation_isomorphism(X2,X1,function_inverse(X3)) ) ) ) ),
c_0_23 ).
fof(c_0_202_203,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
c_0_24 ).
fof(c_0_203_204,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_25 ).
fof(c_0_204_205,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(X1,X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
c_0_26 ).
fof(c_0_205_206,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_27]) ).
fof(c_0_206_207,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_28 ).
fof(c_0_207_208,lemma,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
c_0_29 ).
fof(c_0_208_209,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
c_0_30 ).
fof(c_0_209_210,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_31 ).
fof(c_0_210_211,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
c_0_32 ).
fof(c_0_211_212,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_33 ).
fof(c_0_212_213,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_34 ).
fof(c_0_213_214,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
c_0_35 ).
fof(c_0_214_215,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
c_0_36 ).
fof(c_0_215_216,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> epred1_2(X2,X1) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_177,theory(equality,[symmetry])]) ).
fof(c_0_216_217,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( well_ordering(X1)
& relation_isomorphism(X1,X2,X3) )
=> well_ordering(X2) ) ) ) ),
c_0_38 ).
fof(c_0_217_218,lemma,
! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
c_0_39 ).
fof(c_0_218_219,lemma,
! [X1] :
( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& in(X2,X1)
& X4 = singleton(X2) )
=> X3 = X4 )
=> ? [X2] :
( relation(X2)
& function(X2)
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(X3,X1)
& X4 = singleton(X3) ) ) ) ),
c_0_40 ).
fof(c_0_219_220,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_41 ).
fof(c_0_220_221,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_42 ).
fof(c_0_221_222,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
c_0_43 ).
fof(c_0_222_223,lemma,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
c_0_44 ).
fof(c_0_223_224,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_45 ).
fof(c_0_224_225,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_46 ).
fof(c_0_225_226,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_47]) ).
fof(c_0_226_227,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_48 ).
fof(c_0_227_228,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_49 ).
fof(c_0_228_229,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
c_0_50 ).
fof(c_0_229_230,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
c_0_51 ).
fof(c_0_230_231,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_52 ).
fof(c_0_231_232,lemma,
! [X1] :
( ~ empty(X1)
=> ~ ( ! [X2] :
~ ( in(X2,X1)
& X2 = empty_set )
& ! [X2] :
( ( relation(X2)
& function(X2) )
=> ~ ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> in(apply(X2,X3),X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_232_233,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
c_0_54 ).
fof(c_0_233_234,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
c_0_55 ).
fof(c_0_234_235,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
c_0_56 ).
fof(c_0_235_236,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
c_0_57 ).
fof(c_0_236_237,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
c_0_58 ).
fof(c_0_237_238,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
c_0_59 ).
fof(c_0_238_239,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_60 ).
fof(c_0_239_240,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_61 ).
fof(c_0_240_241,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_62 ).
fof(c_0_241_242,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_63 ).
fof(c_0_242_243,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_64 ).
fof(c_0_243_244,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_65 ).
fof(c_0_244_245,lemma,
! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
c_0_66 ).
fof(c_0_245_246,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
c_0_67 ).
fof(c_0_246_247,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_68 ).
fof(c_0_247_248,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( well_ordering(X2)
& equipotent(X1,relation_field(X2))
& ! [X3] :
( relation(X3)
=> ~ well_orders(X3,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_248_249,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_70]) ).
fof(c_0_249_250,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_71 ).
fof(c_0_250_251,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_72 ).
fof(c_0_251_252,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_73 ).
fof(c_0_252_253,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
c_0_74 ).
fof(c_0_253_254,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
& subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
c_0_75 ).
fof(c_0_254_255,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
c_0_76 ).
fof(c_0_255_256,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
c_0_77 ).
fof(c_0_256_257,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
c_0_78 ).
fof(c_0_257_258,lemma,
! [X1] :
( ? [X2] :
( ordinal(X2)
& in(X2,X1) )
=> ? [X2] :
( ordinal(X2)
& in(X2,X1)
& ! [X3] :
( ordinal(X3)
=> ( in(X3,X1)
=> ordinal_subset(X2,X3) ) ) ) ),
c_0_79 ).
fof(c_0_258_259,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
c_0_80 ).
fof(c_0_259_260,lemma,
! [X1,X2] :
( relation(X2)
=> ( ( well_ordering(X2)
& subset(X1,relation_field(X2)) )
=> relation_field(relation_restriction(X2,X1)) = X1 ) ),
c_0_81 ).
fof(c_0_260_261,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
c_0_82 ).
fof(c_0_261_262,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_83]) ).
fof(c_0_262_263,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_263_264,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
c_0_85 ).
fof(c_0_264_265,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
c_0_86 ).
fof(c_0_265_266,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_87 ).
fof(c_0_266_267,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_88]) ).
fof(c_0_267_268,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
c_0_89 ).
fof(c_0_268_269,lemma,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
c_0_90 ).
fof(c_0_269_270,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
c_0_91 ).
fof(c_0_270_271,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_92 ).
fof(c_0_271_272,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_93 ).
fof(c_0_272_273,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
c_0_94 ).
fof(c_0_273_274,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_rng_restriction(X1,relation_dom_restriction(X2,X1)) ),
c_0_95 ).
fof(c_0_274_275,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_dom_restriction(relation_rng_restriction(X1,X2),X1) ),
c_0_96 ).
fof(c_0_275_276,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
c_0_97 ).
fof(c_0_276_277,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_orders(X2,X1)
=> ( relation_field(relation_restriction(X2,X1)) = X1
& well_ordering(relation_restriction(X2,X1)) ) ) ),
c_0_98 ).
fof(c_0_277_278,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_99 ).
fof(c_0_278_279,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_100 ).
fof(c_0_279_280,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
c_0_101 ).
fof(c_0_280_281,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
c_0_102 ).
fof(c_0_281_282,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_282_283,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_104 ).
fof(c_0_283_284,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_105 ).
fof(c_0_284_285,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_106 ).
fof(c_0_285_286,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_107 ).
fof(c_0_286_287,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
c_0_108 ).
fof(c_0_287_288,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
c_0_109 ).
fof(c_0_288_289,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
c_0_110 ).
fof(c_0_289_290,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
c_0_111 ).
fof(c_0_290_291,lemma,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
c_0_112 ).
fof(c_0_291_292,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_113 ).
fof(c_0_292_293,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
c_0_114 ).
fof(c_0_293_294,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
c_0_115 ).
fof(c_0_294_295,lemma,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
c_0_116 ).
fof(c_0_295_296,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_117 ).
fof(c_0_296_297,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_118 ).
fof(c_0_297_298,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_119 ).
fof(c_0_298_299,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_299_300,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_121 ).
fof(c_0_300_301,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
c_0_122 ).
fof(c_0_301_302,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
c_0_123 ).
fof(c_0_302_303,lemma,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
c_0_124 ).
fof(c_0_303_304,lemma,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
c_0_125 ).
fof(c_0_304_305,lemma,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
c_0_126 ).
fof(c_0_305_306,lemma,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
c_0_127 ).
fof(c_0_306_307,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_128 ).
fof(c_0_307_308,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
c_0_129 ).
fof(c_0_308_309,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
c_0_130 ).
fof(c_0_309_310,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_131 ).
fof(c_0_310_311,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
c_0_132 ).
fof(c_0_311_312,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_133 ).
fof(c_0_312_313,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_134 ).
fof(c_0_313_314,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_135 ).
fof(c_0_314_315,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
c_0_136 ).
fof(c_0_315_316,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_137 ).
fof(c_0_316_317,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_138 ).
fof(c_0_317_318,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_139 ).
fof(c_0_318_319,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_140 ).
fof(c_0_319_320,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_141 ).
fof(c_0_320_321,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_142 ).
fof(c_0_321_322,negated_conjecture,
~ ! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
inference(assume_negation,[status(cth)],[c_0_143]) ).
fof(c_0_322_323,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_144 ).
fof(c_0_323_324,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_145 ).
fof(c_0_324_325,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_146 ).
fof(c_0_325_326,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_147 ).
fof(c_0_326_327,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_148 ).
fof(c_0_327_328,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_328_329,plain,
! [X1,X2] :
( epred1_2(X2,X1)
=> ( ( reflexive(X1)
=> reflexive(X2) )
& ( transitive(X1)
=> transitive(X2) )
& ( connected(X1)
=> connected(X2) )
& ( antisymmetric(X1)
=> antisymmetric(X2) )
& ( well_founded_relation(X1)
=> well_founded_relation(X2) ) ) ),
inference(split_equiv,[status(thm)],[c_0_177]) ).
fof(c_0_329_330,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
c_0_150 ).
fof(c_0_330_331,lemma,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
c_0_151 ).
fof(c_0_331_332,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
c_0_152 ).
fof(c_0_332_333,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
c_0_153 ).
fof(c_0_333_334,lemma,
! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
c_0_154 ).
fof(c_0_334_335,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_155 ).
fof(c_0_335_336,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_156 ).
fof(c_0_336_337,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_157]) ).
fof(c_0_337_338,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_158 ).
fof(c_0_338_339,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
c_0_159 ).
fof(c_0_339_340,lemma,
! [X1] :
? [X2] :
( relation(X2)
& well_orders(X2,X1) ),
c_0_160 ).
fof(c_0_340_341,lemma,
! [X1] : in(X1,succ(X1)),
c_0_161 ).
fof(c_0_341_342,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
c_0_162 ).
fof(c_0_342_343,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_163 ).
fof(c_0_343_344,lemma,
! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
c_0_164 ).
fof(c_0_344_345,lemma,
! [X1] :
( ordinal(X1)
=> well_founded_relation(inclusion_relation(X1)) ),
c_0_165 ).
fof(c_0_345_346,lemma,
! [X1] :
( ordinal(X1)
=> connected(inclusion_relation(X1)) ),
c_0_166 ).
fof(c_0_346_347,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
c_0_167 ).
fof(c_0_347_348,lemma,
! [X1] : subset(empty_set,X1),
c_0_168 ).
fof(c_0_348_349,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_169 ).
fof(c_0_349_350,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
c_0_170 ).
fof(c_0_350_351,lemma,
! [X1] : antisymmetric(inclusion_relation(X1)),
c_0_171 ).
fof(c_0_351_352,lemma,
! [X1] : transitive(inclusion_relation(X1)),
c_0_172 ).
fof(c_0_352_353,lemma,
! [X1] : reflexive(inclusion_relation(X1)),
c_0_173 ).
fof(c_0_353_354,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_174 ).
fof(c_0_354_355,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_175 ).
fof(c_0_355_356,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_176 ).
fof(c_0_356_357,lemma,
! [X10,X11,X12,X14,X18,X19,X20,X21,X22] :
( ( in(X14,cartesian_product2(X10,X12))
| ~ in(X14,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( ordered_pair(esk26_4(X10,X11,X12,X14),esk27_4(X10,X11,X12,X14)) = X14
| ~ in(X14,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( in(esk26_4(X10,X11,X12,X14),X10)
| ~ in(X14,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( esk26_4(X10,X11,X12,X14) = esk28_4(X10,X11,X12,X14)
| ~ in(X14,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( in(esk27_4(X10,X11,X12,X14),esk28_4(X10,X11,X12,X14))
| ~ in(X14,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( ~ in(X18,esk28_4(X10,X11,X12,X14))
| in(ordered_pair(esk27_4(X10,X11,X12,X14),X18),X11)
| ~ in(X14,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( in(esk29_7(X10,X11,X12,X19,X20,X21,X22),X22)
| ~ in(X21,X22)
| X20 != X22
| ~ in(X20,X10)
| ordered_pair(X20,X21) != X19
| ~ in(X19,cartesian_product2(X10,X12))
| in(X19,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( ~ in(ordered_pair(X21,esk29_7(X10,X11,X12,X19,X20,X21,X22)),X11)
| ~ in(X21,X22)
| X20 != X22
| ~ in(X20,X10)
| ordered_pair(X20,X21) != X19
| ~ in(X19,cartesian_product2(X10,X12))
| in(X19,esk25_3(X10,X11,X12))
| empty(X10)
| ~ relation(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_178])])])])])]) ).
fof(c_0_357_358,lemma,
! [X12,X13,X18,X20,X22,X23,X25,X26,X27,X28] :
( ( relation(esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk14_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk12_2(X12,X13),esk14_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| ~ in(X18,esk14_2(X12,X13))
| in(ordered_pair(esk12_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk11_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| esk11_2(X12,X13) = esk15_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| in(esk13_2(X12,X13),esk15_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| ~ in(X20,esk15_2(X12,X13))
| in(ordered_pair(esk13_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( relation(esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( function(esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,X12)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( X22 = esk17_4(X12,X13,X22,X23)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X23,esk17_4(X12,X13,X22,X23))
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk17_4(X12,X13,X22,X23))
| in(ordered_pair(X23,X25),X13)
| ~ in(ordered_pair(X22,X23),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk18_5(X12,X13,X26,X27,X28),X28)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X27,esk18_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X27,X28)
| X26 != X28
| ~ in(X26,X12)
| ~ in(X26,X12)
| in(ordered_pair(X26,X27),esk16_2(X12,X13))
| esk12_2(X12,X13) != esk13_2(X12,X13)
| empty(X12)
| ~ relation(X13) ) ),
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_358_359,lemma,
! [X8,X9,X10,X12,X15,X16,X17] :
( ( in(X12,cartesian_product2(X8,X8))
| ~ in(X12,esk33_3(X8,X9,X10))
| ~ relation(X9)
| ~ relation(X10)
| ~ function(X10) )
& ( X12 = ordered_pair(esk34_4(X8,X9,X10,X12),esk35_4(X8,X9,X10,X12))
| ~ in(X12,esk33_3(X8,X9,X10))
| ~ relation(X9)
| ~ relation(X10)
| ~ function(X10) )
& ( in(ordered_pair(apply(X10,esk34_4(X8,X9,X10,X12)),apply(X10,esk35_4(X8,X9,X10,X12))),X9)
| ~ in(X12,esk33_3(X8,X9,X10))
| ~ relation(X9)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(X15,cartesian_product2(X8,X8))
| X15 != ordered_pair(X16,X17)
| ~ in(ordered_pair(apply(X10,X16),apply(X10,X17)),X9)
| in(X15,esk33_3(X8,X9,X10))
| ~ relation(X9)
| ~ relation(X10)
| ~ function(X10) ) ),
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_359_360,lemma,
! [X14,X15,X20,X22,X24,X25,X28,X30] :
( ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk39_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk42_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk40_2(X14,X15),esk42_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X20,esk42_2(X14,X15))
| in(ordered_pair(esk40_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk39_2(X14,X15) = esk43_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| in(esk41_2(X14,X15),esk43_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| ~ in(X22,esk43_2(X14,X15))
| in(ordered_pair(esk41_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk44_2(X14,X15),X14)
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk44_2(X14,X15),X14)
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk44_2(X14,X15),X14)
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk45_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk46_2(X14,X15))
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk46_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk47_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk46_2(X14,X15),X28),esk47_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk47_3(X14,X15,X28))
| in(ordered_pair(apply(esk46_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk45_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk44_2(X14,X15) != X25
| esk40_2(X14,X15) != esk41_2(X14,X15)
| empty(X14)
| ~ relation(X15) ) ),
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_181])])])])]) ).
fof(c_0_360_361,lemma,
! [X6,X7,X8,X10,X11] :
( ( in(esk61_3(X6,X7,X8),X7)
| relation_rng_as_subset(X6,X7,X8) = X7
| ~ relation_of2_as_subset(X8,X6,X7) )
& ( ~ in(ordered_pair(X10,esk61_3(X6,X7,X8)),X8)
| relation_rng_as_subset(X6,X7,X8) = X7
| ~ relation_of2_as_subset(X8,X6,X7) )
& ( relation_rng_as_subset(X6,X7,X8) != X7
| ~ in(X11,X7)
| in(ordered_pair(esk62_4(X6,X7,X8,X11),X11),X8)
| ~ relation_of2_as_subset(X8,X6,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_182])])])])]) ).
fof(c_0_361_362,lemma,
! [X6,X7,X8,X10,X11] :
( ( in(esk59_3(X6,X7,X8),X7)
| relation_dom_as_subset(X7,X6,X8) = X7
| ~ relation_of2_as_subset(X8,X7,X6) )
& ( ~ in(ordered_pair(esk59_3(X6,X7,X8),X10),X8)
| relation_dom_as_subset(X7,X6,X8) = X7
| ~ relation_of2_as_subset(X8,X7,X6) )
& ( relation_dom_as_subset(X7,X6,X8) != X7
| ~ in(X11,X7)
| in(ordered_pair(X11,esk60_4(X6,X7,X8,X11)),X8)
| ~ relation_of2_as_subset(X8,X7,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_183])])])])]) ).
fof(c_0_362_363,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(esk79_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,esk79_3(X5,X6,X7)) != apply(X7,esk79_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_184])])])])]) ).
fof(c_0_363_364,lemma,
! [X7,X8,X9,X11,X12,X13,X14] :
( ( relation(esk24_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(X9) )
& ( in(X11,X7)
| ~ in(ordered_pair(X11,X12),esk24_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(X9) )
& ( in(X12,X7)
| ~ in(ordered_pair(X11,X12),esk24_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(X9) )
& ( in(ordered_pair(apply(X9,X11),apply(X9,X12)),X8)
| ~ in(ordered_pair(X11,X12),esk24_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X13,X7)
| ~ in(X14,X7)
| ~ in(ordered_pair(apply(X9,X13),apply(X9,X14)),X8)
| in(ordered_pair(X13,X14),esk24_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(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_185])])])])])]) ).
fof(c_0_364_365,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(esk76_2(X5,X6),relation_dom(X5))
| in(esk73_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) )
& ( esk75_2(X5,X6) = apply(X5,esk76_2(X5,X6))
| in(esk73_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(esk75_2(X5,X6),relation_rng(X5))
| esk76_2(X5,X6) != apply(X6,esk75_2(X5,X6))
| in(esk73_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(esk76_2(X5,X6),relation_dom(X5))
| esk74_2(X5,X6) = apply(X6,esk73_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) )
& ( esk75_2(X5,X6) = apply(X5,esk76_2(X5,X6))
| esk74_2(X5,X6) = apply(X6,esk73_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(esk75_2(X5,X6),relation_rng(X5))
| esk76_2(X5,X6) != apply(X6,esk75_2(X5,X6))
| esk74_2(X5,X6) = apply(X6,esk73_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(esk76_2(X5,X6),relation_dom(X5))
| ~ in(esk74_2(X5,X6),relation_dom(X5))
| esk73_2(X5,X6) != apply(X5,esk74_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) )
& ( esk75_2(X5,X6) = apply(X5,esk76_2(X5,X6))
| ~ in(esk74_2(X5,X6),relation_dom(X5))
| esk73_2(X5,X6) != apply(X5,esk74_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(esk75_2(X5,X6),relation_rng(X5))
| esk76_2(X5,X6) != apply(X6,esk75_2(X5,X6))
| ~ in(esk74_2(X5,X6),relation_dom(X5))
| esk73_2(X5,X6) != apply(X5,esk74_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_186])])])])])]) ).
fof(c_0_365_366,lemma,
! [X5,X6,X7,X9] :
( ( in(esk58_3(X5,X6,X7),relation_rng(X7))
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(X5,esk58_3(X5,X6,X7)),X7)
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(esk58_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_187])])])])]) ).
fof(c_0_366_367,lemma,
! [X5,X6,X7,X9] :
( ( in(esk55_3(X5,X6,X7),relation_dom(X7))
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(esk55_3(X5,X6,X7),X5),X7)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(esk55_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_188])])])])]) ).
fof(c_0_367_368,lemma,
! [X6,X7,X8,X9,X10,X11] :
( ( in(X10,X6)
| ~ in(X10,relation_inverse_image(X9,X8))
| X7 = empty_set
| ~ function(X9)
| ~ quasi_total(X9,X6,X7)
| ~ relation_of2_as_subset(X9,X6,X7) )
& ( in(apply(X9,X10),X8)
| ~ in(X10,relation_inverse_image(X9,X8))
| X7 = empty_set
| ~ function(X9)
| ~ quasi_total(X9,X6,X7)
| ~ relation_of2_as_subset(X9,X6,X7) )
& ( ~ in(X11,X6)
| ~ in(apply(X9,X11),X8)
| in(X11,relation_inverse_image(X9,X8))
| X7 = empty_set
| ~ function(X9)
| ~ quasi_total(X9,X6,X7)
| ~ relation_of2_as_subset(X9,X6,X7) ) ),
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_189])])])])]) ).
fof(c_0_368_369,lemma,
! [X6,X7,X8,X9,X10] :
( ~ function(X9)
| ~ quasi_total(X9,X6,X7)
| ~ relation_of2_as_subset(X9,X6,X7)
| ~ relation(X10)
| ~ function(X10)
| ~ in(X8,X6)
| X7 = empty_set
| apply(relation_composition(X9,X10),X8) = apply(X10,apply(X9,X8)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])]) ).
fof(c_0_369_370,lemma,
! [X7,X8,X10,X13,X14,X15] :
( ( in(X10,cartesian_product2(X7,X8))
| ~ in(X10,esk30_2(X7,X8)) )
& ( ordered_pair(esk31_3(X7,X8,X10),esk32_3(X7,X8,X10)) = X10
| ~ in(X10,esk30_2(X7,X8)) )
& ( in(esk31_3(X7,X8,X10),X7)
| ~ in(X10,esk30_2(X7,X8)) )
& ( esk32_3(X7,X8,X10) = singleton(esk31_3(X7,X8,X10))
| ~ in(X10,esk30_2(X7,X8)) )
& ( ~ in(X13,cartesian_product2(X7,X8))
| ordered_pair(X14,X15) != X13
| ~ in(X14,X7)
| X15 != singleton(X14)
| in(X13,esk30_2(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_191])])])])])]) ).
fof(c_0_370_371,lemma,
! [X5,X6,X7,X8] :
( ( function(X8)
| X6 = empty_set
| ~ subset(X6,X7)
| ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6) )
& ( quasi_total(X8,X5,X7)
| X6 = empty_set
| ~ subset(X6,X7)
| ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6) )
& ( relation_of2_as_subset(X8,X5,X7)
| X6 = empty_set
| ~ subset(X6,X7)
| ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6) )
& ( function(X8)
| X5 != empty_set
| ~ subset(X6,X7)
| ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6) )
& ( quasi_total(X8,X5,X7)
| X5 != empty_set
| ~ subset(X6,X7)
| ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6) )
& ( relation_of2_as_subset(X8,X5,X7)
| X5 != empty_set
| ~ subset(X6,X7)
| ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])])]) ).
fof(c_0_371_372,lemma,
! [X5,X6,X7,X8] :
( ~ function(X8)
| ~ quasi_total(X8,X5,X6)
| ~ relation_of2_as_subset(X8,X5,X6)
| ~ in(X7,X5)
| X6 = empty_set
| in(apply(X8,X7),relation_rng(X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_193])]) ).
fof(c_0_372_373,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_194])])]) ).
fof(c_0_373_374,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_195])])])]) ).
fof(c_0_374_375,lemma,
! [X6,X7,X9,X11,X12] :
( ( in(X9,succ(X7))
| ~ in(X9,esk37_2(X6,X7))
| ~ ordinal(X7) )
& ( ordinal(esk38_3(X6,X7,X9))
| ~ in(X9,esk37_2(X6,X7))
| ~ ordinal(X7) )
& ( X9 = esk38_3(X6,X7,X9)
| ~ in(X9,esk37_2(X6,X7))
| ~ ordinal(X7) )
& ( in(esk38_3(X6,X7,X9),X6)
| ~ in(X9,esk37_2(X6,X7))
| ~ ordinal(X7) )
& ( ~ in(X11,succ(X7))
| ~ ordinal(X12)
| X11 != X12
| ~ in(X12,X6)
| in(X11,esk37_2(X6,X7))
| ~ ordinal(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_196])])])])])]) ).
fof(c_0_375_376,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_197])]) ).
fof(c_0_376_377,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(esk2_1(X5),esk3_1(X5)),X5)
| transitive(X5)
| ~ relation(X5) )
& ( in(ordered_pair(esk3_1(X5),esk4_1(X5)),X5)
| transitive(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk2_1(X5),esk4_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_198])])])])]) ).
fof(c_0_377_378,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_199])]) ).
fof(c_0_378_379,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_200])]) ).
fof(c_0_379_380,lemma,
! [X4,X5,X6] :
( ~ relation(X4)
| ~ relation(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ relation_isomorphism(X4,X5,X6)
| relation_isomorphism(X5,X4,function_inverse(X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])]) ).
fof(c_0_380_381,lemma,
! [X5,X6,X7,X8] :
( ~ relation_of2_as_subset(X8,X7,X5)
| ~ subset(relation_rng(X8),X6)
| relation_of2_as_subset(X8,X7,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])]) ).
fof(c_0_381_382,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_203])])]) ).
fof(c_0_382_383,lemma,
! [X5,X6,X7,X8] :
( ~ relation_of2_as_subset(X8,X7,X5)
| ~ subset(X5,X6)
| relation_of2_as_subset(X8,X7,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])]) ).
fof(c_0_383_384,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(esk8_1(X4),relation_field(X4))
| connected(X4)
| ~ relation(X4) )
& ( in(esk9_1(X4),relation_field(X4))
| connected(X4)
| ~ relation(X4) )
& ( esk8_1(X4) != esk9_1(X4)
| connected(X4)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk8_1(X4),esk9_1(X4)),X4)
| connected(X4)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk9_1(X4),esk8_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_205])])])])])]) ).
fof(c_0_384_385,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_206])])]) ).
fof(c_0_385_386,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(esk6_1(X4),esk7_1(X4)),X4)
| antisymmetric(X4)
| ~ relation(X4) )
& ( in(ordered_pair(esk7_1(X4),esk6_1(X4)),X4)
| antisymmetric(X4)
| ~ relation(X4) )
& ( esk6_1(X4) != esk7_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_207])])])])]) ).
fof(c_0_386_387,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_208])])])]) ).
fof(c_0_387_388,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_209])])]) ).
fof(c_0_388_389,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_field(X6))
| ~ in(X4,relation_field(relation_restriction(X6,X5)))
| ~ relation(X6) )
& ( in(X4,X5)
| ~ in(X4,relation_field(relation_restriction(X6,X5)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])])]) ).
fof(c_0_389_390,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_211])])]) ).
fof(c_0_390_391,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_212])])]) ).
fof(c_0_391_392,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_213])])]) ).
fof(c_0_392_393,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_214])]) ).
fof(c_0_393_394,lemma,
! [X4,X5,X6] :
( ~ relation(X4)
| ~ relation(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ relation_isomorphism(X4,X5,X6)
| epred1_2(X5,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_215])])]) ).
fof(c_0_394_395,lemma,
! [X4,X5,X6] :
( ~ relation(X4)
| ~ relation(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ well_ordering(X4)
| ~ relation_isomorphism(X4,X5,X6)
| well_ordering(X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_216])])]) ).
fof(c_0_395_396,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| subset(fiber(relation_restriction(X6,X4),X5),fiber(X6,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_217])]) ).
fof(c_0_396_397,lemma,
! [X5,X10,X11,X12,X13] :
( ( relation(esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( function(esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( X11 = singleton(X10)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( ~ in(X12,X5)
| ~ in(X12,X5)
| X13 != singleton(X12)
| in(ordered_pair(X12,X13),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( relation(esk22_1(X5))
| esk20_1(X5) = singleton(esk19_1(X5)) )
& ( function(esk22_1(X5))
| esk20_1(X5) = singleton(esk19_1(X5)) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk20_1(X5) = singleton(esk19_1(X5)) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk20_1(X5) = singleton(esk19_1(X5)) )
& ( X11 = singleton(X10)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk20_1(X5) = singleton(esk19_1(X5)) )
& ( ~ in(X12,X5)
| ~ in(X12,X5)
| X13 != singleton(X12)
| in(ordered_pair(X12,X13),esk22_1(X5))
| esk20_1(X5) = singleton(esk19_1(X5)) )
& ( relation(esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( function(esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( X11 = singleton(X10)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( ~ in(X12,X5)
| ~ in(X12,X5)
| X13 != singleton(X12)
| in(ordered_pair(X12,X13),esk22_1(X5))
| in(esk19_1(X5),X5) )
& ( relation(esk22_1(X5))
| esk21_1(X5) = singleton(esk19_1(X5)) )
& ( function(esk22_1(X5))
| esk21_1(X5) = singleton(esk19_1(X5)) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk21_1(X5) = singleton(esk19_1(X5)) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk21_1(X5) = singleton(esk19_1(X5)) )
& ( X11 = singleton(X10)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk21_1(X5) = singleton(esk19_1(X5)) )
& ( ~ in(X12,X5)
| ~ in(X12,X5)
| X13 != singleton(X12)
| in(ordered_pair(X12,X13),esk22_1(X5))
| esk21_1(X5) = singleton(esk19_1(X5)) )
& ( relation(esk22_1(X5))
| esk20_1(X5) != esk21_1(X5) )
& ( function(esk22_1(X5))
| esk20_1(X5) != esk21_1(X5) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk20_1(X5) != esk21_1(X5) )
& ( in(X10,X5)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk20_1(X5) != esk21_1(X5) )
& ( X11 = singleton(X10)
| ~ in(ordered_pair(X10,X11),esk22_1(X5))
| esk20_1(X5) != esk21_1(X5) )
& ( ~ in(X12,X5)
| ~ in(X12,X5)
| X13 != singleton(X12)
| in(ordered_pair(X12,X13),esk22_1(X5))
| esk20_1(X5) != esk21_1(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_218])])])])])]) ).
fof(c_0_397_398,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_219])])])])]) ).
fof(c_0_398_399,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_220])])])])]) ).
fof(c_0_399_400,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_221])]) ).
fof(c_0_400_401,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_222])])])])]) ).
fof(c_0_401_402,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(esk68_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk68_2(X4,X5)) != esk68_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_223])])])])]) ).
fof(c_0_402_403,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_224])]) ).
fof(c_0_403_404,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_225])])]) ).
fof(c_0_404_405,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_226])])]) ).
fof(c_0_405_406,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_227])])]) ).
fof(c_0_406_407,lemma,
! [X4,X5,X6] :
( ( subset(relation_dom(X6),X4)
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( subset(relation_rng(X6),X5)
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_228])])]) ).
fof(c_0_407_408,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_229])]) ).
fof(c_0_408_409,lemma,
! [X5,X6,X8] :
( ( ordinal(esk67_2(X5,X6))
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) )
& ( in(esk67_2(X5,X6),X5)
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) )
& ( ~ ordinal(X8)
| ~ in(X8,X5)
| ordinal_subset(esk67_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_230])])])])]) ).
fof(c_0_409_410,lemma,
! [X4,X7] :
( ( relation(esk65_1(X4))
| in(esk64_1(X4),X4)
| empty(X4) )
& ( function(esk65_1(X4))
| in(esk64_1(X4),X4)
| empty(X4) )
& ( relation_dom(esk65_1(X4)) = X4
| in(esk64_1(X4),X4)
| empty(X4) )
& ( ~ in(X7,X4)
| in(apply(esk65_1(X4),X7),X7)
| in(esk64_1(X4),X4)
| empty(X4) )
& ( relation(esk65_1(X4))
| esk64_1(X4) = empty_set
| empty(X4) )
& ( function(esk65_1(X4))
| esk64_1(X4) = empty_set
| empty(X4) )
& ( relation_dom(esk65_1(X4)) = X4
| esk64_1(X4) = empty_set
| empty(X4) )
& ( ~ in(X7,X4)
| in(apply(esk65_1(X4),X7),X7)
| esk64_1(X4) = empty_set
| empty(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_231])])])])]) ).
fof(c_0_410_411,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_232])]) ).
fof(c_0_411_412,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_233])])]) ).
fof(c_0_412_413,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_234])])]) ).
fof(c_0_413_414,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_235])]) ).
fof(c_0_414_415,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_236])])]) ).
fof(c_0_415_416,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_237])])]) ).
fof(c_0_416_417,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_238])])]) ).
fof(c_0_417_418,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_239])])]) ).
fof(c_0_418_419,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_240])])])]) ).
fof(c_0_419_420,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_241])])])]) ).
fof(c_0_420_421,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_242])])])]) ).
fof(c_0_421_422,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_243])])])])]) ).
fof(c_0_422_423,lemma,
! [X5,X10,X12] :
( ( relation(esk52_1(X5))
| in(esk51_1(X5),X5)
| in(esk48_1(X5),X5) )
& ( function(esk52_1(X5))
| in(esk51_1(X5),X5)
| in(esk48_1(X5),X5) )
& ( relation_dom(esk52_1(X5)) = X5
| in(esk51_1(X5),X5)
| in(esk48_1(X5),X5) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| in(esk51_1(X5),X5)
| in(esk48_1(X5),X5) )
& ( relation(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| in(esk48_1(X5),X5) )
& ( function(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| in(esk48_1(X5),X5) )
& ( relation_dom(esk52_1(X5)) = X5
| X10 != singleton(esk51_1(X5))
| in(esk48_1(X5),X5) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| X10 != singleton(esk51_1(X5))
| in(esk48_1(X5),X5) )
& ( relation(esk52_1(X5))
| in(esk51_1(X5),X5)
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( function(esk52_1(X5))
| in(esk51_1(X5),X5)
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( relation_dom(esk52_1(X5)) = X5
| in(esk51_1(X5),X5)
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| in(esk51_1(X5),X5)
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( relation(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( function(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( relation_dom(esk52_1(X5)) = X5
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) = singleton(esk48_1(X5)) )
& ( relation(esk52_1(X5))
| in(esk51_1(X5),X5)
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( function(esk52_1(X5))
| in(esk51_1(X5),X5)
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( relation_dom(esk52_1(X5)) = X5
| in(esk51_1(X5),X5)
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| in(esk51_1(X5),X5)
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( relation(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( function(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( relation_dom(esk52_1(X5)) = X5
| X10 != singleton(esk51_1(X5))
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| X10 != singleton(esk51_1(X5))
| esk50_1(X5) = singleton(esk48_1(X5)) )
& ( relation(esk52_1(X5))
| in(esk51_1(X5),X5)
| esk49_1(X5) != esk50_1(X5) )
& ( function(esk52_1(X5))
| in(esk51_1(X5),X5)
| esk49_1(X5) != esk50_1(X5) )
& ( relation_dom(esk52_1(X5)) = X5
| in(esk51_1(X5),X5)
| esk49_1(X5) != esk50_1(X5) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| in(esk51_1(X5),X5)
| esk49_1(X5) != esk50_1(X5) )
& ( relation(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) != esk50_1(X5) )
& ( function(esk52_1(X5))
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) != esk50_1(X5) )
& ( relation_dom(esk52_1(X5)) = X5
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) != esk50_1(X5) )
& ( ~ in(X12,X5)
| apply(esk52_1(X5),X12) = singleton(X12)
| X10 != singleton(esk51_1(X5))
| esk49_1(X5) != esk50_1(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_244])])])])]) ).
fof(c_0_423_424,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_245])]) ).
fof(c_0_424_425,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_246])]) ).
fof(c_0_425_426,lemma,
! [X4,X5] :
( ( relation(esk5_2(X4,X5))
| ~ equipotent(X4,relation_field(X5))
| ~ well_ordering(X5)
| ~ relation(X5) )
& ( well_orders(esk5_2(X4,X5),X4)
| ~ equipotent(X4,relation_field(X5))
| ~ well_ordering(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_247])])])]) ).
fof(c_0_426_427,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk72_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_248])])])])]) ).
fof(c_0_427_428,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_249])]) ).
fof(c_0_428_429,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_250])])])])]) ).
fof(c_0_429_430,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_251])]) ).
fof(c_0_430_431,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_252])]) ).
fof(c_0_431_432,lemma,
! [X3,X4] :
( ( subset(relation_field(relation_restriction(X4,X3)),relation_field(X4))
| ~ relation(X4) )
& ( subset(relation_field(relation_restriction(X4,X3)),X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_253])])]) ).
fof(c_0_432_433,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_254])]) ).
fof(c_0_433_434,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_dom(relation_rng_restriction(X3,X4)),relation_dom(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_255])]) ).
fof(c_0_434_435,lemma,
! [X4,X5] :
( ( in(esk10_2(X4,X5),X4)
| element(X4,powerset(X5)) )
& ( ~ in(esk10_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_256])])])]) ).
fof(c_0_435_436,lemma,
! [X4,X5,X7] :
( ( ordinal(esk23_1(X4))
| ~ ordinal(X5)
| ~ in(X5,X4) )
& ( in(esk23_1(X4),X4)
| ~ ordinal(X5)
| ~ in(X5,X4) )
& ( ~ ordinal(X7)
| ~ in(X7,X4)
| ordinal_subset(esk23_1(X4),X7)
| ~ ordinal(X5)
| ~ in(X5,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_257])])])])]) ).
fof(c_0_436_437,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_258])]) ).
fof(c_0_437_438,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ well_ordering(X4)
| ~ subset(X3,relation_field(X4))
| relation_field(relation_restriction(X4,X3)) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_259])]) ).
fof(c_0_438_439,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_260])]) ).
fof(c_0_439_440,lemma,
! [X5,X7,X8,X9,X10] :
( in(X5,esk54_1(X5))
& ( ~ in(X7,esk54_1(X5))
| ~ subset(X8,X7)
| in(X8,esk54_1(X5)) )
& ( ~ in(X9,esk54_1(X5))
| in(powerset(X9),esk54_1(X5)) )
& ( ~ subset(X10,esk54_1(X5))
| are_equipotent(X10,esk54_1(X5))
| in(X10,esk54_1(X5)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_261])])])]) ).
fof(c_0_440_441,lemma,
! [X4] :
( ~ relation(X4)
| in(ordered_pair(esk77_1(X4),esk78_1(X4)),X4)
| X4 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_262])])]) ).
fof(c_0_441_442,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_263])]) ).
fof(c_0_442_443,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_264])]) ).
fof(c_0_443_444,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_265])])]) ).
fof(c_0_444_445,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk69_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk69_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_266])])])])])]) ).
fof(c_0_445_446,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_267])])])]) ).
fof(c_0_446_447,lemma,
! [X3,X4] :
( ( ~ being_limit_ordinal(X3)
| ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3)
| ~ ordinal(X3) )
& ( ordinal(esk70_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( in(esk70_1(X3),X3)
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( ~ in(succ(esk70_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_268])])])])]) ).
fof(c_0_447_448,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_269])])]) ).
fof(c_0_448_449,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_270])]) ).
fof(c_0_449_450,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_271])])])]) ).
fof(c_0_450_451,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_272])]) ).
fof(c_0_451_452,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_273])]) ).
fof(c_0_452_453,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_274])]) ).
fof(c_0_453_454,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_275])])])]) ).
fof(c_0_454_455,lemma,
! [X3,X4] :
( ( relation_field(relation_restriction(X4,X3)) = X3
| ~ well_orders(X4,X3)
| ~ relation(X4) )
& ( well_ordering(relation_restriction(X4,X3))
| ~ well_orders(X4,X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_276])])]) ).
fof(c_0_455_456,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_277])]) ).
fof(c_0_456_457,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_278])]) ).
fof(c_0_457_458,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_279])]) ).
fof(c_0_458_459,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_280])]) ).
fof(c_0_459_460,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_281])])])]) ).
fof(c_0_460_461,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_282])]) ).
fof(c_0_461_462,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_462_463,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_463_464,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_464_465,lemma,
! [X3] :
( ( in(esk66_1(X3),X3)
| ordinal(X3) )
& ( ~ ordinal(esk66_1(X3))
| ~ subset(esk66_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_286])])])]) ).
fof(c_0_465_466,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_287])]) ).
fof(c_0_466_467,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_288])]) ).
fof(c_0_467_468,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_289])])]) ).
fof(c_0_468_469,lemma,
! [X4,X6,X7] :
( ( in(X6,X4)
| ~ in(X6,esk36_1(X4)) )
& ( ordinal(X6)
| ~ in(X6,esk36_1(X4)) )
& ( ~ in(X7,X4)
| ~ ordinal(X7)
| in(X7,esk36_1(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_290])])])])])]) ).
fof(c_0_469_470,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_291])]) ).
fof(c_0_470_471,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_dom_restriction(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_292])]) ).
fof(c_0_471_472,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng_restriction(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_293])]) ).
fof(c_0_472_473,lemma,
! [X4,X6] :
( relation(esk53_1(X4))
& function(esk53_1(X4))
& relation_dom(esk53_1(X4)) = X4
& ( ~ in(X6,X4)
| apply(esk53_1(X4),X6) = singleton(X6) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_294])])])]) ).
fof(c_0_473_474,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_295])])])]) ).
fof(c_0_474_475,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_296])])])]) ).
fof(c_0_475_476,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_297])])]) ).
fof(c_0_476_477,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_298])])]) ).
fof(c_0_477_478,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_299])]) ).
fof(c_0_478_479,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ well_ordering(X4)
| well_ordering(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_300])]) ).
fof(c_0_479_480,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ well_founded_relation(X4)
| well_founded_relation(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_301])]) ).
fof(c_0_480_481,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ antisymmetric(X4)
| antisymmetric(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_302])]) ).
fof(c_0_481_482,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ transitive(X4)
| transitive(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_303])]) ).
fof(c_0_482_483,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ connected(X4)
| connected(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_304])]) ).
fof(c_0_483_484,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ reflexive(X4)
| reflexive(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_305])]) ).
fof(c_0_484_485,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_306])]) ).
fof(c_0_485_486,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_307])])]) ).
fof(c_0_486_487,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_308])])]) ).
fof(c_0_487_488,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_309])]) ).
fof(c_0_488_489,lemma,
! [X3,X4] :
( ~ in(X4,X3)
| apply(identity_relation(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_310])]) ).
fof(c_0_489_490,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_311])]) ).
fof(c_0_490_491,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_312])]) ).
fof(c_0_491_492,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_313])]) ).
fof(c_0_492_493,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_314])]) ).
fof(c_0_493_494,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_315]) ).
fof(c_0_494_495,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_316]) ).
fof(c_0_495_496,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_317]) ).
fof(c_0_496_497,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_318])])])])]) ).
fof(c_0_497_498,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_319])])])])]) ).
fof(c_0_498_499,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_320])])])]) ).
fof(c_0_499_500,negated_conjecture,
( finite(esk56_0)
& ~ finite(set_intersection2(esk56_0,esk57_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_321])])])]) ).
fof(c_0_500_501,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_322])]) ).
fof(c_0_501_502,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_323])]) ).
fof(c_0_502_503,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_324])])])]) ).
fof(c_0_503_504,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_325])])])]) ).
fof(c_0_504_505,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_326])])]) ).
fof(c_0_505_506,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_327])]) ).
fof(c_0_506_507,plain,
! [X3,X4] :
( ( ~ reflexive(X3)
| reflexive(X4)
| ~ epred1_2(X4,X3) )
& ( ~ transitive(X3)
| transitive(X4)
| ~ epred1_2(X4,X3) )
& ( ~ connected(X3)
| connected(X4)
| ~ epred1_2(X4,X3) )
& ( ~ antisymmetric(X3)
| antisymmetric(X4)
| ~ epred1_2(X4,X3) )
& ( ~ well_founded_relation(X3)
| well_founded_relation(X4)
| ~ epred1_2(X4,X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_328])])]) ).
fof(c_0_507_508,lemma,
! [X3,X4] :
( ~ ordinal(X4)
| ~ in(X3,X4)
| ordinal(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_329])]) ).
fof(c_0_508_509,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ finite(X4)
| finite(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_330])])])]) ).
fof(c_0_509_510,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_331])]) ).
fof(c_0_510_511,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_332])]) ).
fof(c_0_511_512,lemma,
! [X3,X4,X5,X6] :
( pair_first(ordered_pair(X3,X4)) = X3
& pair_second(ordered_pair(X5,X6)) = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_333])])]) ).
fof(c_0_512_513,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_334])]) ).
fof(c_0_513_514,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_335])])])]) ).
fof(c_0_514_515,lemma,
! [X3,X5] :
( ( ordinal(esk71_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( X3 = succ(esk71_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_336])])])])]) ).
fof(c_0_515_516,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_337])]) ).
fof(c_0_516_517,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_338])])]) ).
fof(c_0_517_518,lemma,
! [X3] :
( relation(esk63_1(X3))
& well_orders(esk63_1(X3),X3) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_339])]) ).
fof(c_0_518_519,lemma,
! [X2] : in(X2,succ(X2)),
inference(variable_rename,[status(thm)],[c_0_340]) ).
fof(c_0_519_520,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_341])])]) ).
fof(c_0_520_521,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_342]) ).
fof(c_0_521_522,lemma,
! [X2] :
( ~ ordinal(X2)
| well_ordering(inclusion_relation(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_343])]) ).
fof(c_0_522_523,lemma,
! [X2] :
( ~ ordinal(X2)
| well_founded_relation(inclusion_relation(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_344])]) ).
fof(c_0_523_524,lemma,
! [X2] :
( ~ ordinal(X2)
| connected(inclusion_relation(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_345])]) ).
fof(c_0_524_525,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_346])])]) ).
fof(c_0_525_526,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_347]) ).
fof(c_0_526_527,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_348]) ).
fof(c_0_527_528,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_349])])]) ).
fof(c_0_528_529,lemma,
! [X2] : antisymmetric(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_350]) ).
fof(c_0_529_530,lemma,
! [X2] : transitive(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_351]) ).
fof(c_0_530_531,lemma,
! [X2] : reflexive(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_352]) ).
fof(c_0_531_532,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_353]) ).
fof(c_0_532_533,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_354 ).
fof(c_0_533_534,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_355 ).
cnf(c_0_534_535,lemma,
( empty(X2)
| in(X3,esk25_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,cartesian_product2(X2,X4))
| ordered_pair(X5,X6) != X3
| ~ in(X5,X2)
| X5 != X7
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,esk29_7(X2,X1,X4,X3,X5,X6,X7)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_535_536,lemma,
( empty(X2)
| in(X3,esk25_3(X2,X1,X4))
| in(esk29_7(X2,X1,X4,X3,X5,X6,X7),X7)
| ~ relation(X1)
| ~ in(X3,cartesian_product2(X2,X4))
| ordered_pair(X5,X6) != X3
| ~ in(X5,X2)
| X5 != X7
| ~ in(X6,X7) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_536_537,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6)
| ~ in(ordered_pair(X5,esk18_5(X2,X1,X4,X5,X6)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_537_538,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6)
| ~ in(ordered_pair(X5,esk18_5(X2,X1,X4,X5,X6)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_538_539,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_539_540,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_540_541,lemma,
( empty(X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_541_542,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_542_543,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_543_544,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_544_545,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_545_546,lemma,
( in(ordered_pair(apply(X1,esk34_4(X4,X2,X1,X3)),apply(X1,esk35_4(X4,X2,X1,X3))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk33_3(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_546_547,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_547_548,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_548_549,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_549_550,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_550_551,lemma,
( empty(X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_551_552,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_552_553,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_553_554,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_554_555,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_555_556,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_556_557,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_557_558,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_558_559,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_559_560,lemma,
( empty(X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_560_561,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_561_562,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_562_563,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_563_564,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_564_565,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_565_566,lemma,
( empty(X2)
| in(ordered_pair(esk27_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4))
| ~ in(X5,esk28_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_566_567,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_567_568,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_568_569,lemma,
( empty(X2)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_569_570,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_570_571,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_571_572,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_572_573,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| X6 = esk47_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_573_574,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| X6 = esk47_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_574_575,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_575_576,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_576_577,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_577_578,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_578_579,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_579_580,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_580_581,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_581_582,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_582_583,lemma,
( empty(X2)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_583_584,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_584_585,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_585_586,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_586_587,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_587_588,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_588_589,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_589_590,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_590_591,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_591_592,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_592_593,lemma,
( empty(X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_593_594,lemma,
( empty(X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_594_595,lemma,
( empty(X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_595_596,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_596_597,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_597_598,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_598_599,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_599_600,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_600_601,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_601_602,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_602_603,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_603_604,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_604_605,lemma,
( in(ordered_pair(esk62_4(X2,X3,X1,X4),X4),X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(X4,X3)
| relation_rng_as_subset(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_605_606,lemma,
( in(ordered_pair(X4,esk60_4(X3,X2,X1,X4)),X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(X4,X2)
| relation_dom_as_subset(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_606_607,lemma,
( X3 = ordered_pair(esk34_4(X4,X2,X1,X3),esk35_4(X4,X2,X1,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk33_3(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_607_608,lemma,
( empty(X2)
| ordered_pair(esk26_4(X2,X1,X4,X3),esk27_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_608_609,lemma,
( empty(X2)
| in(esk27_4(X2,X1,X4,X3),esk28_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_609_610,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_610_611,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_611_612,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(ordered_pair(X5,X6),X1)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ in(X6,esk17_4(X2,X1,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_612_613,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(ordered_pair(X5,X6),X1)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ in(X6,esk17_4(X2,X1,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_613_614,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_614_615,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_615_616,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_616_617,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_617_618,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_618_619,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_619_620,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_620_621,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_621_622,lemma,
( empty(X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_622_623,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_623_624,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_624_625,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_625_626,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_626_627,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_627_628,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_628_629,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_629_630,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_630_631,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_631_632,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_632_633,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_633_634,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_634_635,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| X6 = esk47_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_635_636,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| X6 = esk47_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_636_637,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(X5,esk17_4(X2,X1,X4,X5))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_637_638,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(X5,esk17_4(X2,X1,X4,X5))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_638_639,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_639_640,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_640_641,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_641_642,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_642_643,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_643_644,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_644_645,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_645_646,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_646_647,lemma,
( empty(X2)
| in(esk26_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_647_648,lemma,
( empty(X2)
| esk26_4(X2,X1,X4,X3) = esk28_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_648_649,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_649_650,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_650_651,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_651_652,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_652_653,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_653_654,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| X5 = esk47_3(X2,X1,X5)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_654_655,lemma,
( empty(X2)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_655_656,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_656_657,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_657_658,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_658_659,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_659_660,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_660_661,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_661_662,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_662_663,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_663_664,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_664_665,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_665_666,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_666_667,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_667_668,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_668_669,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_669_670,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_670_671,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_671_672,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_672_673,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_673_674,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_674_675,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_675_676,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_676_677,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_677_678,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk47_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_678_679,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk47_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_679_680,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(X4,esk61_3(X2,X3,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_680_681,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(esk59_3(X3,X2,X1),X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_681_682,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_682_683,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_683_684,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| X4 = esk17_4(X2,X1,X4,X5)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_684_685,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| X4 = esk17_4(X2,X1,X4,X5)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_685_686,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_686_687,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_687_688,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_688_689,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_689_690,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,esk79_3(X3,X1,X2)) != apply(X2,esk79_3(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_690_691,lemma,
( in(X3,esk33_3(X4,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X3 != ordered_pair(X5,X6)
| ~ in(X3,cartesian_product2(X4,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_691_692,lemma,
( in(ordered_pair(X3,X4),esk24_3(X5,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X3),apply(X1,X4)),X2)
| ~ in(X4,X5)
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_692_693,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_693_694,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_694_695,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X4),esk47_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_695_696,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X4),esk47_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_696_697,lemma,
( empty(X2)
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_697_698,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_698_699,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_699_700,lemma,
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk24_3(X5,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_700_701,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_701_702,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| X3 = esk17_4(X2,X1,X3,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_702_703,lemma,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk73_2(X1,X2) != apply(X1,esk74_2(X1,X2))
| ~ in(esk74_2(X1,X2),relation_dom(X1))
| esk76_2(X1,X2) != apply(X2,esk75_2(X1,X2))
| ~ in(esk75_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_703_704,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_704_705,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_705_706,lemma,
( in(ordered_pair(X2,esk58_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_706_707,lemma,
( in(ordered_pair(esk55_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_707_708,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_708_709,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_709_710,lemma,
( X3 = empty_set
| in(X4,relation_inverse_image(X1,X5))
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ in(apply(X1,X4),X5)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_710_711,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_711_712,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_712_713,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| X4 = empty_set
| ~ in(X3,X5)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_of2_as_subset(X1,X5,X4)
| ~ quasi_total(X1,X5,X4)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_713_714,lemma,
( ordered_pair(esk31_3(X2,X3,X1),esk32_3(X2,X3,X1)) = X1
| ~ in(X1,esk30_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_714_715,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| X4 = esk47_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_715_716,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| X4 = esk47_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_716_717,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_717_718,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_718_719,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_719_720,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_720_721,lemma,
( X3 = empty_set
| in(apply(X1,X4),X5)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ in(X4,relation_inverse_image(X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_721_722,lemma,
( in(X3,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk24_3(X5,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_722_723,lemma,
( in(X4,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk24_3(X5,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_723_724,lemma,
( X2 = function_inverse(X1)
| esk74_2(X1,X2) = apply(X2,esk73_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk76_2(X1,X2) != apply(X2,esk75_2(X1,X2))
| ~ in(esk75_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_724_725,lemma,
( X2 = function_inverse(X1)
| esk75_2(X1,X2) = apply(X1,esk76_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk73_2(X1,X2) != apply(X1,esk74_2(X1,X2))
| ~ in(esk74_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_725_726,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| in(esk61_3(X2,X3,X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_726_727,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| in(esk59_3(X3,X2,X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_727_728,lemma,
( quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_728_729,lemma,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_729_730,lemma,
( X3 = empty_set
| in(X4,X2)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ in(X4,relation_inverse_image(X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_730_731,lemma,
( X2 = function_inverse(X1)
| in(esk73_2(X1,X2),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk76_2(X1,X2) != apply(X2,esk75_2(X1,X2))
| ~ in(esk75_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_731_732,lemma,
( X2 = function_inverse(X1)
| in(esk76_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk73_2(X1,X2) != apply(X1,esk74_2(X1,X2))
| ~ in(esk74_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_732_733,lemma,
( X3 = empty_set
| quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_733_734,lemma,
( X3 = empty_set
| relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_734_735,lemma,
( in(X3,cartesian_product2(X4,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk33_3(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_735_736,lemma,
( in(apply(X1,X2),relation_rng(X1))
| X3 = empty_set
| ~ in(X2,X4)
| ~ relation_of2_as_subset(X1,X4,X3)
| ~ quasi_total(X1,X4,X3)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_736_737,lemma,
( empty(X2)
| in(X3,cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_737_738,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_738_739,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_739_740,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_740_741,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_741_742,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_742_743,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_743_744,lemma,
( esk32_3(X2,X3,X1) = singleton(esk31_3(X2,X3,X1))
| ~ in(X1,esk30_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_744_745,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_372]) ).
cnf(c_0_745_746,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk79_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_362]) ).
cnf(c_0_746_747,lemma,
( function(X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_747_748,lemma,
( X3 = empty_set
| function(X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_748_749,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_373]) ).
cnf(c_0_749_750,lemma,
( in(esk58_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_750_751,lemma,
( in(esk55_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_751_752,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_752_753,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_753_754,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_754_755,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_755_756,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| X3 = esk47_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_756_757,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| X3 = esk47_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_757_758,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_758_759,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_759_760,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_760_761,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_761_762,lemma,
( in(esk58_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_762_763,lemma,
( in(esk55_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_763_764,lemma,
( in(esk38_3(X3,X1,X2),X3)
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_764_765,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_373]) ).
cnf(c_0_765_766,lemma,
( in(esk31_3(X2,X3,X1),X2)
| ~ in(X1,esk30_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_766_767,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_375]) ).
cnf(c_0_767_768,lemma,
( ordinal(esk38_3(X3,X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_768_769,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_376]) ).
cnf(c_0_769_770,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_377]) ).
cnf(c_0_770_771,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_378]) ).
cnf(c_0_771_772,lemma,
( relation_isomorphism(X1,X2,function_inverse(X3))
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_772_773,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| X3 = esk47_3(X2,X1,X3)
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_773_774,lemma,
( empty(X2)
| in(X3,X2)
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_774_775,lemma,
( empty(X2)
| in(X3,X2)
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_775_776,lemma,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_776_777,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_381]) ).
cnf(c_0_777_778,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_381]) ).
cnf(c_0_778_779,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| X3 = esk47_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_779_780,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_780_781,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_781_782,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_782_783,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_783_784,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_365]) ).
cnf(c_0_784_785,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_366]) ).
cnf(c_0_785_786,lemma,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(X4,X3)
| ~ relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_786_787,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_373]) ).
cnf(c_0_787_788,lemma,
( X2 = function_inverse(X1)
| esk74_2(X1,X2) = apply(X2,esk73_2(X1,X2))
| esk75_2(X1,X2) = apply(X1,esk76_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_364]) ).
cnf(c_0_788_789,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_383]) ).
cnf(c_0_789_790,lemma,
( in(X1,esk30_2(X2,X3))
| X4 != singleton(X5)
| ~ in(X5,X2)
| ordered_pair(X5,X4) != X1
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_790_791,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| X3 = esk47_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_791_792,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| X3 = esk47_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_792_793,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_793_794,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_794_795,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_795_796,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_796_797,lemma,
( X2 = function_inverse(X1)
| in(esk73_2(X1,X2),relation_rng(X1))
| esk75_2(X1,X2) = apply(X1,esk76_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_364]) ).
cnf(c_0_797_798,lemma,
( X2 = function_inverse(X1)
| esk74_2(X1,X2) = apply(X2,esk73_2(X1,X2))
| in(esk76_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_364]) ).
cnf(c_0_798_799,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_799_800,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_800_801,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_801_802,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_802_803,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_803_804,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_804_805,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_384]) ).
cnf(c_0_805_806,lemma,
( X2 = function_inverse(X1)
| in(esk73_2(X1,X2),relation_rng(X1))
| in(esk76_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_364]) ).
cnf(c_0_806_807,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_807_808,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_385]) ).
cnf(c_0_808_809,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_386]) ).
cnf(c_0_809_810,lemma,
( in(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_810_811,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_384]) ).
cnf(c_0_811_812,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_812_813,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_813_814,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_814_815,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_390]) ).
cnf(c_0_815_816,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_816_817,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_817_818,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_818_819,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_387]) ).
cnf(c_0_819_820,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_389]) ).
cnf(c_0_820_821,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_391]) ).
cnf(c_0_821_822,lemma,
( relation(esk24_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_822_823,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_392]) ).
cnf(c_0_823_824,lemma,
( epred1_2(X1,X2)
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_824_825,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_386]) ).
cnf(c_0_825_826,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_826_827,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_827_828,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk40_2(X2,X1) != esk41_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_828_829,lemma,
( well_ordering(X1)
| ~ relation_isomorphism(X2,X1,X3)
| ~ well_ordering(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_829_830,lemma,
( X2 = esk38_3(X3,X1,X2)
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_830_831,lemma,
( subset(fiber(relation_restriction(X1,X2),X3),fiber(X1,X3))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_831_832,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_832_833,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_833_834,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_834_835,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_364]) ).
cnf(c_0_835_836,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_364]) ).
cnf(c_0_836_837,lemma,
( in(esk19_1(X1),X1)
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_837_838,lemma,
( in(esk19_1(X1),X1)
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_838_839,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_839_840,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_840_841,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_841_842,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_842_843,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_843_844,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_364]) ).
cnf(c_0_844_845,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_364]) ).
cnf(c_0_845_846,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_846_847,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_847_848,lemma,
( in(ordered_pair(X2,X3),esk22_1(X1))
| esk20_1(X1) != esk21_1(X1)
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_848_849,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk8_1(X1),esk9_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_849_850,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk9_1(X1),esk8_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_850_851,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk2_1(X1),esk4_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_851_852,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk1_1(X1),esk1_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_852_853,lemma,
( in(X2,esk37_2(X3,X1))
| ~ ordinal(X1)
| ~ in(X4,X3)
| X2 != X4
| ~ ordinal(X4)
| ~ in(X2,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_853_854,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_362]) ).
cnf(c_0_854_855,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk68_2(X2,X1)) != esk68_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_855_856,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_856_857,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_857_858,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_858_859,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_859_860,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_860_861,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_403]) ).
cnf(c_0_861_862,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_404]) ).
cnf(c_0_862_863,lemma,
( in(X2,cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_863_864,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_864_865,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk42_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_865_866,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_866_867,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_867_868,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_868_869,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_869_870,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_870_871,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_871_872,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_872_873,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_873_874,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_874_875,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_875_876,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_405]) ).
cnf(c_0_876_877,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_405]) ).
cnf(c_0_877_878,lemma,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_878_879,lemma,
( subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_879_880,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_880_881,lemma,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk30_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_881_882,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_882_883,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_883_884,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_884_885,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_885_886,lemma,
( X2 = empty_set
| ordinal_subset(esk67_2(X2,X1),X3)
| ~ ordinal(X1)
| ~ subset(X2,X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_886_887,lemma,
( in(X2,X1)
| esk20_1(X1) != esk21_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_887_888,lemma,
( in(X2,X1)
| esk20_1(X1) != esk21_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_888_889,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| in(apply(esk65_1(X1),X2),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_889_890,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_890_891,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_891_892,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_892_893,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_893_894,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_894_895,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_895_896,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_896_897,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_897_898,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_898_899,lemma,
( X3 = singleton(X2)
| esk20_1(X1) != esk21_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_899_900,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_413]) ).
cnf(c_0_900_901,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_901_902,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_902_903,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_903_904,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_904_905,lemma,
( in(X2,succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_905_906,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_416]) ).
cnf(c_0_906_907,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_417]) ).
cnf(c_0_907_908,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_908_909,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_909_910,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_910_911,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_911_912,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_912_913,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_913_914,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_423]) ).
cnf(c_0_914_915,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_424]) ).
cnf(c_0_915_916,lemma,
( well_orders(esk5_2(X2,X1),X2)
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_916_917,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_917_918,lemma,
( empty(X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_918_919,lemma,
( empty(X2)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| esk12_2(X2,X1) != esk13_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_919_920,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_920_921,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_921_922,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_922_923,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_923_924,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_924_925,lemma,
( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_925_926,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_926_927,lemma,
( in(esk48_1(X1),X1)
| apply(esk52_1(X1),X3) = singleton(X3)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_927_928,lemma,
( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_928_929,lemma,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_929_930,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| in(apply(esk65_1(X1),X2),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_930_931,lemma,
( element(X1,powerset(X2))
| ~ in(esk10_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_931_932,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_932_933,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_933_934,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_934_935,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_935_936,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_936_937,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_937_938,lemma,
( in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| esk49_1(X1) != esk50_1(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_938_939,lemma,
( in(esk72_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_939_940,lemma,
( ordinal_subset(esk23_1(X2),X3)
| ~ in(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_940_941,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_941_942,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_942_943,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| apply(esk52_1(X1),X3) = singleton(X3)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_943_944,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| apply(esk52_1(X1),X3) = singleton(X3)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_944_945,lemma,
( apply(esk52_1(X1),X3) = singleton(X3)
| esk49_1(X1) != esk50_1(X1)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_945_946,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ subset(X2,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_946_947,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_947_948,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_948_949,lemma,
( relation(esk5_2(X2,X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_949_950,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_362]) ).
cnf(c_0_950_951,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk6_1(X1),esk7_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_951_952,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk7_1(X1),esk6_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_952_953,lemma,
( transitive(X1)
| in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_953_954,lemma,
( transitive(X1)
| in(ordered_pair(esk3_1(X1),esk4_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_954_955,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_955_956,lemma,
( in(X1,esk54_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk54_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_956_957,lemma,
( X1 = empty_set
| in(ordered_pair(esk77_1(X1),esk78_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_957_958,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_958_959,lemma,
( in(X1,esk54_1(X2))
| are_equipotent(X1,esk54_1(X2))
| ~ subset(X1,esk54_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_959_960,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_960_961,lemma,
( X2 = empty_set
| in(esk67_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_961_962,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_962_963,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk14_2(X2,X1)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_963_964,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_964_965,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_965_966,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_966_967,lemma,
( X1 = identity_relation(X2)
| in(esk68_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_967_968,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_968_969,lemma,
( ~ in(X1,X2)
| ~ in(X3,X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_969_970,lemma,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_970_971,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_971_972,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_972_973,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_973_974,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_974_975,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_450]) ).
cnf(c_0_975_976,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk70_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_976_977,lemma,
( X2 = empty_set
| ordinal(esk67_2(X2,X1))
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_977_978,lemma,
( relation_restriction(X1,X2) = relation_rng_restriction(X2,relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_978_979,lemma,
( relation_restriction(X1,X2) = relation_dom_restriction(relation_rng_restriction(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_979_980,lemma,
( in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(succ(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_980_981,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_981_982,lemma,
( element(X1,powerset(X2))
| in(esk10_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_982_983,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_983_984,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_984_985,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_985_986,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_986_987,lemma,
( in(powerset(X1),esk54_1(X2))
| ~ in(X1,esk54_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_987_988,lemma,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_988_989,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_989_990,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_990_991,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_991_992,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_992_993,lemma,
( disjoint(X1,X2)
| in(esk69_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_993_994,lemma,
( disjoint(X1,X2)
| in(esk69_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_994_995,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_995_996,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_996_997,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_997_998,lemma,
( ordinal(X1)
| ~ subset(esk66_1(X1),X1)
| ~ ordinal(esk66_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_998_999,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_999_1000,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_1000_1001,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_364]) ).
cnf(c_0_1001_1002,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1002_1003,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| relation(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1003_1004,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| function(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1004_1005,lemma,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_1005_1006,lemma,
( in(X1,esk36_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1006_1007,lemma,
( in(esk23_1(X2),X2)
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_1007_1008,lemma,
( in(esk48_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1008_1009,lemma,
( in(esk48_1(X1),X1)
| relation(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1009_1010,lemma,
( in(esk48_1(X1),X1)
| function(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1010_1011,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1011_1012,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_1012_1013,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_1013_1014,lemma,
( apply(esk53_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1014_1015,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1015_1016,lemma,
( in(X1,X2)
| ~ in(X1,esk36_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1016_1017,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_1017_1018,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1018_1019,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1019_1020,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1020_1021,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1021_1022,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| relation(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1022_1023,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| function(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1023_1024,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| relation(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1024_1025,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| in(esk51_1(X1),X1)
| function(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1025_1026,lemma,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_1026_1027,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_1027_1028,lemma,
( in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1
| esk49_1(X1) != esk50_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1028_1029,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1029_1030,lemma,
( well_founded_relation(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_1030_1031,lemma,
( antisymmetric(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_1031_1032,lemma,
( transitive(relation_restriction(X1,X2))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_1032_1033,lemma,
( connected(relation_restriction(X1,X2))
| ~ connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1033_1034,lemma,
( reflexive(relation_restriction(X1,X2))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_1034_1035,lemma,
( in(esk51_1(X1),X1)
| relation(esk52_1(X1))
| esk49_1(X1) != esk50_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1035_1036,lemma,
( in(esk51_1(X1),X1)
| function(esk52_1(X1))
| esk49_1(X1) != esk50_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1036_1037,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_1037_1038,lemma,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_orders(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_1038_1039,lemma,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1039_1040,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1040_1041,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1041_1042,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_1042_1043,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| relation_dom(esk52_1(X1)) = X1
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1043_1044,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| relation_dom(esk52_1(X1)) = X1
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1044_1045,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_1045_1046,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1046_1047,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_1047_1048,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_1048_1049,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| relation(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1049_1050,lemma,
( esk49_1(X1) = singleton(esk48_1(X1))
| function(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1050_1051,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| relation(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1051_1052,lemma,
( esk50_1(X1) = singleton(esk48_1(X1))
| function(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1052_1053,lemma,
( relation_dom(esk52_1(X1)) = X1
| esk49_1(X1) != esk50_1(X1)
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1053_1054,lemma,
( relation(esk52_1(X1))
| esk49_1(X1) != esk50_1(X1)
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1054_1055,lemma,
( function(esk52_1(X1))
| esk49_1(X1) != esk50_1(X1)
| X2 != singleton(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_1055_1056,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_1056_1057,lemma,
( ordinal(esk23_1(X2))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_1057_1058,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_1058_1059,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_1059_1060,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_1060_1061,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_1061_1062,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1062_1063,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_1063_1064,lemma,
( connected(X1)
| in(esk8_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_1064_1065,lemma,
( connected(X1)
| in(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_1065_1066,lemma,
( reflexive(X1)
| in(esk1_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_1066_1067,negated_conjecture,
~ finite(set_intersection2(esk56_0,esk57_0)),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_1067_1068,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_1068_1069,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_1069_1070,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_1070_1071,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1071_1072,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1072_1073,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1073_1074,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1074_1075,lemma,
( ordinal(X1)
| ~ in(X1,esk36_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1075_1076,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| relation_dom(esk65_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_1076_1077,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1077_1078,lemma,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1078_1079,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_1079_1080,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| relation(esk65_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_1080_1081,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| function(esk65_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_1081_1082,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_1082_1083,lemma,
( well_orders(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_1083_1084,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1084_1085,plain,
( reflexive(X1)
| ~ epred1_2(X1,X2)
| ~ reflexive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1085_1086,plain,
( transitive(X1)
| ~ epred1_2(X1,X2)
| ~ transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1086_1087,plain,
( connected(X1)
| ~ epred1_2(X1,X2)
| ~ connected(X2) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1087_1088,plain,
( antisymmetric(X1)
| ~ epred1_2(X1,X2)
| ~ antisymmetric(X2) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1088_1089,plain,
( well_founded_relation(X1)
| ~ epred1_2(X1,X2)
| ~ well_founded_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1089_1090,lemma,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1090_1091,lemma,
( finite(X1)
| ~ finite(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_1091_1092,lemma,
( being_limit_ordinal(X1)
| in(esk70_1(X1),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1092_1093,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1093_1094,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_510]) ).
cnf(c_0_1094_1095,lemma,
pair_first(ordered_pair(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_1095_1096,lemma,
pair_second(ordered_pair(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_1096_1097,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1097_1098,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1098_1099,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1099_1100,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1100_1101,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_512]) ).
cnf(c_0_1101_1102,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_1102_1103,lemma,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| X1 != succ(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1103_1104,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_1104_1105,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1105_1106,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_1106_1107,lemma,
( ordinal(X1)
| in(esk66_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1107_1108,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1108_1109,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1109_1110,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1110_1111,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1111_1112,lemma,
( connected(X1)
| ~ relation(X1)
| esk8_1(X1) != esk9_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_1112_1113,lemma,
( antisymmetric(X1)
| ~ relation(X1)
| esk6_1(X1) != esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_1113_1114,lemma,
( relation(esk22_1(X1))
| esk20_1(X1) != esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1114_1115,lemma,
( function(esk22_1(X1))
| esk20_1(X1) != esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_1115_1116,lemma,
( being_limit_ordinal(X1)
| X1 = succ(esk71_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1116_1117,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_1117_1118,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1118_1119,lemma,
( being_limit_ordinal(X1)
| ordinal(esk71_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1119_1120,lemma,
( being_limit_ordinal(X1)
| ordinal(esk70_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_1120_1121,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_1121_1122,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_1122_1123,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_1123_1124,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| relation_dom(esk65_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_1124_1125,lemma,
well_orders(esk63_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_1125_1126,lemma,
in(X1,esk54_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_1126_1127,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_518]) ).
cnf(c_0_1127_1128,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| relation(esk65_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_1128_1129,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| function(esk65_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_1129_1130,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_1130_1131,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_1131_1132,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_1132_1133,lemma,
( well_ordering(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_521]) ).
cnf(c_0_1133_1134,lemma,
( well_founded_relation(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_522]) ).
cnf(c_0_1134_1135,lemma,
( connected(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_1135_1136,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_1136_1137,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_1137_1138,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1138_1139,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_1139_1140,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_1140_1141,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_1141_1142,lemma,
relation_dom(esk53_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1142_1143,lemma,
antisymmetric(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_528]) ).
cnf(c_0_1143_1144,lemma,
transitive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_529]) ).
cnf(c_0_1144_1145,lemma,
reflexive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_530]) ).
cnf(c_0_1145_1146,lemma,
relation(esk63_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_1146_1147,lemma,
relation(esk53_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1147_1148,lemma,
function(esk53_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1148_1149,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1149_1150,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1150_1151,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_1151_1152,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_1152_1153,negated_conjecture,
finite(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_1153_1154,lemma,
( empty(X2)
| in(X3,esk25_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,cartesian_product2(X2,X4))
| ordered_pair(X5,X6) != X3
| ~ in(X5,X2)
| X5 != X7
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,esk29_7(X2,X1,X4,X3,X5,X6,X7)),X1) ),
c_0_534,
[final] ).
cnf(c_0_1154_1155,lemma,
( empty(X2)
| in(X3,esk25_3(X2,X1,X4))
| in(esk29_7(X2,X1,X4,X3,X5,X6,X7),X7)
| ~ relation(X1)
| ~ in(X3,cartesian_product2(X2,X4))
| ordered_pair(X5,X6) != X3
| ~ in(X5,X2)
| X5 != X7
| ~ in(X6,X7) ),
c_0_535,
[final] ).
cnf(c_0_1155_1156,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6)
| ~ in(ordered_pair(X5,esk18_5(X2,X1,X4,X5,X6)),X1) ),
c_0_536,
[final] ).
cnf(c_0_1156_1157,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6)
| ~ in(ordered_pair(X5,esk18_5(X2,X1,X4,X5,X6)),X1) ),
c_0_537,
[final] ).
cnf(c_0_1157_1158,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_538,
[final] ).
cnf(c_0_1158_1159,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_539,
[final] ).
cnf(c_0_1159_1160,lemma,
( empty(X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_540,
[final] ).
cnf(c_0_1160_1161,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_541,
[final] ).
cnf(c_0_1161_1162,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_542,
[final] ).
cnf(c_0_1162_1163,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_543,
[final] ).
cnf(c_0_1163_1164,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5)
| ~ in(ordered_pair(X4,esk18_5(X2,X1,X3,X4,X5)),X1) ),
c_0_544,
[final] ).
cnf(c_0_1164_1165,lemma,
( in(ordered_pair(apply(X1,esk34_4(X4,X2,X1,X3)),apply(X1,esk35_4(X4,X2,X1,X3))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk33_3(X4,X2,X1)) ),
c_0_545,
[final] ).
cnf(c_0_1165_1166,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6) ),
c_0_546,
[final] ).
cnf(c_0_1166_1167,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X6
| ~ in(X5,X6) ),
c_0_547,
[final] ).
cnf(c_0_1167_1168,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_548,
[final] ).
cnf(c_0_1168_1169,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_549,
[final] ).
cnf(c_0_1169_1170,lemma,
( empty(X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_550,
[final] ).
cnf(c_0_1170_1171,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_551,
[final] ).
cnf(c_0_1171_1172,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_552,
[final] ).
cnf(c_0_1172_1173,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_553,
[final] ).
cnf(c_0_1173_1174,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(ordered_pair(X3,X4),esk16_2(X2,X1))
| in(esk18_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X3,X2)
| X3 != X5
| ~ in(X4,X5) ),
c_0_554,
[final] ).
cnf(c_0_1174_1175,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
c_0_555,
[final] ).
cnf(c_0_1175_1176,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
c_0_556,
[final] ).
cnf(c_0_1176_1177,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_557,
[final] ).
cnf(c_0_1177_1178,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_558,
[final] ).
cnf(c_0_1178_1179,lemma,
( empty(X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_559,
[final] ).
cnf(c_0_1179_1180,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_560,
[final] ).
cnf(c_0_1180_1181,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_561,
[final] ).
cnf(c_0_1181_1182,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_562,
[final] ).
cnf(c_0_1182_1183,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_563,
[final] ).
cnf(c_0_1183_1184,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_564,
[final] ).
cnf(c_0_1184_1185,lemma,
( empty(X2)
| in(ordered_pair(esk27_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4))
| ~ in(X5,esk28_4(X2,X1,X4,X3)) ),
c_0_565,
[final] ).
cnf(c_0_1185_1186,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_566,
[final] ).
cnf(c_0_1186_1187,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_567,
[final] ).
cnf(c_0_1187_1188,lemma,
( empty(X2)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_568,
[final] ).
cnf(c_0_1188_1189,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_569,
[final] ).
cnf(c_0_1189_1190,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_570,
[final] ).
cnf(c_0_1190_1191,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_571,
[final] ).
cnf(c_0_1191_1192,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| esk47_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_572,
[final] ).
cnf(c_0_1192_1193,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| esk47_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_573,
[final] ).
cnf(c_0_1193_1194,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
c_0_574,
[final] ).
cnf(c_0_1194_1195,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
c_0_575,
[final] ).
cnf(c_0_1195_1196,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
c_0_576,
[final] ).
cnf(c_0_1196_1197,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
c_0_577,
[final] ).
cnf(c_0_1197_1198,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
c_0_578,
[final] ).
cnf(c_0_1198_1199,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk45_4(X2,X1,X5,X4)),X1) ),
c_0_579,
[final] ).
cnf(c_0_1199_1200,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_580,
[final] ).
cnf(c_0_1200_1201,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_581,
[final] ).
cnf(c_0_1201_1202,lemma,
( empty(X2)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_582,
[final] ).
cnf(c_0_1202_1203,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_583,
[final] ).
cnf(c_0_1203_1204,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_584,
[final] ).
cnf(c_0_1204_1205,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_585,
[final] ).
cnf(c_0_1205_1206,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_586,
[final] ).
cnf(c_0_1206_1207,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_587,
[final] ).
cnf(c_0_1207_1208,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_588,
[final] ).
cnf(c_0_1208_1209,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_589,
[final] ).
cnf(c_0_1209_1210,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_590,
[final] ).
cnf(c_0_1210_1211,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_591,
[final] ).
cnf(c_0_1211_1212,lemma,
( empty(X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_592,
[final] ).
cnf(c_0_1212_1213,lemma,
( empty(X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_593,
[final] ).
cnf(c_0_1213_1214,lemma,
( empty(X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_594,
[final] ).
cnf(c_0_1214_1215,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_595,
[final] ).
cnf(c_0_1215_1216,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_596,
[final] ).
cnf(c_0_1216_1217,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_597,
[final] ).
cnf(c_0_1217_1218,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_598,
[final] ).
cnf(c_0_1218_1219,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_599,
[final] ).
cnf(c_0_1219_1220,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_600,
[final] ).
cnf(c_0_1220_1221,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_601,
[final] ).
cnf(c_0_1221_1222,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_602,
[final] ).
cnf(c_0_1222_1223,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk45_4(X2,X1,X4,X3)),X1) ),
c_0_603,
[final] ).
cnf(c_0_1223_1224,lemma,
( in(ordered_pair(esk62_4(X2,X3,X1,X4),X4),X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(X4,X3)
| relation_rng_as_subset(X2,X3,X1) != X3 ),
c_0_604,
[final] ).
cnf(c_0_1224_1225,lemma,
( in(ordered_pair(X4,esk60_4(X3,X2,X1,X4)),X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(X4,X2)
| relation_dom_as_subset(X2,X3,X1) != X2 ),
c_0_605,
[final] ).
cnf(c_0_1225_1226,lemma,
( ordered_pair(esk34_4(X4,X2,X1,X3),esk35_4(X4,X2,X1,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk33_3(X4,X2,X1)) ),
c_0_606,
[final] ).
cnf(c_0_1226_1227,lemma,
( empty(X2)
| ordered_pair(esk26_4(X2,X1,X4,X3),esk27_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
c_0_607,
[final] ).
cnf(c_0_1227_1228,lemma,
( empty(X2)
| in(esk27_4(X2,X1,X4,X3),esk28_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
c_0_608,
[final] ).
cnf(c_0_1228_1229,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
c_0_609,
[final] ).
cnf(c_0_1229_1230,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk46_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk47_3(X2,X1,X6)) ),
c_0_610,
[final] ).
cnf(c_0_1230_1231,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(ordered_pair(X5,X6),X1)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ in(X6,esk17_4(X2,X1,X4,X5)) ),
c_0_611,
[final] ).
cnf(c_0_1231_1232,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(ordered_pair(X5,X6),X1)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1))
| ~ in(X6,esk17_4(X2,X1,X4,X5)) ),
c_0_612,
[final] ).
cnf(c_0_1232_1233,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_613,
[final] ).
cnf(c_0_1233_1234,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_614,
[final] ).
cnf(c_0_1234_1235,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_615,
[final] ).
cnf(c_0_1235_1236,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_616,
[final] ).
cnf(c_0_1236_1237,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_617,
[final] ).
cnf(c_0_1237_1238,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_618,
[final] ).
cnf(c_0_1238_1239,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_619,
[final] ).
cnf(c_0_1239_1240,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk46_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk47_3(X2,X1,X5)) ),
c_0_620,
[final] ).
cnf(c_0_1240_1241,lemma,
( empty(X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_621,
[final] ).
cnf(c_0_1241_1242,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_622,
[final] ).
cnf(c_0_1242_1243,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_623,
[final] ).
cnf(c_0_1243_1244,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_624,
[final] ).
cnf(c_0_1244_1245,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1))
| ~ in(X5,esk17_4(X2,X1,X3,X4)) ),
c_0_625,
[final] ).
cnf(c_0_1245_1246,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_626,
[final] ).
cnf(c_0_1246_1247,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| in(apply(esk46_2(X2,X1),X6),esk47_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_627,
[final] ).
cnf(c_0_1247_1248,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_628,
[final] ).
cnf(c_0_1248_1249,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_629,
[final] ).
cnf(c_0_1249_1250,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_630,
[final] ).
cnf(c_0_1250_1251,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_631,
[final] ).
cnf(c_0_1251_1252,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_632,
[final] ).
cnf(c_0_1252_1253,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| in(apply(esk46_2(X2,X1),X5),esk47_3(X2,X1,X5))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_633,
[final] ).
cnf(c_0_1253_1254,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| esk47_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_634,
[final] ).
cnf(c_0_1254_1255,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| esk47_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_635,
[final] ).
cnf(c_0_1255_1256,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(X5,esk17_4(X2,X1,X4,X5))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_636,
[final] ).
cnf(c_0_1256_1257,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(X5,esk17_4(X2,X1,X4,X5))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_637,
[final] ).
cnf(c_0_1257_1258,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_638,
[final] ).
cnf(c_0_1258_1259,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_639,
[final] ).
cnf(c_0_1259_1260,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_640,
[final] ).
cnf(c_0_1260_1261,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_641,
[final] ).
cnf(c_0_1261_1262,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_642,
[final] ).
cnf(c_0_1262_1263,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk45_4(X2,X1,X5,X4),X4)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| esk44_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_643,
[final] ).
cnf(c_0_1263_1264,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_644,
[final] ).
cnf(c_0_1264_1265,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_645,
[final] ).
cnf(c_0_1265_1266,lemma,
( empty(X2)
| in(esk26_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
c_0_646,
[final] ).
cnf(c_0_1266_1267,lemma,
( empty(X2)
| esk26_4(X2,X1,X4,X3) = esk28_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
c_0_647,
[final] ).
cnf(c_0_1267_1268,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_648,
[final] ).
cnf(c_0_1268_1269,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_649,
[final] ).
cnf(c_0_1269_1270,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_650,
[final] ).
cnf(c_0_1270_1271,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_651,
[final] ).
cnf(c_0_1271_1272,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_652,
[final] ).
cnf(c_0_1272_1273,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| esk47_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_653,
[final] ).
cnf(c_0_1273_1274,lemma,
( empty(X2)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_654,
[final] ).
cnf(c_0_1274_1275,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_655,
[final] ).
cnf(c_0_1275_1276,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_656,
[final] ).
cnf(c_0_1276_1277,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_657,
[final] ).
cnf(c_0_1277_1278,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_658,
[final] ).
cnf(c_0_1278_1279,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_659,
[final] ).
cnf(c_0_1279_1280,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_660,
[final] ).
cnf(c_0_1280_1281,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_661,
[final] ).
cnf(c_0_1281_1282,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_662,
[final] ).
cnf(c_0_1282_1283,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_663,
[final] ).
cnf(c_0_1283_1284,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(X4,esk17_4(X2,X1,X3,X4))
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_664,
[final] ).
cnf(c_0_1284_1285,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_665,
[final] ).
cnf(c_0_1285_1286,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_666,
[final] ).
cnf(c_0_1286_1287,lemma,
( empty(X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_667,
[final] ).
cnf(c_0_1287_1288,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_668,
[final] ).
cnf(c_0_1288_1289,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_669,
[final] ).
cnf(c_0_1289_1290,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_670,
[final] ).
cnf(c_0_1290_1291,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_671,
[final] ).
cnf(c_0_1291_1292,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_672,
[final] ).
cnf(c_0_1292_1293,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_673,
[final] ).
cnf(c_0_1293_1294,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_674,
[final] ).
cnf(c_0_1294_1295,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_675,
[final] ).
cnf(c_0_1295_1296,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk45_4(X2,X1,X4,X3),X3)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk44_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_676,
[final] ).
cnf(c_0_1296_1297,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk47_3(X2,X1,X4)) ),
c_0_677,
[final] ).
cnf(c_0_1297_1298,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk47_3(X2,X1,X4)) ),
c_0_678,
[final] ).
cnf(c_0_1298_1299,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(X4,esk61_3(X2,X3,X1)),X1) ),
c_0_679,
[final] ).
cnf(c_0_1299_1300,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(esk59_3(X3,X2,X1),X4),X1) ),
c_0_680,
[final] ).
cnf(c_0_1300_1301,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
c_0_681,
[final] ).
cnf(c_0_1301_1302,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
c_0_682,
[final] ).
cnf(c_0_1302_1303,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| esk17_4(X2,X1,X4,X5) = X4
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_683,
[final] ).
cnf(c_0_1303_1304,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| esk17_4(X2,X1,X4,X5) = X4
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_684,
[final] ).
cnf(c_0_1304_1305,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
c_0_685,
[final] ).
cnf(c_0_1305_1306,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
c_0_686,
[final] ).
cnf(c_0_1306_1307,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
c_0_687,
[final] ).
cnf(c_0_1307_1308,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(ordered_pair(apply(esk46_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk47_3(X2,X1,X3)) ),
c_0_688,
[final] ).
cnf(c_0_1308_1309,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,esk79_3(X3,X1,X2)) != apply(X2,esk79_3(X3,X1,X2)) ),
c_0_689,
[final] ).
cnf(c_0_1309_1310,lemma,
( in(X3,esk33_3(X4,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| X3 != ordered_pair(X5,X6)
| ~ in(X3,cartesian_product2(X4,X4)) ),
c_0_690,
[final] ).
cnf(c_0_1310_1311,lemma,
( in(ordered_pair(X3,X4),esk24_3(X5,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(X1,X3),apply(X1,X4)),X2)
| ~ in(X4,X5)
| ~ in(X3,X5) ),
c_0_691,
[final] ).
cnf(c_0_1311_1312,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_692,
[final] ).
cnf(c_0_1312_1313,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_693,
[final] ).
cnf(c_0_1313_1314,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X4),esk47_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| ~ in(X4,X2) ),
c_0_694,
[final] ).
cnf(c_0_1314_1315,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X4),esk47_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| ~ in(X4,X2) ),
c_0_695,
[final] ).
cnf(c_0_1315_1316,lemma,
( empty(X2)
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_696,
[final] ).
cnf(c_0_1316_1317,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_697,
[final] ).
cnf(c_0_1317_1318,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_698,
[final] ).
cnf(c_0_1318_1319,lemma,
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk24_3(X5,X2,X1)) ),
c_0_699,
[final] ).
cnf(c_0_1319_1320,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_700,
[final] ).
cnf(c_0_1320_1321,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| esk17_4(X2,X1,X3,X4) = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_701,
[final] ).
cnf(c_0_1321_1322,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,esk74_2(X1,X2)) != esk73_2(X1,X2)
| ~ in(esk74_2(X1,X2),relation_dom(X1))
| apply(X2,esk75_2(X1,X2)) != esk76_2(X1,X2)
| ~ in(esk75_2(X1,X2),relation_rng(X1)) ),
c_0_702,
[final] ).
cnf(c_0_1322_1323,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_703,
[final] ).
cnf(c_0_1323_1324,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_704,
[final] ).
cnf(c_0_1324_1325,lemma,
( in(ordered_pair(X2,esk58_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_705,
[final] ).
cnf(c_0_1325_1326,lemma,
( in(ordered_pair(esk55_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_706,
[final] ).
cnf(c_0_1326_1327,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| ~ in(X3,X2) ),
c_0_707,
[final] ).
cnf(c_0_1327_1328,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_708,
[final] ).
cnf(c_0_1328_1329,lemma,
( X3 = empty_set
| in(X4,relation_inverse_image(X1,X5))
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ in(apply(X1,X4),X5)
| ~ in(X4,X2) ),
c_0_709,
[final] ).
cnf(c_0_1329_1330,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_710,
[final] ).
cnf(c_0_1330_1331,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| in(apply(esk46_2(X2,X1),X3),esk47_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_711,
[final] ).
cnf(c_0_1331_1332,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| X4 = empty_set
| ~ in(X3,X5)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_of2_as_subset(X1,X5,X4)
| ~ quasi_total(X1,X5,X4)
| ~ function(X1) ),
c_0_712,
[final] ).
cnf(c_0_1332_1333,lemma,
( ordered_pair(esk31_3(X2,X3,X1),esk32_3(X2,X3,X1)) = X1
| ~ in(X1,esk30_2(X2,X3)) ),
c_0_713,
[final] ).
cnf(c_0_1333_1334,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1))
| ~ in(X4,X2) ),
c_0_714,
[final] ).
cnf(c_0_1334_1335,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1))
| ~ in(X4,X2) ),
c_0_715,
[final] ).
cnf(c_0_1335_1336,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_716,
[final] ).
cnf(c_0_1336_1337,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_717,
[final] ).
cnf(c_0_1337_1338,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_718,
[final] ).
cnf(c_0_1338_1339,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| in(X4,X2)
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1))
| ~ in(ordered_pair(X4,X5),esk16_2(X2,X1)) ),
c_0_719,
[final] ).
cnf(c_0_1339_1340,lemma,
( X3 = empty_set
| in(apply(X1,X4),X5)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ in(X4,relation_inverse_image(X1,X5)) ),
c_0_720,
[final] ).
cnf(c_0_1340_1341,lemma,
( in(X3,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk24_3(X5,X2,X1)) ),
c_0_721,
[final] ).
cnf(c_0_1341_1342,lemma,
( in(X4,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk24_3(X5,X2,X1)) ),
c_0_722,
[final] ).
cnf(c_0_1342_1343,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk73_2(X1,X2)) = esk74_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X2,esk75_2(X1,X2)) != esk76_2(X1,X2)
| ~ in(esk75_2(X1,X2),relation_rng(X1)) ),
c_0_723,
[final] ).
cnf(c_0_1343_1344,lemma,
( X2 = function_inverse(X1)
| apply(X1,esk76_2(X1,X2)) = esk75_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk74_2(X1,X2)) != esk73_2(X1,X2)
| ~ in(esk74_2(X1,X2),relation_dom(X1)) ),
c_0_724,
[final] ).
cnf(c_0_1344_1345,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| in(esk61_3(X2,X3,X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_725,
[final] ).
cnf(c_0_1345_1346,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| in(esk59_3(X3,X2,X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_726,
[final] ).
cnf(c_0_1346_1347,lemma,
( quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4)
| X2 != empty_set ),
c_0_727,
[final] ).
cnf(c_0_1347_1348,lemma,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4)
| X2 != empty_set ),
c_0_728,
[final] ).
cnf(c_0_1348_1349,lemma,
( X3 = empty_set
| in(X4,X2)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ in(X4,relation_inverse_image(X1,X5)) ),
c_0_729,
[final] ).
cnf(c_0_1349_1350,lemma,
( X2 = function_inverse(X1)
| in(esk73_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,esk75_2(X1,X2)) != esk76_2(X1,X2)
| ~ in(esk75_2(X1,X2),relation_rng(X1)) ),
c_0_730,
[final] ).
cnf(c_0_1350_1351,lemma,
( X2 = function_inverse(X1)
| in(esk76_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,esk74_2(X1,X2)) != esk73_2(X1,X2)
| ~ in(esk74_2(X1,X2),relation_dom(X1)) ),
c_0_731,
[final] ).
cnf(c_0_1351_1352,lemma,
( X3 = empty_set
| quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4) ),
c_0_732,
[final] ).
cnf(c_0_1352_1353,lemma,
( X3 = empty_set
| relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4) ),
c_0_733,
[final] ).
cnf(c_0_1353_1354,lemma,
( in(X3,cartesian_product2(X4,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk33_3(X4,X2,X1)) ),
c_0_734,
[final] ).
cnf(c_0_1354_1355,lemma,
( in(apply(X1,X2),relation_rng(X1))
| X3 = empty_set
| ~ in(X2,X4)
| ~ relation_of2_as_subset(X1,X4,X3)
| ~ quasi_total(X1,X4,X3)
| ~ function(X1) ),
c_0_735,
[final] ).
cnf(c_0_1355_1356,lemma,
( empty(X2)
| in(X3,cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk25_3(X2,X1,X4)) ),
c_0_736,
[final] ).
cnf(c_0_1356_1357,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1)) ),
c_0_737,
[final] ).
cnf(c_0_1357_1358,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1)) ),
c_0_738,
[final] ).
cnf(c_0_1358_1359,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1)) ),
c_0_739,
[final] ).
cnf(c_0_1359_1360,lemma,
( empty(X2)
| in(ordered_pair(esk40_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk42_2(X2,X1)) ),
c_0_740,
[final] ).
cnf(c_0_1360_1361,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1)) ),
c_0_741,
[final] ).
cnf(c_0_1361_1362,lemma,
( empty(X2)
| in(ordered_pair(esk41_2(X2,X1),X3),X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk43_2(X2,X1)) ),
c_0_742,
[final] ).
cnf(c_0_1362_1363,lemma,
( singleton(esk31_3(X2,X3,X1)) = esk32_3(X2,X3,X1)
| ~ in(X1,esk30_2(X2,X3)) ),
c_0_743,
[final] ).
cnf(c_0_1363_1364,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_744,
[final] ).
cnf(c_0_1364_1365,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk79_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_745,
[final] ).
cnf(c_0_1365_1366,lemma,
( function(X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4)
| X2 != empty_set ),
c_0_746,
[final] ).
cnf(c_0_1366_1367,lemma,
( X3 = empty_set
| function(X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ subset(X3,X4) ),
c_0_747,
[final] ).
cnf(c_0_1367_1368,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_748,
[final] ).
cnf(c_0_1368_1369,lemma,
( in(esk58_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_749,
[final] ).
cnf(c_0_1369_1370,lemma,
( in(esk55_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_750,
[final] ).
cnf(c_0_1370_1371,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1)) ),
c_0_751,
[final] ).
cnf(c_0_1371_1372,lemma,
( empty(X2)
| in(ordered_pair(esk12_2(X2,X1),X3),X1)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk14_2(X2,X1)) ),
c_0_752,
[final] ).
cnf(c_0_1372_1373,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1)) ),
c_0_753,
[final] ).
cnf(c_0_1373_1374,lemma,
( empty(X2)
| in(ordered_pair(esk13_2(X2,X1),X3),X1)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk15_2(X2,X1)) ),
c_0_754,
[final] ).
cnf(c_0_1374_1375,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_755,
[final] ).
cnf(c_0_1375_1376,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_756,
[final] ).
cnf(c_0_1376_1377,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_757,
[final] ).
cnf(c_0_1377_1378,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_758,
[final] ).
cnf(c_0_1378_1379,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_759,
[final] ).
cnf(c_0_1379_1380,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_760,
[final] ).
cnf(c_0_1380_1381,lemma,
( in(esk58_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_761,
[final] ).
cnf(c_0_1381_1382,lemma,
( in(esk55_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_762,
[final] ).
cnf(c_0_1382_1383,lemma,
( in(esk38_3(X3,X1,X2),X3)
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
c_0_763,
[final] ).
cnf(c_0_1383_1384,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_764,
[final] ).
cnf(c_0_1384_1385,lemma,
( in(esk31_3(X2,X3,X1),X2)
| ~ in(X1,esk30_2(X2,X3)) ),
c_0_765,
[final] ).
cnf(c_0_1385_1386,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_766,
[final] ).
cnf(c_0_1386_1387,lemma,
( ordinal(esk38_3(X3,X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
c_0_767,
[final] ).
cnf(c_0_1387_1388,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_768,
[final] ).
cnf(c_0_1388_1389,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_769,
[final] ).
cnf(c_0_1389_1390,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_770,
[final] ).
cnf(c_0_1390_1391,lemma,
( relation_isomorphism(X1,X2,function_inverse(X3))
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_771,
[final] ).
cnf(c_0_1391_1392,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X3) = X3
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1)
| ~ in(X3,X2) ),
c_0_772,
[final] ).
cnf(c_0_1392_1393,lemma,
( empty(X2)
| in(X3,X2)
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_773,
[final] ).
cnf(c_0_1393_1394,lemma,
( empty(X2)
| in(X3,X2)
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_774,
[final] ).
cnf(c_0_1394_1395,lemma,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X4) ),
c_0_775,
[final] ).
cnf(c_0_1395_1396,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_776,
[final] ).
cnf(c_0_1396_1397,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_777,
[final] ).
cnf(c_0_1397_1398,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_778,
[final] ).
cnf(c_0_1398_1399,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_779,
[final] ).
cnf(c_0_1399_1400,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_780,
[final] ).
cnf(c_0_1400_1401,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_781,
[final] ).
cnf(c_0_1401_1402,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_782,
[final] ).
cnf(c_0_1402_1403,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_783,
[final] ).
cnf(c_0_1403_1404,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_784,
[final] ).
cnf(c_0_1404_1405,lemma,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(X4,X3)
| ~ relation_of2_as_subset(X1,X2,X4) ),
c_0_785,
[final] ).
cnf(c_0_1405_1406,lemma,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
c_0_786,
[final] ).
cnf(c_0_1406_1407,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk73_2(X1,X2)) = esk74_2(X1,X2)
| apply(X1,esk76_2(X1,X2)) = esk75_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_787,
[final] ).
cnf(c_0_1407_1408,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_788,
[final] ).
cnf(c_0_1408_1409,lemma,
( in(X1,esk30_2(X2,X3))
| X4 != singleton(X5)
| ~ in(X5,X2)
| ordered_pair(X5,X4) != X1
| ~ in(X1,cartesian_product2(X2,X3)) ),
c_0_789,
[final] ).
cnf(c_0_1409_1410,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_790,
[final] ).
cnf(c_0_1410_1411,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| esk47_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_791,
[final] ).
cnf(c_0_1411_1412,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_792,
[final] ).
cnf(c_0_1412_1413,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_793,
[final] ).
cnf(c_0_1413_1414,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_794,
[final] ).
cnf(c_0_1414_1415,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| in(X3,X2)
| ~ relation(X1)
| ~ in(ordered_pair(X3,X4),esk16_2(X2,X1)) ),
c_0_795,
[final] ).
cnf(c_0_1415_1416,lemma,
( X2 = function_inverse(X1)
| in(esk73_2(X1,X2),relation_rng(X1))
| apply(X1,esk76_2(X1,X2)) = esk75_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_796,
[final] ).
cnf(c_0_1416_1417,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk73_2(X1,X2)) = esk74_2(X1,X2)
| in(esk76_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_797,
[final] ).
cnf(c_0_1417_1418,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_798,
[final] ).
cnf(c_0_1418_1419,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_799,
[final] ).
cnf(c_0_1419_1420,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_800,
[final] ).
cnf(c_0_1420_1421,lemma,
( empty(X2)
| in(esk40_2(X2,X1),esk42_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_801,
[final] ).
cnf(c_0_1421_1422,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_802,
[final] ).
cnf(c_0_1422_1423,lemma,
( empty(X2)
| in(esk41_2(X2,X1),esk43_2(X2,X1))
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_803,
[final] ).
cnf(c_0_1423_1424,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_804,
[final] ).
cnf(c_0_1424_1425,lemma,
( X2 = function_inverse(X1)
| in(esk73_2(X1,X2),relation_rng(X1))
| in(esk76_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_805,
[final] ).
cnf(c_0_1425_1426,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_806,
[final] ).
cnf(c_0_1426_1427,lemma,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ antisymmetric(X1) ),
c_0_807,
[final] ).
cnf(c_0_1427_1428,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
c_0_808,
[final] ).
cnf(c_0_1428_1429,lemma,
( in(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_809,
[final] ).
cnf(c_0_1429_1430,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X2,relation_dom(X1)) ),
c_0_810,
[final] ).
cnf(c_0_1430_1431,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_811,
[final] ).
cnf(c_0_1431_1432,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
c_0_812,
[final] ).
cnf(c_0_1432_1433,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_813,
[final] ).
cnf(c_0_1433_1434,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_814,
[final] ).
cnf(c_0_1434_1435,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_815,
[final] ).
cnf(c_0_1435_1436,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
c_0_816,
[final] ).
cnf(c_0_1436_1437,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_817,
[final] ).
cnf(c_0_1437_1438,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
c_0_818,
[final] ).
cnf(c_0_1438_1439,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
c_0_819,
[final] ).
cnf(c_0_1439_1440,lemma,
( in(X2,relation_restriction(X1,X3))
| ~ relation(X1)
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
c_0_820,
[final] ).
cnf(c_0_1440_1441,lemma,
( relation(esk24_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_821,
[final] ).
cnf(c_0_1441_1442,lemma,
( subset(X1,relation_inverse_image(X2,relation_image(X2,X1)))
| ~ subset(X1,relation_dom(X2))
| ~ relation(X2) ),
c_0_822,
[final] ).
cnf(c_0_1442_1443,lemma,
( epred1_2(X1,X2)
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_823,
[final] ).
cnf(c_0_1443_1444,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
c_0_824,
[final] ).
cnf(c_0_1444_1445,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1) ),
c_0_825,
[final] ).
cnf(c_0_1445_1446,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1) ),
c_0_826,
[final] ).
cnf(c_0_1446_1447,lemma,
( empty(X2)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1)
| esk41_2(X2,X1) != esk40_2(X2,X1) ),
c_0_827,
[final] ).
cnf(c_0_1447_1448,lemma,
( well_ordering(X1)
| ~ relation_isomorphism(X2,X1,X3)
| ~ well_ordering(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_828,
[final] ).
cnf(c_0_1448_1449,lemma,
( esk38_3(X3,X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
c_0_829,
[final] ).
cnf(c_0_1449_1450,lemma,
( subset(fiber(relation_restriction(X1,X2),X3),fiber(X1,X3))
| ~ relation(X1) ),
c_0_830,
[final] ).
cnf(c_0_1450_1451,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_831,
[final] ).
cnf(c_0_1451_1452,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_832,
[final] ).
cnf(c_0_1452_1453,lemma,
( empty(X2)
| in(esk39_2(X2,X1),X2)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_833,
[final] ).
cnf(c_0_1453_1454,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_834,
[final] ).
cnf(c_0_1454_1455,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_835,
[final] ).
cnf(c_0_1455_1456,lemma,
( in(esk19_1(X1),X1)
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
c_0_836,
[final] ).
cnf(c_0_1456_1457,lemma,
( in(esk19_1(X1),X1)
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
c_0_837,
[final] ).
cnf(c_0_1457_1458,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_838,
[final] ).
cnf(c_0_1458_1459,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_839,
[final] ).
cnf(c_0_1459_1460,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_840,
[final] ).
cnf(c_0_1460_1461,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_841,
[final] ).
cnf(c_0_1461_1462,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
c_0_842,
[final] ).
cnf(c_0_1462_1463,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_843,
[final] ).
cnf(c_0_1463_1464,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_844,
[final] ).
cnf(c_0_1464_1465,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
c_0_845,
[final] ).
cnf(c_0_1465_1466,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| in(ordered_pair(X2,X3),esk22_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
c_0_846,
[final] ).
cnf(c_0_1466_1467,lemma,
( in(ordered_pair(X2,X3),esk22_1(X1))
| esk21_1(X1) != esk20_1(X1)
| X3 != singleton(X2)
| ~ in(X2,X1)
| ~ in(X2,X1) ),
c_0_847,
[final] ).
cnf(c_0_1467_1468,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk8_1(X1),esk9_1(X1)),X1) ),
c_0_848,
[final] ).
cnf(c_0_1468_1469,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk9_1(X1),esk8_1(X1)),X1) ),
c_0_849,
[final] ).
cnf(c_0_1469_1470,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk2_1(X1),esk4_1(X1)),X1) ),
c_0_850,
[final] ).
cnf(c_0_1470_1471,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk1_1(X1),esk1_1(X1)),X1) ),
c_0_851,
[final] ).
cnf(c_0_1471_1472,lemma,
( in(X2,esk37_2(X3,X1))
| ~ ordinal(X1)
| ~ in(X4,X3)
| X2 != X4
| ~ ordinal(X4)
| ~ in(X2,succ(X1)) ),
c_0_852,
[final] ).
cnf(c_0_1472_1473,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_853,
[final] ).
cnf(c_0_1473_1474,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk68_2(X2,X1)) != esk68_2(X2,X1) ),
c_0_854,
[final] ).
cnf(c_0_1474_1475,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_855,
[final] ).
cnf(c_0_1475_1476,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_856,
[final] ).
cnf(c_0_1476_1477,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_857,
[final] ).
cnf(c_0_1477_1478,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_858,
[final] ).
cnf(c_0_1478_1479,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation_dom(esk46_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_859,
[final] ).
cnf(c_0_1479_1480,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
c_0_860,
[final] ).
cnf(c_0_1480_1481,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1)) ),
c_0_861,
[final] ).
cnf(c_0_1481_1482,lemma,
( in(X2,cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_862,
[final] ).
cnf(c_0_1482_1483,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_863,
[final] ).
cnf(c_0_1483_1484,lemma,
( empty(X2)
| esk42_2(X2,X1) = esk39_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_864,
[final] ).
cnf(c_0_1484_1485,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| relation(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_865,
[final] ).
cnf(c_0_1485_1486,lemma,
( empty(X2)
| esk39_2(X2,X1) = esk43_2(X2,X1)
| in(esk44_2(X2,X1),X2)
| function(esk46_2(X2,X1))
| ~ relation(X1) ),
c_0_866,
[final] ).
cnf(c_0_1486_1487,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_867,
[final] ).
cnf(c_0_1487_1488,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_868,
[final] ).
cnf(c_0_1488_1489,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_869,
[final] ).
cnf(c_0_1489_1490,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_870,
[final] ).
cnf(c_0_1490_1491,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_871,
[final] ).
cnf(c_0_1491_1492,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_872,
[final] ).
cnf(c_0_1492_1493,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_873,
[final] ).
cnf(c_0_1493_1494,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_874,
[final] ).
cnf(c_0_1494_1495,lemma,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
c_0_875,
[final] ).
cnf(c_0_1495_1496,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_876,
[final] ).
cnf(c_0_1496_1497,lemma,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_877,
[final] ).
cnf(c_0_1497_1498,lemma,
( subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_878,
[final] ).
cnf(c_0_1498_1499,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_879,
[final] ).
cnf(c_0_1499_1500,lemma,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk30_2(X2,X3)) ),
c_0_880,
[final] ).
cnf(c_0_1500_1501,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_881,
[final] ).
cnf(c_0_1501_1502,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_882,
[final] ).
cnf(c_0_1502_1503,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_883,
[final] ).
cnf(c_0_1503_1504,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_884,
[final] ).
cnf(c_0_1504_1505,lemma,
( X2 = empty_set
| ordinal_subset(esk67_2(X2,X1),X3)
| ~ ordinal(X1)
| ~ subset(X2,X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
c_0_885,
[final] ).
cnf(c_0_1505_1506,lemma,
( in(X2,X1)
| esk21_1(X1) != esk20_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_886,
[final] ).
cnf(c_0_1506_1507,lemma,
( in(X2,X1)
| esk21_1(X1) != esk20_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_887,
[final] ).
cnf(c_0_1507_1508,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| in(apply(esk65_1(X1),X2),X2)
| ~ in(X2,X1) ),
c_0_888,
[final] ).
cnf(c_0_1508_1509,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_889,
[final] ).
cnf(c_0_1509_1510,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_890,
[final] ).
cnf(c_0_1510_1511,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_891,
[final] ).
cnf(c_0_1511_1512,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
c_0_892,
[final] ).
cnf(c_0_1512_1513,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_893,
[final] ).
cnf(c_0_1513_1514,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_894,
[final] ).
cnf(c_0_1514_1515,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_895,
[final] ).
cnf(c_0_1515_1516,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_896,
[final] ).
cnf(c_0_1516_1517,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_897,
[final] ).
cnf(c_0_1517_1518,lemma,
( X3 = singleton(X2)
| esk21_1(X1) != esk20_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_898,
[final] ).
cnf(c_0_1518_1519,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_899,
[final] ).
cnf(c_0_1519_1520,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_900,
[final] ).
cnf(c_0_1520_1521,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_901,
[final] ).
cnf(c_0_1521_1522,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_902,
[final] ).
cnf(c_0_1522_1523,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_903,
[final] ).
cnf(c_0_1523_1524,lemma,
( in(X2,succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk37_2(X3,X1)) ),
c_0_904,
[final] ).
cnf(c_0_1524_1525,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
c_0_905,
[final] ).
cnf(c_0_1525_1526,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_906,
[final] ).
cnf(c_0_1526_1527,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_907,
[final] ).
cnf(c_0_1527_1528,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_908,
[final] ).
cnf(c_0_1528_1529,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_909,
[final] ).
cnf(c_0_1529_1530,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_910,
[final] ).
cnf(c_0_1530_1531,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_911,
[final] ).
cnf(c_0_1531_1532,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_912,
[final] ).
cnf(c_0_1532_1533,lemma,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ subset(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_913,
[final] ).
cnf(c_0_1533_1534,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
c_0_914,
[final] ).
cnf(c_0_1534_1535,lemma,
( well_orders(esk5_2(X2,X1),X2)
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
c_0_915,
[final] ).
cnf(c_0_1535_1536,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
c_0_916,
[final] ).
cnf(c_0_1536_1537,lemma,
( empty(X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1) ),
c_0_917,
[final] ).
cnf(c_0_1537_1538,lemma,
( empty(X2)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1) ),
c_0_918,
[final] ).
cnf(c_0_1538_1539,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_919,
[final] ).
cnf(c_0_1539_1540,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_920,
[final] ).
cnf(c_0_1540_1541,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_921,
[final] ).
cnf(c_0_1541_1542,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_922,
[final] ).
cnf(c_0_1542_1543,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
c_0_923,
[final] ).
cnf(c_0_1543_1544,lemma,
( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
c_0_924,
[final] ).
cnf(c_0_1544_1545,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
c_0_925,
[final] ).
cnf(c_0_1545_1546,lemma,
( in(esk48_1(X1),X1)
| apply(esk52_1(X1),X3) = singleton(X3)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
c_0_926,
[final] ).
cnf(c_0_1546_1547,lemma,
( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(X2) ),
c_0_927,
[final] ).
cnf(c_0_1547_1548,lemma,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_928,
[final] ).
cnf(c_0_1548_1549,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| in(apply(esk65_1(X1),X2),X2)
| ~ in(X2,X1) ),
c_0_929,
[final] ).
cnf(c_0_1549_1550,lemma,
( element(X1,powerset(X2))
| ~ in(esk10_2(X1,X2),X2) ),
c_0_930,
[final] ).
cnf(c_0_1550_1551,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_931,
[final] ).
cnf(c_0_1551_1552,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_932,
[final] ).
cnf(c_0_1552_1553,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_933,
[final] ).
cnf(c_0_1553_1554,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_934,
[final] ).
cnf(c_0_1554_1555,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_935,
[final] ).
cnf(c_0_1555_1556,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_936,
[final] ).
cnf(c_0_1556_1557,lemma,
( in(esk51_1(X1),X1)
| apply(esk52_1(X1),X2) = singleton(X2)
| esk50_1(X1) != esk49_1(X1)
| ~ in(X2,X1) ),
c_0_937,
[final] ).
cnf(c_0_1557_1558,lemma,
( in(esk72_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_938,
[final] ).
cnf(c_0_1558_1559,lemma,
( ordinal_subset(esk23_1(X2),X3)
| ~ in(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
c_0_939,
[final] ).
cnf(c_0_1559_1560,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
c_0_940,
[final] ).
cnf(c_0_1560_1561,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
c_0_941,
[final] ).
cnf(c_0_1561_1562,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| apply(esk52_1(X1),X3) = singleton(X3)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
c_0_942,
[final] ).
cnf(c_0_1562_1563,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| apply(esk52_1(X1),X3) = singleton(X3)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
c_0_943,
[final] ).
cnf(c_0_1563_1564,lemma,
( apply(esk52_1(X1),X3) = singleton(X3)
| esk50_1(X1) != esk49_1(X1)
| X2 != singleton(esk51_1(X1))
| ~ in(X3,X1) ),
c_0_944,
[final] ).
cnf(c_0_1564_1565,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ subset(X2,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
c_0_945,
[final] ).
cnf(c_0_1565_1566,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_946,
[final] ).
cnf(c_0_1566_1567,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_947,
[final] ).
cnf(c_0_1567_1568,lemma,
( relation(esk5_2(X2,X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
c_0_948,
[final] ).
cnf(c_0_1568_1569,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_949,
[final] ).
cnf(c_0_1569_1570,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk6_1(X1),esk7_1(X1)),X1)
| ~ relation(X1) ),
c_0_950,
[final] ).
cnf(c_0_1570_1571,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk7_1(X1),esk6_1(X1)),X1)
| ~ relation(X1) ),
c_0_951,
[final] ).
cnf(c_0_1571_1572,lemma,
( transitive(X1)
| in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| ~ relation(X1) ),
c_0_952,
[final] ).
cnf(c_0_1572_1573,lemma,
( transitive(X1)
| in(ordered_pair(esk3_1(X1),esk4_1(X1)),X1)
| ~ relation(X1) ),
c_0_953,
[final] ).
cnf(c_0_1573_1574,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_954,
[final] ).
cnf(c_0_1574_1575,lemma,
( in(X1,esk54_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk54_1(X2)) ),
c_0_955,
[final] ).
cnf(c_0_1575_1576,lemma,
( X1 = empty_set
| in(ordered_pair(esk77_1(X1),esk78_1(X1)),X1)
| ~ relation(X1) ),
c_0_956,
[final] ).
cnf(c_0_1576_1577,lemma,
( relation_image(X1,set_intersection2(relation_dom(X1),X2)) = relation_image(X1,X2)
| ~ relation(X1) ),
c_0_957,
[final] ).
cnf(c_0_1577_1578,lemma,
( in(X1,esk54_1(X2))
| are_equipotent(X1,esk54_1(X2))
| ~ subset(X1,esk54_1(X2)) ),
c_0_958,
[final] ).
cnf(c_0_1578_1579,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
c_0_959,
[final] ).
cnf(c_0_1579_1580,lemma,
( X2 = empty_set
| in(esk67_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
c_0_960,
[final] ).
cnf(c_0_1580_1581,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_961,
[final] ).
cnf(c_0_1581_1582,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_962,
[final] ).
cnf(c_0_1582_1583,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_963,
[final] ).
cnf(c_0_1583_1584,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_964,
[final] ).
cnf(c_0_1584_1585,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
c_0_965,
[final] ).
cnf(c_0_1585_1586,lemma,
( X1 = identity_relation(X2)
| in(esk68_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
c_0_966,
[final] ).
cnf(c_0_1586_1587,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_967,
[final] ).
cnf(c_0_1587_1588,lemma,
( ~ in(X1,X2)
| ~ in(X3,X1)
| ~ in(X2,X3) ),
c_0_968,
[final] ).
cnf(c_0_1588_1589,lemma,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X1) ),
c_0_969,
[final] ).
cnf(c_0_1589_1590,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_970,
[final] ).
cnf(c_0_1590_1591,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_971,
[final] ).
cnf(c_0_1591_1592,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_972,
[final] ).
cnf(c_0_1592_1593,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_973,
[final] ).
cnf(c_0_1593_1594,lemma,
( X2 = empty_set
| relation_inverse_image(X1,X2) != empty_set
| ~ subset(X2,relation_rng(X1))
| ~ relation(X1) ),
c_0_974,
[final] ).
cnf(c_0_1594_1595,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk70_1(X1)),X1) ),
c_0_975,
[final] ).
cnf(c_0_1595_1596,lemma,
( X2 = empty_set
| ordinal(esk67_2(X2,X1))
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
c_0_976,
[final] ).
cnf(c_0_1596_1597,lemma,
( relation_rng_restriction(X2,relation_dom_restriction(X1,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_977,
[final] ).
cnf(c_0_1597_1598,lemma,
( relation_dom_restriction(relation_rng_restriction(X2,X1),X2) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_978,
[final] ).
cnf(c_0_1598_1599,lemma,
( in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(succ(X1),X2) ),
c_0_979,
[final] ).
cnf(c_0_1599_1600,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_980,
[final] ).
cnf(c_0_1600_1601,lemma,
( element(X1,powerset(X2))
| in(esk10_2(X1,X2),X1) ),
c_0_981,
[final] ).
cnf(c_0_1601_1602,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
c_0_982,
[final] ).
cnf(c_0_1602_1603,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_983,
[final] ).
cnf(c_0_1603_1604,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_984,
[final] ).
cnf(c_0_1604_1605,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_985,
[final] ).
cnf(c_0_1605_1606,lemma,
( in(powerset(X1),esk54_1(X2))
| ~ in(X1,esk54_1(X2)) ),
c_0_986,
[final] ).
cnf(c_0_1606_1607,lemma,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
c_0_987,
[final] ).
cnf(c_0_1607_1608,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
c_0_988,
[final] ).
cnf(c_0_1608_1609,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
c_0_989,
[final] ).
cnf(c_0_1609_1610,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_990,
[final] ).
cnf(c_0_1610_1611,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_991,
[final] ).
cnf(c_0_1611_1612,lemma,
( disjoint(X1,X2)
| in(esk69_2(X1,X2),X1) ),
c_0_992,
[final] ).
cnf(c_0_1612_1613,lemma,
( disjoint(X1,X2)
| in(esk69_2(X1,X2),X2) ),
c_0_993,
[final] ).
cnf(c_0_1613_1614,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_994,
[final] ).
cnf(c_0_1614_1615,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_995,
[final] ).
cnf(c_0_1615_1616,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_996,
[final] ).
cnf(c_0_1616_1617,lemma,
( ordinal(X1)
| ~ subset(esk66_1(X1),X1)
| ~ ordinal(esk66_1(X1)) ),
c_0_997,
[final] ).
cnf(c_0_1617_1618,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
c_0_998,
[final] ).
cnf(c_0_1618_1619,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
c_0_999,
[final] ).
cnf(c_0_1619_1620,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_1000,
[final] ).
cnf(c_0_1620_1621,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1 ),
c_0_1001,
[final] ).
cnf(c_0_1621_1622,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| relation(esk52_1(X1)) ),
c_0_1002,
[final] ).
cnf(c_0_1622_1623,lemma,
( in(esk48_1(X1),X1)
| in(esk51_1(X1),X1)
| function(esk52_1(X1)) ),
c_0_1003,
[final] ).
cnf(c_0_1623_1624,lemma,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
c_0_1004,
[final] ).
cnf(c_0_1624_1625,lemma,
( in(X1,esk36_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
c_0_1005,
[final] ).
cnf(c_0_1625_1626,lemma,
( in(esk23_1(X2),X2)
| ~ in(X1,X2)
| ~ ordinal(X1) ),
c_0_1006,
[final] ).
cnf(c_0_1626_1627,lemma,
( in(esk48_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1
| X2 != singleton(esk51_1(X1)) ),
c_0_1007,
[final] ).
cnf(c_0_1627_1628,lemma,
( in(esk48_1(X1),X1)
| relation(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
c_0_1008,
[final] ).
cnf(c_0_1628_1629,lemma,
( in(esk48_1(X1),X1)
| function(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
c_0_1009,
[final] ).
cnf(c_0_1629_1630,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_1010,
[final] ).
cnf(c_0_1630_1631,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
c_0_1011,
[final] ).
cnf(c_0_1631_1632,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
c_0_1012,
[final] ).
cnf(c_0_1632_1633,lemma,
( apply(esk53_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_1013,
[final] ).
cnf(c_0_1633_1634,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_1014,
[final] ).
cnf(c_0_1634_1635,lemma,
( in(X1,X2)
| ~ in(X1,esk36_1(X2)) ),
c_0_1015,
[final] ).
cnf(c_0_1635_1636,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_1016,
[final] ).
cnf(c_0_1636_1637,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_1017,
[final] ).
cnf(c_0_1637_1638,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_1018,
[final] ).
cnf(c_0_1638_1639,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1 ),
c_0_1019,
[final] ).
cnf(c_0_1639_1640,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1 ),
c_0_1020,
[final] ).
cnf(c_0_1640_1641,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| in(esk51_1(X1),X1)
| relation(esk52_1(X1)) ),
c_0_1021,
[final] ).
cnf(c_0_1641_1642,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| in(esk51_1(X1),X1)
| function(esk52_1(X1)) ),
c_0_1022,
[final] ).
cnf(c_0_1642_1643,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| in(esk51_1(X1),X1)
| relation(esk52_1(X1)) ),
c_0_1023,
[final] ).
cnf(c_0_1643_1644,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| in(esk51_1(X1),X1)
| function(esk52_1(X1)) ),
c_0_1024,
[final] ).
cnf(c_0_1644_1645,lemma,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
c_0_1025,
[final] ).
cnf(c_0_1645_1646,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_1026,
[final] ).
cnf(c_0_1646_1647,lemma,
( in(esk51_1(X1),X1)
| relation_dom(esk52_1(X1)) = X1
| esk50_1(X1) != esk49_1(X1) ),
c_0_1027,
[final] ).
cnf(c_0_1647_1648,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ well_ordering(X1)
| ~ relation(X1) ),
c_0_1028,
[final] ).
cnf(c_0_1648_1649,lemma,
( well_founded_relation(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
c_0_1029,
[final] ).
cnf(c_0_1649_1650,lemma,
( antisymmetric(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
c_0_1030,
[final] ).
cnf(c_0_1650_1651,lemma,
( transitive(relation_restriction(X1,X2))
| ~ transitive(X1)
| ~ relation(X1) ),
c_0_1031,
[final] ).
cnf(c_0_1651_1652,lemma,
( connected(relation_restriction(X1,X2))
| ~ connected(X1)
| ~ relation(X1) ),
c_0_1032,
[final] ).
cnf(c_0_1652_1653,lemma,
( reflexive(relation_restriction(X1,X2))
| ~ reflexive(X1)
| ~ relation(X1) ),
c_0_1033,
[final] ).
cnf(c_0_1653_1654,lemma,
( in(esk51_1(X1),X1)
| relation(esk52_1(X1))
| esk50_1(X1) != esk49_1(X1) ),
c_0_1034,
[final] ).
cnf(c_0_1654_1655,lemma,
( in(esk51_1(X1),X1)
| function(esk52_1(X1))
| esk50_1(X1) != esk49_1(X1) ),
c_0_1035,
[final] ).
cnf(c_0_1655_1656,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_1036,
[final] ).
cnf(c_0_1656_1657,lemma,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_orders(X1,relation_field(X1)) ),
c_0_1037,
[final] ).
cnf(c_0_1657_1658,lemma,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
c_0_1038,
[final] ).
cnf(c_0_1658_1659,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_1039,
[final] ).
cnf(c_0_1659_1660,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
c_0_1040,
[final] ).
cnf(c_0_1660_1661,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_1041,
[final] ).
cnf(c_0_1661_1662,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| relation_dom(esk52_1(X1)) = X1
| X2 != singleton(esk51_1(X1)) ),
c_0_1042,
[final] ).
cnf(c_0_1662_1663,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| relation_dom(esk52_1(X1)) = X1
| X2 != singleton(esk51_1(X1)) ),
c_0_1043,
[final] ).
cnf(c_0_1663_1664,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_1044,
[final] ).
cnf(c_0_1664_1665,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_1045,
[final] ).
cnf(c_0_1665_1666,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_1046,
[final] ).
cnf(c_0_1666_1667,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_1047,
[final] ).
cnf(c_0_1667_1668,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| relation(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
c_0_1048,
[final] ).
cnf(c_0_1668_1669,lemma,
( singleton(esk48_1(X1)) = esk49_1(X1)
| function(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
c_0_1049,
[final] ).
cnf(c_0_1669_1670,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| relation(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
c_0_1050,
[final] ).
cnf(c_0_1670_1671,lemma,
( singleton(esk48_1(X1)) = esk50_1(X1)
| function(esk52_1(X1))
| X2 != singleton(esk51_1(X1)) ),
c_0_1051,
[final] ).
cnf(c_0_1671_1672,lemma,
( relation_dom(esk52_1(X1)) = X1
| esk50_1(X1) != esk49_1(X1)
| X2 != singleton(esk51_1(X1)) ),
c_0_1052,
[final] ).
cnf(c_0_1672_1673,lemma,
( relation(esk52_1(X1))
| esk50_1(X1) != esk49_1(X1)
| X2 != singleton(esk51_1(X1)) ),
c_0_1053,
[final] ).
cnf(c_0_1673_1674,lemma,
( function(esk52_1(X1))
| esk50_1(X1) != esk49_1(X1)
| X2 != singleton(esk51_1(X1)) ),
c_0_1054,
[final] ).
cnf(c_0_1674_1675,lemma,
( relation_composition(identity_relation(X2),X1) = relation_dom_restriction(X1,X2)
| ~ relation(X1) ),
c_0_1055,
[final] ).
cnf(c_0_1675_1676,lemma,
( ordinal(esk23_1(X2))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
c_0_1056,
[final] ).
cnf(c_0_1676_1677,lemma,
subset(X1,set_union2(X1,X2)),
c_0_1057,
[final] ).
cnf(c_0_1677_1678,lemma,
subset(set_difference(X1,X2),X1),
c_0_1058,
[final] ).
cnf(c_0_1678_1679,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_1059,
[final] ).
cnf(c_0_1679_1680,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_1060,
[final] ).
cnf(c_0_1680_1681,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_1061,
[final] ).
cnf(c_0_1681_1682,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_1062,
[final] ).
cnf(c_0_1682_1683,lemma,
( connected(X1)
| in(esk8_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1063,
[final] ).
cnf(c_0_1683_1684,lemma,
( connected(X1)
| in(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1064,
[final] ).
cnf(c_0_1684_1685,lemma,
( reflexive(X1)
| in(esk1_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1065,
[final] ).
cnf(c_0_1685_1686,negated_conjecture,
~ finite(set_intersection2(esk56_0,esk57_0)),
c_0_1066,
[final] ).
cnf(c_0_1686_1687,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_1067,
[final] ).
cnf(c_0_1687_1688,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_1068,
[final] ).
cnf(c_0_1688_1689,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_1069,
[final] ).
cnf(c_0_1689_1690,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_1070,
[final] ).
cnf(c_0_1690_1691,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_1071,
[final] ).
cnf(c_0_1691_1692,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_1072,
[final] ).
cnf(c_0_1692_1693,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_1073,
[final] ).
cnf(c_0_1693_1694,lemma,
( ordinal(X1)
| ~ in(X1,esk36_1(X2)) ),
c_0_1074,
[final] ).
cnf(c_0_1694_1695,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| relation_dom(esk65_1(X1)) = X1 ),
c_0_1075,
[final] ).
cnf(c_0_1695_1696,lemma,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_1076,
[final] ).
cnf(c_0_1696_1697,lemma,
( relation_rng(function_inverse(X1)) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_1077,
[final] ).
cnf(c_0_1697_1698,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_1078,
[final] ).
cnf(c_0_1698_1699,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| relation(esk65_1(X1)) ),
c_0_1079,
[final] ).
cnf(c_0_1699_1700,lemma,
( empty(X1)
| in(esk64_1(X1),X1)
| function(esk65_1(X1)) ),
c_0_1080,
[final] ).
cnf(c_0_1700_1701,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_1081,
[final] ).
cnf(c_0_1701_1702,lemma,
( well_orders(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1082,
[final] ).
cnf(c_0_1702_1703,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
c_0_1083,
[final] ).
cnf(c_0_1703_1704,plain,
( reflexive(X1)
| ~ epred1_2(X1,X2)
| ~ reflexive(X2) ),
c_0_1084,
[final] ).
cnf(c_0_1704_1705,plain,
( transitive(X1)
| ~ epred1_2(X1,X2)
| ~ transitive(X2) ),
c_0_1085,
[final] ).
cnf(c_0_1705_1706,plain,
( connected(X1)
| ~ epred1_2(X1,X2)
| ~ connected(X2) ),
c_0_1086,
[final] ).
cnf(c_0_1706_1707,plain,
( antisymmetric(X1)
| ~ epred1_2(X1,X2)
| ~ antisymmetric(X2) ),
c_0_1087,
[final] ).
cnf(c_0_1707_1708,plain,
( well_founded_relation(X1)
| ~ epred1_2(X1,X2)
| ~ well_founded_relation(X2) ),
c_0_1088,
[final] ).
cnf(c_0_1708_1709,lemma,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
c_0_1089,
[final] ).
cnf(c_0_1709_1710,lemma,
( finite(X1)
| ~ finite(X2)
| ~ subset(X1,X2) ),
c_0_1090,
[final] ).
cnf(c_0_1710_1711,lemma,
( being_limit_ordinal(X1)
| in(esk70_1(X1),X1)
| ~ ordinal(X1) ),
c_0_1091,
[final] ).
cnf(c_0_1711_1712,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1092,
[final] ).
cnf(c_0_1712_1713,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_1093,
[final] ).
cnf(c_0_1713_1714,lemma,
pair_first(ordered_pair(X1,X2)) = X1,
c_0_1094,
[final] ).
cnf(c_0_1714_1715,lemma,
pair_second(ordered_pair(X1,X2)) = X2,
c_0_1095,
[final] ).
cnf(c_0_1715_1716,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
c_0_1096,
[final] ).
cnf(c_0_1716_1717,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
c_0_1097,
[final] ).
cnf(c_0_1717_1718,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
c_0_1098,
[final] ).
cnf(c_0_1718_1719,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
c_0_1099,
[final] ).
cnf(c_0_1719_1720,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_1100,
[final] ).
cnf(c_0_1720_1721,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_1101,
[final] ).
cnf(c_0_1721_1722,lemma,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| X1 != succ(X2)
| ~ ordinal(X2) ),
c_0_1102,
[final] ).
cnf(c_0_1722_1723,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_1103,
[final] ).
cnf(c_0_1723_1724,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_1104,
[final] ).
cnf(c_0_1724_1725,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
c_0_1105,
[final] ).
cnf(c_0_1725_1726,lemma,
( ordinal(X1)
| in(esk66_1(X1),X1) ),
c_0_1106,
[final] ).
cnf(c_0_1726_1727,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| relation(esk22_1(X1)) ),
c_0_1107,
[final] ).
cnf(c_0_1727_1728,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| function(esk22_1(X1)) ),
c_0_1108,
[final] ).
cnf(c_0_1728_1729,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| relation(esk22_1(X1)) ),
c_0_1109,
[final] ).
cnf(c_0_1729_1730,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| function(esk22_1(X1)) ),
c_0_1110,
[final] ).
cnf(c_0_1730_1731,lemma,
( connected(X1)
| ~ relation(X1)
| esk8_1(X1) != esk9_1(X1) ),
c_0_1111,
[final] ).
cnf(c_0_1731_1732,lemma,
( antisymmetric(X1)
| ~ relation(X1)
| esk7_1(X1) != esk6_1(X1) ),
c_0_1112,
[final] ).
cnf(c_0_1732_1733,lemma,
( relation(esk22_1(X1))
| esk21_1(X1) != esk20_1(X1) ),
c_0_1113,
[final] ).
cnf(c_0_1733_1734,lemma,
( function(esk22_1(X1))
| esk21_1(X1) != esk20_1(X1) ),
c_0_1114,
[final] ).
cnf(c_0_1734_1735,lemma,
( being_limit_ordinal(X1)
| succ(esk71_1(X1)) = X1
| ~ ordinal(X1) ),
c_0_1115,
[final] ).
cnf(c_0_1735_1736,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_1116,
[final] ).
cnf(c_0_1736_1737,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_1117,
[final] ).
cnf(c_0_1737_1738,lemma,
( being_limit_ordinal(X1)
| ordinal(esk71_1(X1))
| ~ ordinal(X1) ),
c_0_1118,
[final] ).
cnf(c_0_1738_1739,lemma,
( being_limit_ordinal(X1)
| ordinal(esk70_1(X1))
| ~ ordinal(X1) ),
c_0_1119,
[final] ).
cnf(c_0_1739_1740,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_1120,
[final] ).
cnf(c_0_1740_1741,lemma,
( relation_dom(relation_inverse(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_1121,
[final] ).
cnf(c_0_1741_1742,lemma,
( relation_rng(relation_inverse(X1)) = relation_dom(X1)
| ~ relation(X1) ),
c_0_1122,
[final] ).
cnf(c_0_1742_1743,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| relation_dom(esk65_1(X1)) = X1 ),
c_0_1123,
[final] ).
cnf(c_0_1743_1744,lemma,
well_orders(esk63_1(X1),X1),
c_0_1124,
[final] ).
cnf(c_0_1744_1745,lemma,
in(X1,esk54_1(X1)),
c_0_1125,
[final] ).
cnf(c_0_1745_1746,lemma,
in(X1,succ(X1)),
c_0_1126,
[final] ).
cnf(c_0_1746_1747,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| relation(esk65_1(X1)) ),
c_0_1127,
[final] ).
cnf(c_0_1747_1748,lemma,
( empty(X1)
| esk64_1(X1) = empty_set
| function(esk65_1(X1)) ),
c_0_1128,
[final] ).
cnf(c_0_1748_1749,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_1129,
[final] ).
cnf(c_0_1749_1750,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_1130,
[final] ).
cnf(c_0_1750_1751,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_1131,
[final] ).
cnf(c_0_1751_1752,lemma,
( well_ordering(inclusion_relation(X1))
| ~ ordinal(X1) ),
c_0_1132,
[final] ).
cnf(c_0_1752_1753,lemma,
( well_founded_relation(inclusion_relation(X1))
| ~ ordinal(X1) ),
c_0_1133,
[final] ).
cnf(c_0_1753_1754,lemma,
( connected(inclusion_relation(X1))
| ~ ordinal(X1) ),
c_0_1134,
[final] ).
cnf(c_0_1754_1755,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_1135,
[final] ).
cnf(c_0_1755_1756,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_1136,
[final] ).
cnf(c_0_1756_1757,lemma,
subset(empty_set,X1),
c_0_1137,
[final] ).
cnf(c_0_1757_1758,lemma,
union(powerset(X1)) = X1,
c_0_1138,
[final] ).
cnf(c_0_1758_1759,lemma,
relation_dom(identity_relation(X1)) = X1,
c_0_1139,
[final] ).
cnf(c_0_1759_1760,lemma,
relation_rng(identity_relation(X1)) = X1,
c_0_1140,
[final] ).
cnf(c_0_1760_1761,lemma,
relation_dom(esk53_1(X1)) = X1,
c_0_1141,
[final] ).
cnf(c_0_1761_1762,lemma,
antisymmetric(inclusion_relation(X1)),
c_0_1142,
[final] ).
cnf(c_0_1762_1763,lemma,
transitive(inclusion_relation(X1)),
c_0_1143,
[final] ).
cnf(c_0_1763_1764,lemma,
reflexive(inclusion_relation(X1)),
c_0_1144,
[final] ).
cnf(c_0_1764_1765,lemma,
relation(esk63_1(X1)),
c_0_1145,
[final] ).
cnf(c_0_1765_1766,lemma,
relation(esk53_1(X1)),
c_0_1146,
[final] ).
cnf(c_0_1766_1767,lemma,
function(esk53_1(X1)),
c_0_1147,
[final] ).
cnf(c_0_1767_1768,lemma,
singleton(X1) != empty_set,
c_0_1148,
[final] ).
cnf(c_0_1768_1769,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_1149,
[final] ).
cnf(c_0_1769_1770,lemma,
relation_dom(empty_set) = empty_set,
c_0_1150,
[final] ).
cnf(c_0_1770_1771,lemma,
relation_rng(empty_set) = empty_set,
c_0_1151,
[final] ).
cnf(c_0_1771_1772,negated_conjecture,
finite(esk56_0),
c_0_1152,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_4203,negated_conjecture,
finite(sk2_esk56_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_2821a5.p',c_0_1771) ).
cnf(c_6400,negated_conjecture,
finite(sk2_esk56_0),
inference(copy,[status(esa)],[c_4203]) ).
cnf(c_6972,negated_conjecture,
finite(sk2_esk56_0),
inference(copy,[status(esa)],[c_6400]) ).
cnf(c_6995,negated_conjecture,
finite(sk2_esk56_0),
inference(copy,[status(esa)],[c_6972]) ).
cnf(c_8392,negated_conjecture,
finite(sk2_esk56_0),
inference(copy,[status(esa)],[c_6995]) ).
cnf(c_20181,negated_conjecture,
finite(sk2_esk56_0),
inference(copy,[status(esa)],[c_8392]) ).
cnf(c_374,plain,
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_2821a5.p',c_0_2235_1) ).
cnf(c_13065,plain,
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ),
inference(copy,[status(esa)],[c_374]) ).
cnf(c_20189,plain,
finite(set_intersection2(sk2_esk56_0,X0)),
inference(resolution,[status(thm)],[c_20181,c_13065]) ).
cnf(c_20190,plain,
finite(set_intersection2(sk2_esk56_0,X0)),
inference(rewriting,[status(thm)],[c_20189]) ).
cnf(c_4175,negated_conjecture,
~ finite(set_intersection2(sk2_esk56_0,sk2_esk57_0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_2821a5.p',c_0_1685) ).
cnf(c_6398,negated_conjecture,
~ finite(set_intersection2(sk2_esk56_0,sk2_esk57_0)),
inference(copy,[status(esa)],[c_4175]) ).
cnf(c_6944,negated_conjecture,
~ finite(set_intersection2(sk2_esk56_0,sk2_esk57_0)),
inference(copy,[status(esa)],[c_6398]) ).
cnf(c_7023,negated_conjecture,
~ finite(set_intersection2(sk2_esk56_0,sk2_esk57_0)),
inference(copy,[status(esa)],[c_6944]) ).
cnf(c_8365,negated_conjecture,
~ finite(set_intersection2(sk2_esk56_0,sk2_esk57_0)),
inference(copy,[status(esa)],[c_7023]) ).
cnf(c_20127,negated_conjecture,
~ finite(set_intersection2(sk2_esk56_0,sk2_esk57_0)),
inference(copy,[status(esa)],[c_8365]) ).
cnf(c_20203,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_20190,c_20127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU295+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n029.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 04:25:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.59 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.59 % FOF problem with conjecture
% 0.19/0.59 % 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_d9c61d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_2821a5.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_233c98 | grep -v "SZS"
% 0.44/0.61
% 0.44/0.61 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.44/0.61
% 0.44/0.61 %
% 0.44/0.61 % ------ iProver source info
% 0.44/0.61
% 0.44/0.61 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.44/0.61 % git: non_committed_changes: true
% 0.44/0.61 % git: last_make_outside_of_git: true
% 0.44/0.61
% 0.44/0.61 %
% 0.44/0.61 % ------ Input Options
% 0.44/0.61
% 0.44/0.61 % --out_options all
% 0.44/0.61 % --tptp_safe_out true
% 0.44/0.61 % --problem_path ""
% 0.44/0.61 % --include_path ""
% 0.44/0.61 % --clausifier .//eprover
% 0.44/0.61 % --clausifier_options --tstp-format
% 0.44/0.61 % --stdin false
% 0.44/0.61 % --dbg_backtrace false
% 0.44/0.61 % --dbg_dump_prop_clauses false
% 0.44/0.61 % --dbg_dump_prop_clauses_file -
% 0.44/0.61 % --dbg_out_stat false
% 0.44/0.61
% 0.44/0.61 % ------ General Options
% 0.44/0.61
% 0.44/0.61 % --fof false
% 0.44/0.61 % --time_out_real 150.
% 0.44/0.61 % --time_out_prep_mult 0.2
% 0.44/0.61 % --time_out_virtual -1.
% 0.44/0.61 % --schedule none
% 0.44/0.61 % --ground_splitting input
% 0.44/0.61 % --splitting_nvd 16
% 0.44/0.61 % --non_eq_to_eq false
% 0.44/0.61 % --prep_gs_sim true
% 0.44/0.61 % --prep_unflatten false
% 0.44/0.61 % --prep_res_sim true
% 0.44/0.61 % --prep_upred true
% 0.44/0.61 % --res_sim_input true
% 0.44/0.61 % --clause_weak_htbl true
% 0.44/0.61 % --gc_record_bc_elim false
% 0.44/0.61 % --symbol_type_check false
% 0.44/0.61 % --clausify_out false
% 0.44/0.61 % --large_theory_mode false
% 0.44/0.61 % --prep_sem_filter none
% 0.44/0.61 % --prep_sem_filter_out false
% 0.44/0.61 % --preprocessed_out false
% 0.44/0.61 % --sub_typing false
% 0.44/0.61 % --brand_transform false
% 0.44/0.61 % --pure_diseq_elim true
% 0.44/0.61 % --min_unsat_core false
% 0.44/0.61 % --pred_elim true
% 0.44/0.61 % --add_important_lit false
% 0.44/0.61 % --soft_assumptions false
% 0.44/0.61 % --reset_solvers false
% 0.44/0.61 % --bc_imp_inh []
% 0.44/0.61 % --conj_cone_tolerance 1.5
% 0.44/0.61 % --prolific_symb_bound 500
% 0.44/0.61 % --lt_threshold 2000
% 0.44/0.61
% 0.44/0.61 % ------ SAT Options
% 0.44/0.61
% 0.44/0.61 % --sat_mode false
% 0.44/0.61 % --sat_fm_restart_options ""
% 0.44/0.61 % --sat_gr_def false
% 0.44/0.61 % --sat_epr_types true
% 0.44/0.61 % --sat_non_cyclic_types false
% 0.44/0.61 % --sat_finite_models false
% 0.44/0.61 % --sat_fm_lemmas false
% 0.44/0.61 % --sat_fm_prep false
% 0.44/0.61 % --sat_fm_uc_incr true
% 0.44/0.61 % --sat_out_model small
% 0.44/0.61 % --sat_out_clauses false
% 0.44/0.61
% 0.44/0.61 % ------ QBF Options
% 0.44/0.61
% 0.44/0.61 % --qbf_mode false
% 0.44/0.61 % --qbf_elim_univ true
% 0.44/0.61 % --qbf_sk_in true
% 0.44/0.61 % --qbf_pred_elim true
% 0.44/0.61 % --qbf_split 32
% 0.44/0.61
% 0.44/0.61 % ------ BMC1 Options
% 0.44/0.61
% 0.44/0.61 % --bmc1_incremental false
% 0.44/0.61 % --bmc1_axioms reachable_all
% 0.44/0.61 % --bmc1_min_bound 0
% 0.44/0.61 % --bmc1_max_bound -1
% 0.44/0.61 % --bmc1_max_bound_default -1
% 0.44/0.61 % --bmc1_symbol_reachability true
% 0.44/0.61 % --bmc1_property_lemmas false
% 0.44/0.61 % --bmc1_k_induction false
% 0.44/0.61 % --bmc1_non_equiv_states false
% 0.44/0.61 % --bmc1_deadlock false
% 0.44/0.61 % --bmc1_ucm false
% 0.44/0.61 % --bmc1_add_unsat_core none
% 0.44/0.61 % --bmc1_unsat_core_children false
% 0.44/0.61 % --bmc1_unsat_core_extrapolate_axioms false
% 0.44/0.61 % --bmc1_out_stat full
% 0.44/0.61 % --bmc1_ground_init false
% 0.44/0.61 % --bmc1_pre_inst_next_state false
% 0.44/0.61 % --bmc1_pre_inst_state false
% 0.44/0.61 % --bmc1_pre_inst_reach_state false
% 0.44/0.61 % --bmc1_out_unsat_core false
% 0.44/0.61 % --bmc1_aig_witness_out false
% 0.44/0.61 % --bmc1_verbose false
% 0.44/0.61 % --bmc1_dump_clauses_tptp false
% 0.44/0.74 % --bmc1_dump_unsat_core_tptp false
% 0.44/0.74 % --bmc1_dump_file -
% 0.44/0.74 % --bmc1_ucm_expand_uc_limit 128
% 0.44/0.74 % --bmc1_ucm_n_expand_iterations 6
% 0.44/0.74 % --bmc1_ucm_extend_mode 1
% 0.44/0.74 % --bmc1_ucm_init_mode 2
% 0.44/0.74 % --bmc1_ucm_cone_mode none
% 0.44/0.74 % --bmc1_ucm_reduced_relation_type 0
% 0.44/0.74 % --bmc1_ucm_relax_model 4
% 0.44/0.74 % --bmc1_ucm_full_tr_after_sat true
% 0.44/0.74 % --bmc1_ucm_expand_neg_assumptions false
% 0.44/0.74 % --bmc1_ucm_layered_model none
% 0.44/0.74 % --bmc1_ucm_max_lemma_size 10
% 0.44/0.74
% 0.44/0.74 % ------ AIG Options
% 0.44/0.74
% 0.44/0.74 % --aig_mode false
% 0.44/0.74
% 0.44/0.74 % ------ Instantiation Options
% 0.44/0.74
% 0.44/0.74 % --instantiation_flag true
% 0.44/0.74 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.44/0.74 % --inst_solver_per_active 750
% 0.44/0.74 % --inst_solver_calls_frac 0.5
% 0.44/0.74 % --inst_passive_queue_type priority_queues
% 0.44/0.74 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.44/0.74 % --inst_passive_queues_freq [25;2]
% 0.44/0.74 % --inst_dismatching true
% 0.44/0.74 % --inst_eager_unprocessed_to_passive true
% 0.44/0.74 % --inst_prop_sim_given true
% 0.44/0.74 % --inst_prop_sim_new false
% 0.44/0.74 % --inst_orphan_elimination true
% 0.44/0.74 % --inst_learning_loop_flag true
% 0.44/0.74 % --inst_learning_start 3000
% 0.44/0.74 % --inst_learning_factor 2
% 0.44/0.74 % --inst_start_prop_sim_after_learn 3
% 0.44/0.74 % --inst_sel_renew solver
% 0.44/0.74 % --inst_lit_activity_flag true
% 0.44/0.74 % --inst_out_proof true
% 0.44/0.74
% 0.44/0.74 % ------ Resolution Options
% 0.44/0.74
% 0.44/0.74 % --resolution_flag true
% 0.44/0.74 % --res_lit_sel kbo_max
% 0.44/0.74 % --res_to_prop_solver none
% 0.44/0.74 % --res_prop_simpl_new false
% 0.44/0.74 % --res_prop_simpl_given false
% 0.44/0.74 % --res_passive_queue_type priority_queues
% 0.44/0.74 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.44/0.74 % --res_passive_queues_freq [15;5]
% 0.44/0.74 % --res_forward_subs full
% 0.44/0.74 % --res_backward_subs full
% 0.44/0.74 % --res_forward_subs_resolution true
% 0.44/0.74 % --res_backward_subs_resolution true
% 0.44/0.74 % --res_orphan_elimination false
% 0.44/0.74 % --res_time_limit 1000.
% 0.44/0.74 % --res_out_proof true
% 0.44/0.74 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d9c61d.s
% 0.44/0.74 % --modulo true
% 0.44/0.74
% 0.44/0.74 % ------ Combination Options
% 0.44/0.74
% 0.44/0.74 % --comb_res_mult 1000
% 0.44/0.74 % --comb_inst_mult 300
% 0.44/0.74 % ------
% 0.44/0.74
% 0.44/0.74 % ------ Parsing...%
% 0.44/0.74
% 0.44/0.74
% 0.44/0.74 % ------ Statistics
% 0.44/0.74
% 0.44/0.74 % ------ General
% 0.44/0.74
% 0.44/0.74 % num_of_input_clauses: 2326
% 0.44/0.74 % num_of_input_neg_conjectures: 0
% 0.44/0.74 % num_of_splits: 0
% 0.44/0.74 % num_of_split_atoms: 0
% 0.44/0.74 % num_of_sem_filtered_clauses: 0
% 0.44/0.74 % num_of_subtypes: 0
% 0.44/0.74 % monotx_restored_types: 0
% 0.44/0.74 % sat_num_of_epr_types: 0
% 0.44/0.74 % sat_num_of_non_cyclic_types: 0
% 0.44/0.74 % sat_guarded_non_collapsed_types: 0
% 0.44/0.74 % is_epr: 0
% 0.44/0.74 % is_horn: 0
% 0.44/0.74 % has_eq: 0
% 0.44/0.74 % num_pure_diseq_elim: 0
% 0.44/0.74 % simp_replaced_by: 0
% 0.44/0.74 % res_preprocessed: 0
% 0.44/0.74 % prep_upred: 0
% 0.44/0.74 % prep_unflattend: 0
% 0.44/0.74 % pred_elim_cands: 0
% 0.44/0.74 % pred_elim: 0
% 0.44/0.74 % pred_elim_cl: 0
% 0.44/0.74 % pred_elim_cycles: 0
% 0.44/0.74 % forced_gc_time: 0
% 0.44/0.74 % gc_basic_clause_elim: 0
% 0.44/0.74 % parsing_time: 0.
% 0.44/0.74 % sem_filter_time: 0.
% 0.44/0.74 % pred_elim_time: 0.
% 0.44/0.74 % out_proof_time: 0.
% 0.44/0.74 % monotx_time: 0.
% 0.44/0.74 % subtype_inf_time: 0.
% 0.44/0.74 % unif_index_cands_time: 0.
% 0.44/0.74 % Fatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_2821a5.p line: 2329 near token: '!='")
% 0.44/0.74 unif_index_add_time: 0.
% 0.44/0.74 % total_time: 0.143
% 0.44/0.74 % num_of_symbols: 214
% 0.44/0.74 % num_of_terms: 2208
% 0.44/0.74
% 0.44/0.74 % ------ Propositional Solver
% 0.44/0.74
% 0.44/0.74 % prop_solver_calls: 0
% 0.44/0.74 % prop_fast_solver_calls: 0
% 0.44/0.74 % prop_num_of_clauses: 0
% 0.44/0.74 % prop_preprocess_simplified: 0
% 0.44/0.74 % prop_fo_subsumed: 0
% 0.44/0.74 % prop_solver_time: 0.
% 0.44/0.74 % prop_fast_solver_time: 0.
% 0.44/0.74 % prop_unsat_core_time: 0.
% 0.44/0.74
% 0.44/0.74 % ------ QBF
% 0.44/0.74
% 0.44/0.74 % qbf_q_res: 0
% 0.44/0.74 % qbf_num_tautologies: 0
% 0.44/0.74 % qbf_prep_cycles: 0
% 0.44/0.74
% 0.44/0.74 % ------ BMC1
% 0.44/0.74
% 0.44/0.74 % bmc1_current_bound: -1
% 0.44/0.74 % bmc1_last_solved_bound: -1
% 0.44/0.74 % bmc1_unsat_core_size: -1
% 0.44/0.74 % bmc1_unsat_core_parents_size: -1
% 0.44/0.74 % bmc1_merge_next_fun: 0
% 0.44/0.74 % bmc1_unsat_core_clauses_time: 0.
% 0.44/0.74
% 0.44/0.74 % ------ Instantiation
% 0.44/0.74
% 0.44/0.74 % inst_num_of_clauses: undef
% 0.44/0.74 % inst_num_in_passive: undef
% 0.44/0.74 % inst_num_in_active: 0
% 0.44/0.74 % inst_num_in_unprocessed: 0
% 0.44/0.74 % inst_num_of_loops: 0
% 0.44/0.74 % inst_num_of_learning_restarts: 0
% 0.44/0.74 % inst_num_moves_active_passive: 0
% 0.44/0.74 % inst_lit_activity: 0
% 0.44/0.74 % inst_lit_activity_moves: 0
% 0.44/0.74 % inst_num_tautologies: 0
% 0.44/0.74 % inst_num_prop_implied: 0
% 0.44/0.74 % inst_num_existing_simplified: 0
% 0.44/0.74 % inst_num_eq_res_simplified: 0
% 0.44/0.74 % inst_num_child_elim: 0
% 0.44/0.74 % inst_num_of_dismatching_blockings: 0
% 0.44/0.74 % inst_num_of_non_proper_insts: 0
% 0.44/0.74 % inst_num_of_duplicates: 0
% 0.44/0.74 % inst_inst_num_from_inst_to_res: 0
% 0.44/0.74 % inst_dismatching_checking_time: 0.
% 0.44/0.74
% 0.44/0.74 % ------ Resolution
% 0.44/0.74
% 0.44/0.74 % res_num_of_clauses: undef
% 0.44/0.74 % res_num_in_passive: undef
% 0.44/0.74 % res_num_in_active: 0
% 0.44/0.74 % res_num_of_loops: 0
% 0.44/0.74 % res_forward_subset_subsumed: 0
% 0.44/0.74 % res_backward_subset_subsumed: 0
% 0.44/0.74 % res_forward_subsumed: 0
% 0.44/0.74 % res_backward_subsumed: 0
% 0.44/0.74 % res_forward_subsumption_resolution: 0
% 0.44/0.74 % res_backward_subsumption_resolution: 0
% 0.44/0.74 % res_clause_to_clause_subsumption: 0
% 0.44/0.74 % res_orphan_elimination: 0
% 0.44/0.74 % res_tautology_del: 0
% 0.44/0.74 % res_num_eq_res_simplified: 0
% 0.44/0.74 % res_num_sel_changes: 0
% 0.44/0.74 % res_moves_from_active_to_pass: 0
% 0.44/0.74
% 0.44/0.74 % Status Unknown
% 0.59/0.92 % Orienting using strategy ClausalAll
% 0.59/0.92 % FOF problem with conjecture
% 0.59/0.92 % 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_d9c61d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_2821a5.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_1dbd7c | grep -v "SZS"
% 0.79/0.95
% 0.79/0.95 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.79/0.95
% 0.79/0.95 %
% 0.79/0.95 % ------ iProver source info
% 0.79/0.95
% 0.79/0.95 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.79/0.95 % git: non_committed_changes: true
% 0.79/0.95 % git: last_make_outside_of_git: true
% 0.79/0.95
% 0.79/0.95 %
% 0.79/0.95 % ------ Input Options
% 0.79/0.95
% 0.79/0.95 % --out_options all
% 0.79/0.95 % --tptp_safe_out true
% 0.79/0.95 % --problem_path ""
% 0.79/0.95 % --include_path ""
% 0.79/0.95 % --clausifier .//eprover
% 0.79/0.95 % --clausifier_options --tstp-format
% 0.79/0.95 % --stdin false
% 0.79/0.95 % --dbg_backtrace false
% 0.79/0.95 % --dbg_dump_prop_clauses false
% 0.79/0.95 % --dbg_dump_prop_clauses_file -
% 0.79/0.95 % --dbg_out_stat false
% 0.79/0.95
% 0.79/0.95 % ------ General Options
% 0.79/0.95
% 0.79/0.95 % --fof false
% 0.79/0.95 % --time_out_real 150.
% 0.79/0.95 % --time_out_prep_mult 0.2
% 0.79/0.95 % --time_out_virtual -1.
% 0.79/0.95 % --schedule none
% 0.79/0.95 % --ground_splitting input
% 0.79/0.95 % --splitting_nvd 16
% 0.79/0.95 % --non_eq_to_eq false
% 0.79/0.95 % --prep_gs_sim true
% 0.79/0.95 % --prep_unflatten false
% 0.79/0.95 % --prep_res_sim true
% 0.79/0.95 % --prep_upred true
% 0.79/0.95 % --res_sim_input true
% 0.79/0.95 % --clause_weak_htbl true
% 0.79/0.95 % --gc_record_bc_elim false
% 0.79/0.95 % --symbol_type_check false
% 0.79/0.95 % --clausify_out false
% 0.79/0.95 % --large_theory_mode false
% 0.79/0.95 % --prep_sem_filter none
% 0.79/0.95 % --prep_sem_filter_out false
% 0.79/0.95 % --preprocessed_out false
% 0.79/0.95 % --sub_typing false
% 0.79/0.95 % --brand_transform false
% 0.79/0.95 % --pure_diseq_elim true
% 0.79/0.95 % --min_unsat_core false
% 0.79/0.95 % --pred_elim true
% 0.79/0.95 % --add_important_lit false
% 0.79/0.95 % --soft_assumptions false
% 0.79/0.95 % --reset_solvers false
% 0.79/0.95 % --bc_imp_inh []
% 0.79/0.95 % --conj_cone_tolerance 1.5
% 0.79/0.95 % --prolific_symb_bound 500
% 0.79/0.95 % --lt_threshold 2000
% 0.79/0.95
% 0.79/0.95 % ------ SAT Options
% 0.79/0.95
% 0.79/0.95 % --sat_mode false
% 0.79/0.95 % --sat_fm_restart_options ""
% 0.79/0.95 % --sat_gr_def false
% 0.79/0.95 % --sat_epr_types true
% 0.79/0.95 % --sat_non_cyclic_types false
% 0.79/0.95 % --sat_finite_models false
% 0.79/0.95 % --sat_fm_lemmas false
% 0.79/0.95 % --sat_fm_prep false
% 0.79/0.95 % --sat_fm_uc_incr true
% 0.79/0.95 % --sat_out_model small
% 0.79/0.95 % --sat_out_clauses false
% 0.79/0.95
% 0.79/0.95 % ------ QBF Options
% 0.79/0.95
% 0.79/0.95 % --qbf_mode false
% 0.79/0.95 % --qbf_elim_univ true
% 0.79/0.95 % --qbf_sk_in true
% 0.79/0.95 % --qbf_pred_elim true
% 0.79/0.95 % --qbf_split 32
% 0.79/0.95
% 0.79/0.95 % ------ BMC1 Options
% 0.79/0.95
% 0.79/0.95 % --bmc1_incremental false
% 0.79/0.95 % --bmc1_axioms reachable_all
% 0.79/0.95 % --bmc1_min_bound 0
% 0.79/0.95 % --bmc1_max_bound -1
% 0.79/0.95 % --bmc1_max_bound_default -1
% 0.79/0.95 % --bmc1_symbol_reachability true
% 0.79/0.95 % --bmc1_property_lemmas false
% 0.79/0.95 % --bmc1_k_induction false
% 0.79/0.95 % --bmc1_non_equiv_states false
% 0.79/0.95 % --bmc1_deadlock false
% 0.79/0.95 % --bmc1_ucm false
% 0.79/0.95 % --bmc1_add_unsat_core none
% 0.79/0.95 % --bmc1_unsat_core_children false
% 0.79/0.95 % --bmc1_unsat_core_extrapolate_axioms false
% 0.79/0.95 % --bmc1_out_stat full
% 0.79/0.95 % --bmc1_ground_init false
% 0.79/0.95 % --bmc1_pre_inst_next_state false
% 0.79/0.95 % --bmc1_pre_inst_state false
% 0.79/0.95 % --bmc1_pre_inst_reach_state false
% 0.79/0.95 % --bmc1_out_unsat_core false
% 0.79/0.95 % --bmc1_aig_witness_out false
% 0.79/0.95 % --bmc1_verbose false
% 0.79/0.95 % --bmc1_dump_clauses_tptp false
% 1.72/1.92 % --bmc1_dump_unsat_core_tptp false
% 1.72/1.92 % --bmc1_dump_file -
% 1.72/1.92 % --bmc1_ucm_expand_uc_limit 128
% 1.72/1.92 % --bmc1_ucm_n_expand_iterations 6
% 1.72/1.92 % --bmc1_ucm_extend_mode 1
% 1.72/1.92 % --bmc1_ucm_init_mode 2
% 1.72/1.92 % --bmc1_ucm_cone_mode none
% 1.72/1.92 % --bmc1_ucm_reduced_relation_type 0
% 1.72/1.92 % --bmc1_ucm_relax_model 4
% 1.72/1.92 % --bmc1_ucm_full_tr_after_sat true
% 1.72/1.92 % --bmc1_ucm_expand_neg_assumptions false
% 1.72/1.92 % --bmc1_ucm_layered_model none
% 1.72/1.92 % --bmc1_ucm_max_lemma_size 10
% 1.72/1.92
% 1.72/1.92 % ------ AIG Options
% 1.72/1.92
% 1.72/1.92 % --aig_mode false
% 1.72/1.92
% 1.72/1.92 % ------ Instantiation Options
% 1.72/1.92
% 1.72/1.92 % --instantiation_flag true
% 1.72/1.92 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.72/1.92 % --inst_solver_per_active 750
% 1.72/1.92 % --inst_solver_calls_frac 0.5
% 1.72/1.92 % --inst_passive_queue_type priority_queues
% 1.72/1.92 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.72/1.92 % --inst_passive_queues_freq [25;2]
% 1.72/1.92 % --inst_dismatching true
% 1.72/1.92 % --inst_eager_unprocessed_to_passive true
% 1.72/1.92 % --inst_prop_sim_given true
% 1.72/1.92 % --inst_prop_sim_new false
% 1.72/1.92 % --inst_orphan_elimination true
% 1.72/1.92 % --inst_learning_loop_flag true
% 1.72/1.92 % --inst_learning_start 3000
% 1.72/1.92 % --inst_learning_factor 2
% 1.72/1.92 % --inst_start_prop_sim_after_learn 3
% 1.72/1.92 % --inst_sel_renew solver
% 1.72/1.92 % --inst_lit_activity_flag true
% 1.72/1.92 % --inst_out_proof true
% 1.72/1.92
% 1.72/1.92 % ------ Resolution Options
% 1.72/1.92
% 1.72/1.92 % --resolution_flag true
% 1.72/1.92 % --res_lit_sel kbo_max
% 1.72/1.92 % --res_to_prop_solver none
% 1.72/1.92 % --res_prop_simpl_new false
% 1.72/1.92 % --res_prop_simpl_given false
% 1.72/1.92 % --res_passive_queue_type priority_queues
% 1.72/1.92 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.72/1.92 % --res_passive_queues_freq [15;5]
% 1.72/1.92 % --res_forward_subs full
% 1.72/1.92 % --res_backward_subs full
% 1.72/1.92 % --res_forward_subs_resolution true
% 1.72/1.92 % --res_backward_subs_resolution true
% 1.72/1.92 % --res_orphan_elimination false
% 1.72/1.92 % --res_time_limit 1000.
% 1.72/1.92 % --res_out_proof true
% 1.72/1.92 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d9c61d.s
% 1.72/1.92 % --modulo true
% 1.72/1.92
% 1.72/1.92 % ------ Combination Options
% 1.72/1.92
% 1.72/1.92 % --comb_res_mult 1000
% 1.72/1.92 % --comb_inst_mult 300
% 1.72/1.92 % ------
% 1.72/1.92
% 1.72/1.92 % ------ Parsing...% successful
% 1.72/1.92
% 1.72/1.92 % ------ 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 %
% 1.72/1.92
% 1.72/1.92 % ------ Proving...
% 1.72/1.92 % ------ Problem Properties
% 1.72/1.92
% 1.72/1.92 %
% 1.72/1.92 % EPR false
% 1.72/1.92 % Horn false
% 1.72/1.92 % Has equality true
% 1.72/1.92
% 1.72/1.92 % % ------ Input Options Time Limit: Unbounded
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Compiling...
% 1.72/1.92 Loading plugin: done.
% 1.72/1.92 Compiling...
% 1.72/1.92 Loading plugin: done.
% 1.72/1.92 Compiling...
% 1.72/1.92 Loading plugin: done.
% 1.72/1.92 Compiling...
% 1.72/1.92 Loading plugin: done.
% 1.72/1.92 Compiling...
% 1.72/1.92 Loading plugin: done.
% 1.72/1.92 % 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
% 1.72/1.92 cnf(c_8146,plain,
% 1.72/1.92 ( ~ relation(X0)
% 1.72/1.92 | ~ function(X0)
% 1.72/1.92 | in(ordered_pair(X1,X2),X0)
% 1.72/1.92 | ~ in(X1,relation_dom(X0))
% 1.72/1.92 | X2 != apply(X0,X1) ),
% 1.72/1.92 inference(copy,[status(esa)],[c_7260]) ).
% 1.72/1.92
% 1.72/1.92 cnf(c_7260,plain,
% 1.72/1.92 ( ~ relation(X0)
% 1.72/1.92 | ~ function(X0)
% 1.72/1.92 | in(ordered_pair(X1,X2),X0)
% 1.72/1.92 | ~ in(X1,relation_dom(X0))
% 1.72/1.92 | X2 != apply(X0,X1) ),
% 1.72/1.92 inference(copy,[status(esa)],[c_6707]) ).
% 1.72/1.92
% 1.72/1.92 cnf(c_6707,plain,
% 1.72/1.92 ( ~ relation(X0)
% 1.72/1.92 | ~ function(X0)
% 1.72/1.92 | in(ordered_pair(X1,X2),X0)
% 1.72/1.92 | ~ in(X1,relation_dom(X0))
% 1.72/1.92 | X2 != apply(X0,X1) ),
% 1.72/1.92 inference(copy,[status(esa)],[c_5818]) ).
% 1.72/1.92
% 1.72/1.92 cnf(c_5818,plain,
% 1.72/1.92 ( ~ relation(X0)
% 1.72/1.92 | ~ function(X0)
% 1.72/1.93 | in(ordered_pair(X1,X2),X0)
% 1.72/1.93 | ~ in(X1,relation_dom(X0))
% 1.72/1.93 | X2 != apply(X0,X1) ),
% 1.72/1.93 inference(copy,[status(esa)],[c_3912]) ).
% 1.72/1.93
% 1.72/1.93 cnf(c_3912,plain,
% 1.72/1.93 ( ~ relation(X0)
% 1.72/1.93 | ~ function(X0)
% 1.72/1.93 | in(ordered_pair(X1,X2),X0)
% 1.72/1.93 | ~ in(X1,relation_dom(X0))
% 1.72/1.93 | X2 != apply(X0,X1) ),
% 1.72/1.93 file('/export/starexec/sandbox/tmp/iprover_modulo_2821a5.p', c_0_1480) ).
% 1.72/1.93
% 1.72/1.93 % % ------ Current options:
% 1.72/1.93
% 1.72/1.93 % ------ Input Options
% 1.72/1.93
% 1.72/1.93 % --out_options all
% 1.72/1.93 % --tptp_safe_out true
% 1.72/1.93 % --problem_path ""
% 1.72/1.93 % --include_path ""
% 1.72/1.93 % --clausifier .//eprover
% 1.72/1.93 % --clausifier_options --tstp-format
% 1.72/1.93 % --stdin false
% 1.72/1.93 % --dbg_backtrace false
% 1.72/1.93 % --dbg_dump_prop_clauses false
% 1.72/1.93 % --dbg_dump_prop_clauses_file -
% 1.72/1.93 % --dbg_out_stat false
% 1.72/1.93
% 1.72/1.93 % ------ General Options
% 1.72/1.93
% 1.72/1.93 % --fof false
% 1.72/1.93 % --time_out_real 150.
% 1.72/1.93 % --time_out_prep_mult 0.2
% 1.72/1.93 % --time_out_virtual -1.
% 1.72/1.93 % --schedule none
% 1.72/1.93 % --ground_splitting input
% 1.72/1.93 % --splitting_nvd 16
% 1.72/1.93 % --non_eq_to_eq false
% 1.72/1.93 % --prep_gs_sim true
% 1.72/1.93 % --prep_unflatten false
% 1.72/1.93 % --prep_res_sim true
% 1.72/1.93 % --prep_upred true
% 1.72/1.93 % --res_sim_input true
% 1.72/1.93 % --clause_weak_htbl true
% 1.72/1.93 % --gc_record_bc_elim false
% 1.72/1.93 % --symbol_type_check false
% 1.72/1.93 % --clausify_out false
% 1.72/1.93 % --large_theory_mode false
% 1.72/1.93 % --prep_sem_filter none
% 1.72/1.93 % --prep_sem_filter_out false
% 1.72/1.93 % --preprocessed_out false
% 1.72/1.93 % --sub_typing false
% 1.72/1.93 % --brand_transform false
% 1.72/1.93 % --pure_diseq_elim true
% 1.72/1.93 % --min_unsat_core false
% 1.72/1.93 % --pred_elim true
% 1.72/1.93 % --add_important_lit false
% 1.72/1.93 % --soft_assumptions false
% 1.72/1.93 % --reset_solvers false
% 1.72/1.93 % --bc_imp_inh []
% 1.72/1.93 % --conj_cone_tolerance 1.5
% 1.72/1.93 % --prolific_symb_bound 500
% 1.72/1.93 % --lt_threshold 2000
% 1.72/1.93
% 1.72/1.93 % ------ SAT Options
% 1.72/1.93
% 1.72/1.93 % --sat_mode false
% 1.72/1.93 % --sat_fm_restart_options ""
% 1.72/1.93 % --sat_gr_def false
% 1.72/1.93 % --sat_epr_types true
% 1.72/1.93 % --sat_non_cyclic_types false
% 1.72/1.93 % --sat_finite_models false
% 1.72/1.93 % --sat_fm_lemmas false
% 1.72/1.93 % --sat_fm_prep false
% 1.72/1.93 % --sat_fm_uc_incr true
% 1.72/1.93 % --sat_out_model small
% 1.72/1.93 % --sat_out_clauses false
% 1.72/1.93
% 1.72/1.93 % ------ QBF Options
% 1.72/1.93
% 1.72/1.93 % --qbf_mode false
% 1.72/1.93 % --qbf_elim_univ true
% 1.72/1.93 % --qbf_sk_in true
% 1.72/1.93 % --qbf_pred_elim true
% 1.72/1.93 % --qbf_split 32
% 1.72/1.93
% 1.72/1.93 % ------ BMC1 Options
% 1.72/1.93
% 1.72/1.93 % --bmc1_incremental false
% 1.72/1.93 % --bmc1_axioms reachable_all
% 1.72/1.93 % --bmc1_min_bound 0
% 1.72/1.93 % --bmc1_max_bound -1
% 1.72/1.93 % --bmc1_max_bound_default -1
% 1.72/1.93 % --bmc1_symbol_reachability true
% 1.72/1.93 % --bmc1_property_lemmas false
% 1.72/1.93 % --bmc1_k_induction false
% 1.72/1.93 % --bmc1_non_equiv_states false
% 1.72/1.93 % --bmc1_deadlock false
% 1.72/1.93 % --bmc1_ucm false
% 1.72/1.93 % --bmc1_add_unsat_core none
% 1.72/1.93 % --bmc1_unsat_core_children false
% 1.72/1.93 % --bmc1_unsat_core_extrapolate_axioms false
% 1.72/1.93 % --bmc1_out_stat full
% 1.72/1.93 % --bmc1_ground_init false
% 1.72/1.93 % --bmc1_pre_inst_next_state false
% 1.72/1.93 % --bmc1_pre_inst_state false
% 1.72/1.93 % --bmc1_pre_inst_reach_state false
% 1.72/1.93 % --bmc1_out_unsat_core false
% 1.72/1.93 % --bmc1_aig_witness_out false
% 1.72/1.93 % --bmc1_verbose false
% 1.72/1.93 % --bmc1_dump_clauses_tptp false
% 1.72/1.93 % --bmc1_dump_unsat_core_tptp false
% 1.72/1.93 % --bmc1_dump_file -
% 1.72/1.93 % --bmc1_ucm_expand_uc_limit 128
% 1.72/1.93 % --bmc1_ucm_n_expand_iterations 6
% 1.72/1.93 % --bmc1_ucm_extend_mode 1
% 1.72/1.93 % --bmc1_ucm_init_mode 2
% 1.72/1.93 % --bmc1_ucm_cone_mode none
% 1.72/1.93 % --bmc1_ucm_reduced_relation_type 0
% 1.72/1.93 % --bmc1_ucm_relax_model 4
% 1.72/1.93 % --bmc1_ucm_full_tr_after_sat true
% 1.72/1.93 % --bmc1_ucm_expand_neg_assumptions false
% 1.72/1.93 % --bmc1_ucm_layered_model none
% 1.72/1.93 % --bmc1_ucm_max_lemma_size 10
% 1.72/1.93
% 1.72/1.93 % ------ AIG Options
% 1.72/1.93
% 1.72/1.93 % --aig_mode false
% 1.72/1.93
% 1.72/1.93 % ------ Instantiation Options
% 1.72/1.93
% 1.72/1.93 % --instantiation_flag true
% 1.72/1.93 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.72/1.93 % --inst_solver_per_active 750
% 1.72/1.93 % --inst_solver_calls_frac 0.5
% 1.72/1.93 % --inst_passive_queue_type priority_queues
% 1.72/1.93 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.72/1.93 % --inst_passive_queues_freq [25;2]
% 1.72/1.93 % --inst_dismatching true
% 1.72/1.93 % --inst_eager_unprocessed_to_passive true
% 1.72/1.93 % --inst_prop_sim_given true
% 1.72/1.93 % --inst_prop_sim_new false
% 1.72/1.93 % --inst_orphan_elimination true
% 1.72/1.93 % --inst_learning_loop_flag true
% 1.72/1.93 % --inst_learning_start 3000
% 1.72/1.93 % --inst_learning_factor 2
% 1.72/1.93 % --inst_start_prop_sim_after_learn 3
% 1.72/1.93 % --inst_sel_renew solver
% 1.72/1.93 % --inst_lit_activity_flag true
% 1.72/1.93 % --inst_out_proof true
% 1.72/1.93
% 1.72/1.93 % ------ Resolution Options
% 1.72/1.93
% 1.72/1.93 % --resolution_flag true
% 1.72/1.93 % --res_lit_sel kbo_max
% 1.72/1.93 % --res_to_prop_solver none
% 1.72/1.93 % --res_prop_simpl_new false
% 1.72/1.93 % --res_prop_simpl_given false
% 1.72/1.93 % --res_passive_queue_type priority_queues
% 1.72/1.93 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.72/1.93 % --res_passive_queues_freq [15;5]
% 1.72/1.93 % --res_forward_subs full
% 1.72/1.93 % --res_backward_subs full
% 1.72/1.93 % --res_forward_subs_resolution true
% 1.72/1.93 % --res_backward_subs_resolution true
% 1.72/1.93 % --res_orphan_elimination false
% 1.72/1.93 % --res_time_limit 1000.
% 1.72/1.93 % --res_out_proof true
% 1.72/1.93 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d9c61d.s
% 1.72/1.93 % --modulo true
% 1.72/1.93
% 1.72/1.93 % ------ Combination Options
% 1.72/1.93
% 1.72/1.93 % --comb_res_mult 1000
% 1.72/1.93 % --comb_inst_mult 300
% 1.72/1.93 % ------
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93 % ------ Proving...
% 1.72/1.93 %
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93 % Resolution empty clause
% 1.72/1.93
% 1.72/1.93 % ------ Statistics
% 1.72/1.93
% 1.72/1.93 % ------ General
% 1.72/1.93
% 1.72/1.93 % num_of_input_clauses: 4204
% 1.72/1.93 % num_of_input_neg_conjectures: 2
% 1.72/1.93 % num_of_splits: 0
% 1.72/1.93 % num_of_split_atoms: 0
% 1.72/1.93 % num_of_sem_filtered_clauses: 0
% 1.72/1.93 % num_of_subtypes: 0
% 1.72/1.93 % monotx_restored_types: 0
% 1.72/1.93 % sat_num_of_epr_types: 0
% 1.72/1.93 % sat_num_of_non_cyclic_types: 0
% 1.72/1.93 % sat_guarded_non_collapsed_types: 0
% 1.72/1.93 % is_epr: 0
% 1.72/1.93 % is_horn: 0
% 1.72/1.93 % has_eq: 1
% 1.72/1.93 % num_pure_diseq_elim: 0
% 1.72/1.93 % simp_replaced_by: 0
% 1.72/1.93 % res_preprocessed: 619
% 1.72/1.93 % prep_upred: 0
% 1.72/1.93 % prep_unflattend: 27
% 1.72/1.93 % pred_elim_cands: 27
% 1.72/1.93 % pred_elim: 7
% 1.72/1.93 % pred_elim_cl: 230
% 1.72/1.93 % pred_elim_cycles: 10
% 1.72/1.93 % forced_gc_time: 0
% 1.72/1.93 % gc_basic_clause_elim: 0
% 1.72/1.93 % parsing_time: 0.247
% 1.72/1.93 % sem_filter_time: 0.
% 1.72/1.93 % pred_elim_time: 0.018
% 1.72/1.93 % out_proof_time: 0.
% 1.72/1.93 % monotx_time: 0.
% 1.72/1.93 % subtype_inf_time: 0.
% 1.72/1.93 % unif_index_cands_time: 0.
% 1.72/1.93 % unif_index_add_time: 0.002
% 1.72/1.93 % total_time: 0.996
% 1.72/1.93 % num_of_symbols: 359
% 1.72/1.93 % num_of_terms: 6661
% 1.72/1.93
% 1.72/1.93 % ------ Propositional Solver
% 1.72/1.93
% 1.72/1.93 % prop_solver_calls: 1
% 1.72/1.93 % prop_fast_solver_calls: 5638
% 1.72/1.93 % prop_num_of_clauses: 3117
% 1.72/1.93 % prop_preprocess_simplified: 19100
% 1.72/1.93 % prop_fo_subsumed: 18
% 1.72/1.93 % prop_solver_time: 0.
% 1.72/1.93 % prop_fast_solver_time: 0.007
% 1.72/1.93 % prop_unsat_core_time: 0.
% 1.72/1.93
% 1.72/1.93 % ------ QBF
% 1.72/1.93
% 1.72/1.93 % qbf_q_res: 0
% 1.72/1.93 % qbf_num_tautologies: 0
% 1.72/1.93 % qbf_prep_cycles: 0
% 1.72/1.93
% 1.72/1.93 % ------ BMC1
% 1.72/1.93
% 1.72/1.93 % bmc1_current_bound: -1
% 1.72/1.93 % bmc1_last_solved_bound: -1
% 1.72/1.93 % bmc1_unsat_core_size: -1
% 1.72/1.93 % bmc1_unsat_core_parents_size: -1
% 1.72/1.93 % bmc1_merge_next_fun: 0
% 1.72/1.93 % bmc1_unsat_core_clauses_time: 0.
% 1.72/1.93
% 1.72/1.93 % ------ Instantiation
% 1.72/1.93
% 1.72/1.93 % inst_num_of_clauses: 3764
% 1.72/1.93 % inst_num_in_passive: 0
% 1.72/1.93 % inst_num_in_active: 0
% 1.72/1.93 % inst_num_in_unprocessed: 3933
% 1.72/1.93 % inst_num_of_loops: 0
% 1.72/1.93 % inst_num_of_learning_restarts: 0
% 1.72/1.93 % inst_num_moves_active_passive: 0
% 1.72/1.93 % inst_lit_activity: 0
% 1.72/1.93 % inst_lit_activity_moves: 0
% 1.72/1.93 % inst_num_tautologies: 0
% 1.72/1.93 % inst_num_prop_implied: 0
% 1.72/1.93 % inst_num_existing_simplified: 0
% 1.72/1.93 % inst_num_eq_res_simplified: 0
% 1.72/1.93 % inst_num_child_elim: 0
% 1.72/1.93 % inst_num_of_dismatching_blockings: 0
% 1.72/1.93 % inst_num_of_non_proper_insts: 0
% 1.72/1.93 % inst_num_of_duplicates: 0
% 1.72/1.93 % inst_inst_num_from_inst_to_res: 0
% 1.72/1.93 % inst_dismatching_checking_time: 0.
% 1.72/1.93
% 1.72/1.93 % ------ Resolution
% 1.72/1.93
% 1.72/1.93 % res_num_of_clauses: 4539
% 1.72/1.93 % res_num_in_passive: 345
% 1.72/1.93 % res_num_in_active: 1115
% 1.72/1.93 % res_num_of_loops: 4
% 1.72/1.93 % res_forward_subset_subsumed: 2458
% 1.72/1.93 % res_backward_subset_subsumed: 0
% 1.72/1.93 % res_forward_subsumed: 0
% 1.72/1.93 % res_backward_subsumed: 0
% 1.72/1.93 % res_forward_subsumption_resolution: 0
% 1.72/1.93 % res_backward_subsumption_resolution: 1
% 1.72/1.93 % res_clause_to_clause_subsumption: 4
% 1.72/1.93 % res_orphan_elimination: 0
% 1.72/1.93 % res_tautology_del: 11
% 1.72/1.93 % res_num_eq_res_simplified: 0
% 1.72/1.93 % res_num_sel_changes: 0
% 1.72/1.93 % res_moves_from_active_to_pass: 0
% 1.72/1.93
% 1.72/1.93 % Status Unsatisfiable
% 1.72/1.93 % SZS status Theorem
% 1.72/1.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------