%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU306+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n032.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 10:27:08 EDT 2022
% Result : Theorem 2.68s 2.97s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 483
% Syntax : Number of formulae : 9727 ( 803 unt; 0 def)
% Number of atoms : 52689 (11295 equ)
% Maximal formula atoms : 1044 ( 5 avg)
% Number of connectives : 72505 (29543 ~;38662 |;2831 &)
% ( 315 <=>;1154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 161 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 62 ( 59 usr; 3 prp; 0-3 aty)
% Number of functors : 566 ( 566 usr; 59 con; 0-8 aty)
% Number of variables : 30406 ( 730 sgn3454 !; 286 ?)
% 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,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3) ),
file('<stdin>',dt_k2_binop_1) ).
fof(c_0_2,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_3,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
file('<stdin>',redefinition_k2_binop_1) ).
fof(c_0_4,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) ) ) ),
file('<stdin>',d2_lattices) ).
fof(c_0_5,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) ) ) ),
file('<stdin>',d1_lattices) ).
fof(c_0_6,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_7,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_8,axiom,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) )
& X2 = X4
& ? [X9] :
( ordinal(X9)
& X4 = X9
& ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( X10 != empty_set
& ! [X11] :
~ ( in(X11,X10)
& ! [X12] :
( ( in(X12,X10)
& subset(X11,X12) )
=> X12 = X11 ) ) ) ) ) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,succ(X1))
& X4 = X3
& ? [X13] :
( ordinal(X13)
& X3 = X13
& ( in(X13,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X13)))
=> ~ ( X14 != empty_set
& ! [X15] :
~ ( in(X15,X14)
& ! [X16] :
( ( in(X16,X14)
& subset(X15,X16) )
=> X16 = X15 ) ) ) ) ) ) ) ) ) ),
file('<stdin>',s1_tarski__e18_27__finset_1__1) ).
fof(c_0_9,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_10,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_11,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_12,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_13,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_14,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_15,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_16,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(powerset(X1)))
& relation(X3)
& function(X3) )
=> ( ! [X4,X5,X6] :
( ( X4 = X5
& in(relation_image(X3,X5),X2)
& X4 = X6
& in(relation_image(X3,X6),X2) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,powerset(relation_dom(X3)))
& X6 = X5
& in(relation_image(X3,X5),X2) ) ) ) ),
file('<stdin>',s1_tarski__e6_27__finset_1__1) ).
fof(c_0_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,axiom,
! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6] :
( in(X6,X2)
& X4 = set_difference(X6,singleton(X1)) )
& X3 = X5
& ? [X7] :
( in(X7,X2)
& X5 = set_difference(X7,singleton(X1)) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(X1))
& X5 = X4
& ? [X8] :
( in(X8,X2)
& X4 = set_difference(X8,singleton(X1)) ) ) ) ) ),
file('<stdin>',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(c_0_28,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_29,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( meet_absorbing(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,meet(X1,X2,X3),X3) = X3 ) ) ) ),
file('<stdin>',d8_lattices) ).
fof(c_0_30,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_31,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_32,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('<stdin>',d3_lattices) ).
fof(c_0_42,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_43,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_44,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_45,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet_commut(X1,X2,X3),the_carrier(X1)) ),
file('<stdin>',dt_k4_lattices) ).
fof(c_0_46,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(join_commut(X1,X2,X3),the_carrier(X1)) ),
file('<stdin>',dt_k3_lattices) ).
fof(c_0_47,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_48,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
file('<stdin>',dt_k2_lattices) ).
fof(c_0_49,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(join(X1,X2,X3),the_carrier(X1)) ),
file('<stdin>',dt_k1_lattices) ).
fof(c_0_50,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
file('<stdin>',redefinition_k4_lattices) ).
fof(c_0_51,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
file('<stdin>',redefinition_k3_lattices) ).
fof(c_0_52,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
file('<stdin>',commutativity_k4_lattices) ).
fof(c_0_53,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
file('<stdin>',commutativity_k3_lattices) ).
fof(c_0_54,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_55,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_56,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_57,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_67,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_68,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('<stdin>',d1_relset_1) ).
fof(c_0_69,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_70,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('<stdin>',dt_u2_lattices) ).
fof(c_0_71,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('<stdin>',dt_u1_lattices) ).
fof(c_0_72,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('<stdin>',cc1_relset_1) ).
fof(c_0_73,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_74,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('<stdin>',t7_tarski) ).
fof(c_0_75,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_76,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_77,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('<stdin>',d1_relat_1) ).
fof(c_0_78,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_79,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_80,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_81,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_82,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_83,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_84,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_85,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3) ),
file('<stdin>',rc2_partfun1) ).
fof(c_0_86,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_87,axiom,
! [X1,X2] :
? [X3] : relation_of2_as_subset(X3,X1,X2),
file('<stdin>',existence_m2_relset_1) ).
fof(c_0_88,axiom,
! [X1,X2] :
? [X3] : relation_of2(X3,X1,X2),
file('<stdin>',existence_m1_relset_1) ).
fof(c_0_89,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k3_subset_1) ).
fof(c_0_90,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_91,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_92,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k3_subset_1) ).
fof(c_0_93,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_94,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('<stdin>',redefinition_k5_setfam_1) ).
fof(c_0_95,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('<stdin>',t4_subset) ).
fof(c_0_96,axiom,
! [X1] :
( X1 = omega
<=> ( in(empty_set,X1)
& being_limit_ordinal(X1)
& ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> ( ( in(empty_set,X2)
& being_limit_ordinal(X2) )
=> subset(X1,X2) ) ) ) ),
file('<stdin>',d5_ordinal2) ).
fof(c_0_97,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_98,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('<stdin>',d6_wellord1) ).
fof(c_0_99,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('<stdin>',d5_subset_1) ).
fof(c_0_100,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_101,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_102,axiom,
! [X1] :
( finite(X1)
<=> ? [X2] :
( relation(X2)
& function(X2)
& relation_rng(X2) = X1
& in(relation_dom(X2),omega) ) ),
file('<stdin>',d1_finset_1) ).
fof(c_0_103,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('<stdin>',fc4_subset_1) ).
fof(c_0_104,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_105,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_106,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_107,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
file('<stdin>',fc13_finset_1) ).
fof(c_0_108,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('<stdin>',redefinition_r1_ordinal1) ).
fof(c_0_109,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2) ) ),
file('<stdin>',rc5_struct_0) ).
fof(c_0_110,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('<stdin>',fc3_subset_1) ).
fof(c_0_111,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_112,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_113,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_114,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('<stdin>',t3_subset) ).
fof(c_0_115,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('<stdin>',dt_k2_pre_topc) ).
fof(c_0_116,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_117,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_118,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_119,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('<stdin>',fc9_finset_1) ).
fof(c_0_120,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_121,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_122,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
file('<stdin>',fc3_relat_1) ).
fof(c_0_123,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('<stdin>',fc2_relat_1) ).
fof(c_0_124,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('<stdin>',fc1_relat_1) ).
fof(c_0_125,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_126,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_127,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('<stdin>',dt_k5_relat_1) ).
fof(c_0_128,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('<stdin>',d2_ordinal1) ).
fof(c_0_129,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('<stdin>',d9_relat_2) ).
fof(c_0_130,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
file('<stdin>',d16_relat_2) ).
fof(c_0_131,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('<stdin>',d14_relat_2) ).
fof(c_0_132,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('<stdin>',d12_relat_2) ).
fof(c_0_133,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('<stdin>',cc2_finset_1) ).
fof(c_0_134,axiom,
! [X1] :
( v5_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2)
& v5_membered(X2) ) ) ),
file('<stdin>',cc20_membered) ).
fof(c_0_135,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2) ) ) ),
file('<stdin>',cc19_membered) ).
fof(c_0_136,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2) ) ) ),
file('<stdin>',cc18_membered) ).
fof(c_0_137,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2) ) ) ),
file('<stdin>',cc17_membered) ).
fof(c_0_138,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> v1_membered(X2) ) ),
file('<stdin>',cc16_membered) ).
fof(c_0_139,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('<stdin>',connectedness_r1_ordinal1) ).
fof(c_0_140,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('<stdin>',t2_subset) ).
fof(c_0_141,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_142,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_143,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
file('<stdin>',fc12_finset_1) ).
fof(c_0_144,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('<stdin>',fc11_finset_1) ).
fof(c_0_145,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
file('<stdin>',fc10_finset_1) ).
fof(c_0_146,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('<stdin>',dt_k8_relat_1) ).
fof(c_0_147,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('<stdin>',dt_k7_relat_1) ).
fof(c_0_148,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('<stdin>',dt_k2_wellord1) ).
fof(c_0_149,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('<stdin>',d6_relat_1) ).
fof(c_0_150,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('<stdin>',t1_subset) ).
fof(c_0_151,axiom,
! [X1,X2] :
( equipotent(X1,X2)
=> equipotent(X2,X1) ),
file('<stdin>',symmetry_r2_wellord2) ).
fof(c_0_152,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_153,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> are_equipotent(X1,X2) ),
file('<stdin>',redefinition_r2_wellord2) ).
fof(c_0_154,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_155,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
file('<stdin>',cc1_arytm_3) ).
fof(c_0_156,axiom,
! [X1] :
( v5_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& natural(X2)
& v1_xreal_0(X2)
& v1_int_1(X2)
& v1_rat_1(X2) ) ) ),
file('<stdin>',cc14_membered) ).
fof(c_0_157,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_int_1(X2)
& v1_rat_1(X2) ) ) ),
file('<stdin>',cc13_membered) ).
fof(c_0_158,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_rat_1(X2) ) ) ),
file('<stdin>',cc12_membered) ).
fof(c_0_159,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2) ) ) ),
file('<stdin>',cc11_membered) ).
fof(c_0_160,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> v1_xcmplx_0(X2) ) ),
file('<stdin>',cc10_membered) ).
fof(c_0_161,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_162,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('<stdin>',rc3_finset_1) ).
fof(c_0_163,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_164,axiom,
! [X1] :
( ( ordinal(X1)
& natural(X1) )
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1))
& natural(succ(X1)) ) ),
file('<stdin>',fc2_arytm_3) ).
fof(c_0_165,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_166,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('<stdin>',d9_funct_1) ).
fof(c_0_167,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('<stdin>',reflexivity_r1_ordinal1) ).
fof(c_0_168,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('<stdin>',fc6_relat_1) ).
fof(c_0_169,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('<stdin>',fc5_relat_1) ).
fof(c_0_170,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('<stdin>',fc1_struct_0) ).
fof(c_0_171,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_172,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_173,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_174,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_175,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_176,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('<stdin>',dt_k2_subset_1) ).
fof(c_0_177,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_178,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_179,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('<stdin>',dt_k2_funct_1) ).
fof(c_0_180,axiom,
! [X1] :
( element(X1,omega)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('<stdin>',cc3_arytm_3) ).
fof(c_0_181,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('<stdin>',d1_ordinal1) ).
fof(c_0_182,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_183,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_184,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_185,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('<stdin>',d4_ordinal1) ).
fof(c_0_186,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('<stdin>',cc2_ordinal1) ).
fof(c_0_187,axiom,
! [X1] :
( ( cup_closed(X1)
& diff_closed(X1) )
=> preboolean(X1) ),
file('<stdin>',cc2_finsub_1) ).
fof(c_0_188,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('<stdin>',cc2_arytm_3) ).
fof(c_0_189,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('<stdin>',involutiveness_k4_relat_1) ).
fof(c_0_190,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('<stdin>',fc8_relat_1) ).
fof(c_0_191,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('<stdin>',fc7_relat_1) ).
fof(c_0_192,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
file('<stdin>',fc4_ordinal1) ).
fof(c_0_193,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
file('<stdin>',fc11_relat_1) ).
fof(c_0_194,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('<stdin>',dt_k4_relat_1) ).
fof(c_0_195,axiom,
! [X1] : ~ empty(singleton(X1)),
file('<stdin>',fc2_subset_1) ).
fof(c_0_196,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_197,axiom,
! [X1] : ~ empty(succ(X1)),
file('<stdin>',fc1_ordinal1) ).
fof(c_0_198,axiom,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
file('<stdin>',fc1_finsub_1) ).
fof(c_0_199,axiom,
! [X1] :
( ~ empty(singleton(X1))
& finite(singleton(X1)) ),
file('<stdin>',fc1_finset_1) ).
fof(c_0_200,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_201,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('<stdin>',d3_pre_topc) ).
fof(c_0_202,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_203,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_204,axiom,
! [X1,X2] : equipotent(X1,X1),
file('<stdin>',reflexivity_r2_wellord2) ).
fof(c_0_205,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_206,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_207,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_208,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_209,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_210,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
file('<stdin>',d6_ordinal1) ).
fof(c_0_211,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('<stdin>',dt_l3_lattices) ).
fof(c_0_212,axiom,
! [X1] :
( join_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('<stdin>',dt_l2_lattices) ).
fof(c_0_213,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('<stdin>',dt_l1_lattices) ).
fof(c_0_214,axiom,
! [X1] :
( v2_membered(X1)
=> v1_membered(X1) ),
file('<stdin>',cc4_membered) ).
fof(c_0_215,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('<stdin>',cc3_ordinal1) ).
fof(c_0_216,axiom,
! [X1] :
( v3_membered(X1)
=> v2_membered(X1) ),
file('<stdin>',cc3_membered) ).
fof(c_0_217,axiom,
! [X1] :
( v4_membered(X1)
=> v3_membered(X1) ),
file('<stdin>',cc2_membered) ).
fof(c_0_218,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('<stdin>',cc1_relat_1) ).
fof(c_0_219,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('<stdin>',cc1_ordinal1) ).
fof(c_0_220,axiom,
! [X1] :
( v5_membered(X1)
=> v4_membered(X1) ),
file('<stdin>',cc1_membered) ).
fof(c_0_221,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('<stdin>',cc1_funct_1) ).
fof(c_0_222,axiom,
! [X1] :
( preboolean(X1)
=> ( cup_closed(X1)
& diff_closed(X1) ) ),
file('<stdin>',cc1_finsub_1) ).
fof(c_0_223,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('<stdin>',cc1_finset_1) ).
fof(c_0_224,axiom,
! [X1] :
( empty(X1)
=> ( v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ) ),
file('<stdin>',cc15_membered) ).
fof(c_0_225,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('<stdin>',fc2_funct_1) ).
fof(c_0_226,axiom,
! [X1] : relation(identity_relation(X1)),
file('<stdin>',dt_k6_relat_1) ).
fof(c_0_227,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('<stdin>',dt_k1_wellord2) ).
fof(c_0_228,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_229,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('<stdin>',d4_subset_1) ).
fof(c_0_230,axiom,
? [X1] :
( one_sorted_str(X1)
& ~ empty_carrier(X1) ),
file('<stdin>',rc3_struct_0) ).
fof(c_0_231,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc3_ordinal1) ).
fof(c_0_232,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_233,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_234,axiom,
? [X1] :
( ~ empty(X1)
& v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ),
file('<stdin>',rc1_membered) ).
fof(c_0_235,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('<stdin>',rc1_finset_1) ).
fof(c_0_236,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('<stdin>',rc1_arytm_3) ).
fof(c_0_237,axiom,
( epsilon_transitive(omega)
& epsilon_connected(omega)
& ordinal(omega)
& ~ empty(omega) ),
file('<stdin>',fc1_ordinal2) ).
fof(c_0_238,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('<stdin>',rc4_funct_1) ).
fof(c_0_239,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_240,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_241,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_242,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_243,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_244,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_245,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
file('<stdin>',rc1_partfun1) ).
fof(c_0_246,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& being_limit_ordinal(X1) ),
file('<stdin>',rc1_ordinal2) ).
fof(c_0_247,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc1_ordinal1) ).
fof(c_0_248,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_249,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('<stdin>',fc6_membered) ).
fof(c_0_250,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('<stdin>',fc4_relat_1) ).
fof(c_0_251,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_252,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_253,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('<stdin>',fc12_relat_1) ).
fof(c_0_254,axiom,
? [X1] : latt_str(X1),
file('<stdin>',existence_l3_lattices) ).
fof(c_0_255,axiom,
? [X1] : join_semilatt_str(X1),
file('<stdin>',existence_l2_lattices) ).
fof(c_0_256,axiom,
? [X1] : one_sorted_str(X1),
file('<stdin>',existence_l1_struct_0) ).
fof(c_0_257,axiom,
? [X1] : meet_semilatt_str(X1),
file('<stdin>',existence_l1_lattices) ).
fof(c_0_258,axiom,
$true,
file('<stdin>',dt_u1_struct_0) ).
fof(c_0_259,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_260,axiom,
$true,
file('<stdin>',dt_m1_relset_1) ).
fof(c_0_261,axiom,
$true,
file('<stdin>',dt_l1_struct_0) ).
fof(c_0_262,axiom,
$true,
file('<stdin>',dt_k9_relat_1) ).
fof(c_0_263,axiom,
$true,
file('<stdin>',dt_k5_ordinal2) ).
fof(c_0_264,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_265,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_266,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_267,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_268,axiom,
$true,
file('<stdin>',dt_k3_relat_1) ).
fof(c_0_269,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_270,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_271,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_272,axiom,
$true,
file('<stdin>',dt_k2_relat_1) ).
fof(c_0_273,axiom,
$true,
file('<stdin>',dt_k2_mcart_1) ).
fof(c_0_274,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_275,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_276,axiom,
$true,
file('<stdin>',dt_k1_wellord1) ).
fof(c_0_277,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_278,axiom,
$true,
file('<stdin>',dt_k1_setfam_1) ).
fof(c_0_279,axiom,
$true,
file('<stdin>',dt_k1_relat_1) ).
fof(c_0_280,axiom,
$true,
file('<stdin>',dt_k1_ordinal1) ).
fof(c_0_281,axiom,
$true,
file('<stdin>',dt_k1_mcart_1) ).
fof(c_0_282,axiom,
$true,
file('<stdin>',dt_k1_funct_1) ).
fof(c_0_283,axiom,
$true,
file('<stdin>',dt_k1_enumset1) ).
fof(c_0_284,axiom,
$true,
file('<stdin>',dt_k1_binop_1) ).
fof(c_0_285,axiom,
$true,
file('<stdin>',dt_k10_relat_1) ).
fof(c_0_286,plain,
! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
<=> ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) )
& X2 = X4
& ? [X9] :
( ordinal(X9)
& X4 = X9
& ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( X10 != empty_set
& ! [X11] :
~ ( in(X11,X10)
& ! [X12] :
( ( in(X12,X10)
& subset(X11,X12) )
=> X12 = X11 ) ) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_287,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_288,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_289,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_2]) ).
fof(c_0_290,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_291,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_292,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_293,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_6 ).
fof(c_0_294,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_7 ).
fof(c_0_295,axiom,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,succ(X1))
& X4 = X3
& ? [X13] :
( ordinal(X13)
& X3 = X13
& ( in(X13,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X13)))
=> ~ ( X14 != empty_set
& ! [X15] :
~ ( in(X15,X14)
& ! [X16] :
( ( in(X16,X14)
& subset(X15,X16) )
=> X16 = X15 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_286,theory(equality,[symmetry])]) ).
fof(c_0_296,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_9 ).
fof(c_0_297,plain,
! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
=> ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) )
& X2 = X4
& ? [X9] :
( ordinal(X9)
& X4 = X9
& ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( X10 != empty_set
& ! [X11] :
~ ( in(X11,X10)
& ! [X12] :
( ( in(X12,X10)
& subset(X11,X12) )
=> X12 = X11 ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_286]) ).
fof(c_0_298,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_10 ).
fof(c_0_299,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_11 ).
fof(c_0_300,axiom,
! [X1,X2,X3,X4] :
( X4 = unordered_triple(X1,X2,X3)
<=> ! [X5] :
( in(X5,X4)
<=> ~ ( X5 != X1
& X5 != X2
& X5 != X3 ) ) ),
c_0_12 ).
fof(c_0_301,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_13 ).
fof(c_0_302,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_14 ).
fof(c_0_303,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_15 ).
fof(c_0_304,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(powerset(X1)))
& relation(X3)
& function(X3) )
=> ( ! [X4,X5,X6] :
( ( X4 = X5
& in(relation_image(X3,X5),X2)
& X4 = X6
& in(relation_image(X3,X6),X2) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,powerset(relation_dom(X3)))
& X6 = X5
& in(relation_image(X3,X5),X2) ) ) ) ),
c_0_16 ).
fof(c_0_305,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_17 ).
fof(c_0_306,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_18 ).
fof(c_0_307,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = fiber(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 != X2
& in(ordered_pair(X4,X2),X1) ) ) ) ),
c_0_19 ).
fof(c_0_308,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_20 ).
fof(c_0_309,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_21 ).
fof(c_0_310,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_22]) ).
fof(c_0_311,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_23 ).
fof(c_0_312,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_24 ).
fof(c_0_313,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_25 ).
fof(c_0_314,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_26 ).
fof(c_0_315,axiom,
! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6] :
( in(X6,X2)
& X4 = set_difference(X6,singleton(X1)) )
& X3 = X5
& ? [X7] :
( in(X7,X2)
& X5 = set_difference(X7,singleton(X1)) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(X1))
& X5 = X4
& ? [X8] :
( in(X8,X2)
& X4 = set_difference(X8,singleton(X1)) ) ) ) ) ),
c_0_27 ).
fof(c_0_316,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
c_0_28 ).
fof(c_0_317,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( meet_absorbing(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,meet(X1,X2,X3),X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_318,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_30 ).
fof(c_0_319,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_31 ).
fof(c_0_320,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_32 ).
fof(c_0_321,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
c_0_33 ).
fof(c_0_322,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
c_0_34 ).
fof(c_0_323,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_35 ).
fof(c_0_324,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_36 ).
fof(c_0_325,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_37]) ).
fof(c_0_326,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
c_0_38 ).
fof(c_0_327,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_39 ).
fof(c_0_328,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_40 ).
fof(c_0_329,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_330,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_42 ).
fof(c_0_331,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
c_0_43 ).
fof(c_0_332,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
c_0_44 ).
fof(c_0_333,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet_commut(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_334,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(join_commut(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_335,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_47 ).
fof(c_0_336,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_337,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(join(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_338,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_339,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_340,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_341,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_342,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
c_0_54 ).
fof(c_0_343,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_55 ).
fof(c_0_344,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
c_0_56 ).
fof(c_0_345,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_57 ).
fof(c_0_346,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
c_0_58 ).
fof(c_0_347,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
c_0_59 ).
fof(c_0_348,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
c_0_60 ).
fof(c_0_349,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_61 ).
fof(c_0_350,axiom,
! [X1] :
( function(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) ),
c_0_62 ).
fof(c_0_351,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_63 ).
fof(c_0_352,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
c_0_64 ).
fof(c_0_353,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_65 ).
fof(c_0_354,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_66 ).
fof(c_0_355,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_67 ).
fof(c_0_356,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
c_0_68 ).
fof(c_0_357,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_69]) ).
fof(c_0_358,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
c_0_70 ).
fof(c_0_359,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
c_0_71 ).
fof(c_0_360,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
c_0_72 ).
fof(c_0_361,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
c_0_73 ).
fof(c_0_362,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
c_0_74 ).
fof(c_0_363,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
c_0_75 ).
fof(c_0_364,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
c_0_76 ).
fof(c_0_365,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
c_0_77 ).
fof(c_0_366,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_78 ).
fof(c_0_367,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_79 ).
fof(c_0_368,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_80]) ).
fof(c_0_369,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_81 ).
fof(c_0_370,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_82 ).
fof(c_0_371,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
c_0_83 ).
fof(c_0_372,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_84]) ).
fof(c_0_373,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3) ),
c_0_85 ).
fof(c_0_374,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3)
& quasi_total(X3,X1,X2) ),
c_0_86 ).
fof(c_0_375,axiom,
! [X1,X2] :
? [X3] : relation_of2_as_subset(X3,X1,X2),
c_0_87 ).
fof(c_0_376,axiom,
! [X1,X2] :
? [X3] : relation_of2(X3,X1,X2),
c_0_88 ).
fof(c_0_377,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
c_0_89 ).
fof(c_0_378,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_90 ).
fof(c_0_379,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_91 ).
fof(c_0_380,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
c_0_92 ).
fof(c_0_381,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
c_0_93 ).
fof(c_0_382,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
c_0_94 ).
fof(c_0_383,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
c_0_95 ).
fof(c_0_384,axiom,
! [X1] :
( X1 = omega
<=> ( in(empty_set,X1)
& being_limit_ordinal(X1)
& ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> ( ( in(empty_set,X2)
& being_limit_ordinal(X2) )
=> subset(X1,X2) ) ) ) ),
c_0_96 ).
fof(c_0_385,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_97 ).
fof(c_0_386,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
c_0_98 ).
fof(c_0_387,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
c_0_99 ).
fof(c_0_388,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_100 ).
fof(c_0_389,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
c_0_101 ).
fof(c_0_390,axiom,
! [X1] :
( finite(X1)
<=> ? [X2] :
( relation(X2)
& function(X2)
& relation_rng(X2) = X1
& in(relation_dom(X2),omega) ) ),
c_0_102 ).
fof(c_0_391,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_392,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_104 ).
fof(c_0_393,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_394,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_395,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
c_0_107 ).
fof(c_0_396,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
c_0_108 ).
fof(c_0_397,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_398,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_399,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_400,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_112 ).
fof(c_0_401,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
c_0_113 ).
fof(c_0_402,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
c_0_114 ).
fof(c_0_403,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
c_0_115 ).
fof(c_0_404,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_405,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_406,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
c_0_118 ).
fof(c_0_407,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
c_0_119 ).
fof(c_0_408,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
c_0_120 ).
fof(c_0_409,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
c_0_121 ).
fof(c_0_410,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
c_0_122 ).
fof(c_0_411,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
c_0_123 ).
fof(c_0_412,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
c_0_124 ).
fof(c_0_413,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_125 ).
fof(c_0_414,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
c_0_126 ).
fof(c_0_415,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
c_0_127 ).
fof(c_0_416,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
c_0_128 ).
fof(c_0_417,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
c_0_129 ).
fof(c_0_418,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
c_0_130 ).
fof(c_0_419,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
c_0_131 ).
fof(c_0_420,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
c_0_132 ).
fof(c_0_421,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
c_0_133 ).
fof(c_0_422,axiom,
! [X1] :
( v5_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2)
& v5_membered(X2) ) ) ),
c_0_134 ).
fof(c_0_423,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2) ) ) ),
c_0_135 ).
fof(c_0_424,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2) ) ) ),
c_0_136 ).
fof(c_0_425,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2) ) ) ),
c_0_137 ).
fof(c_0_426,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> v1_membered(X2) ) ),
c_0_138 ).
fof(c_0_427,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
c_0_139 ).
fof(c_0_428,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
c_0_140 ).
fof(c_0_429,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_141]) ).
fof(c_0_430,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_142 ).
fof(c_0_431,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
c_0_143 ).
fof(c_0_432,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
c_0_144 ).
fof(c_0_433,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
c_0_145 ).
fof(c_0_434,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
c_0_146 ).
fof(c_0_435,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
c_0_147 ).
fof(c_0_436,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
c_0_148 ).
fof(c_0_437,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
c_0_149 ).
fof(c_0_438,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
c_0_150 ).
fof(c_0_439,axiom,
! [X1,X2] :
( equipotent(X1,X2)
=> equipotent(X2,X1) ),
c_0_151 ).
fof(c_0_440,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_152 ).
fof(c_0_441,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> are_equipotent(X1,X2) ),
c_0_153 ).
fof(c_0_442,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_154 ).
fof(c_0_443,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
c_0_155 ).
fof(c_0_444,axiom,
! [X1] :
( v5_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& natural(X2)
& v1_xreal_0(X2)
& v1_int_1(X2)
& v1_rat_1(X2) ) ) ),
c_0_156 ).
fof(c_0_445,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_int_1(X2)
& v1_rat_1(X2) ) ) ),
c_0_157 ).
fof(c_0_446,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_rat_1(X2) ) ) ),
c_0_158 ).
fof(c_0_447,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2) ) ) ),
c_0_159 ).
fof(c_0_448,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> v1_xcmplx_0(X2) ) ),
c_0_160 ).
fof(c_0_449,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
c_0_161 ).
fof(c_0_450,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_451,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_452,plain,
! [X1] :
( ( ordinal(X1)
& natural(X1) )
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1))
& natural(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_453,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_165 ).
fof(c_0_454,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
c_0_166 ).
fof(c_0_455,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
c_0_167 ).
fof(c_0_456,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_457,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_458,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_459,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_171 ).
fof(c_0_460,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_172 ).
fof(c_0_461,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_173 ).
fof(c_0_462,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_174 ).
fof(c_0_463,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_175 ).
fof(c_0_464,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
c_0_176 ).
fof(c_0_465,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_177 ).
fof(c_0_466,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_467,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
c_0_179 ).
fof(c_0_468,axiom,
! [X1] :
( element(X1,omega)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
c_0_180 ).
fof(c_0_469,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
c_0_181 ).
fof(c_0_470,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_182]) ).
fof(c_0_471,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_472,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_184 ).
fof(c_0_473,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
c_0_185 ).
fof(c_0_474,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
c_0_186 ).
fof(c_0_475,axiom,
! [X1] :
( ( cup_closed(X1)
& diff_closed(X1) )
=> preboolean(X1) ),
c_0_187 ).
fof(c_0_476,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
c_0_188 ).
fof(c_0_477,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
c_0_189 ).
fof(c_0_478,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
c_0_190 ).
fof(c_0_479,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
c_0_191 ).
fof(c_0_480,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
c_0_192 ).
fof(c_0_481,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
c_0_193 ).
fof(c_0_482,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
c_0_194 ).
fof(c_0_483,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_484,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_485,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_486,plain,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_487,plain,
! [X1] :
( ~ empty(singleton(X1))
& finite(singleton(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_488,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_200 ).
fof(c_0_489,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
c_0_201 ).
fof(c_0_490,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_202 ).
fof(c_0_491,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_203 ).
fof(c_0_492,axiom,
! [X1,X2] : equipotent(X1,X1),
c_0_204 ).
fof(c_0_493,axiom,
! [X1,X2] : subset(X1,X1),
c_0_205 ).
fof(c_0_494,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_206 ).
fof(c_0_495,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_207 ).
fof(c_0_496,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_208 ).
fof(c_0_497,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_209 ).
fof(c_0_498,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
c_0_210 ).
fof(c_0_499,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
c_0_211 ).
fof(c_0_500,axiom,
! [X1] :
( join_semilatt_str(X1)
=> one_sorted_str(X1) ),
c_0_212 ).
fof(c_0_501,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
c_0_213 ).
fof(c_0_502,axiom,
! [X1] :
( v2_membered(X1)
=> v1_membered(X1) ),
c_0_214 ).
fof(c_0_503,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
c_0_215 ).
fof(c_0_504,axiom,
! [X1] :
( v3_membered(X1)
=> v2_membered(X1) ),
c_0_216 ).
fof(c_0_505,axiom,
! [X1] :
( v4_membered(X1)
=> v3_membered(X1) ),
c_0_217 ).
fof(c_0_506,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
c_0_218 ).
fof(c_0_507,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
c_0_219 ).
fof(c_0_508,axiom,
! [X1] :
( v5_membered(X1)
=> v4_membered(X1) ),
c_0_220 ).
fof(c_0_509,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
c_0_221 ).
fof(c_0_510,axiom,
! [X1] :
( preboolean(X1)
=> ( cup_closed(X1)
& diff_closed(X1) ) ),
c_0_222 ).
fof(c_0_511,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
c_0_223 ).
fof(c_0_512,axiom,
! [X1] :
( empty(X1)
=> ( v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ) ),
c_0_224 ).
fof(c_0_513,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
c_0_225 ).
fof(c_0_514,axiom,
! [X1] : relation(identity_relation(X1)),
c_0_226 ).
fof(c_0_515,axiom,
! [X1] : relation(inclusion_relation(X1)),
c_0_227 ).
fof(c_0_516,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_228 ).
fof(c_0_517,axiom,
! [X1] : cast_to_subset(X1) = X1,
c_0_229 ).
fof(c_0_518,plain,
? [X1] :
( one_sorted_str(X1)
& ~ empty_carrier(X1) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_519,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_520,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_521,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_522,plain,
? [X1] :
( ~ empty(X1)
& v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_523,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_524,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_525,plain,
( epsilon_transitive(omega)
& epsilon_connected(omega)
& ordinal(omega)
& ~ empty(omega) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_526,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
c_0_238 ).
fof(c_0_527,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_239 ).
fof(c_0_528,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_240 ).
fof(c_0_529,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_241 ).
fof(c_0_530,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_242 ).
fof(c_0_531,axiom,
? [X1] : empty(X1),
c_0_243 ).
fof(c_0_532,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_244 ).
fof(c_0_533,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
c_0_245 ).
fof(c_0_534,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& being_limit_ordinal(X1) ),
c_0_246 ).
fof(c_0_535,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_247 ).
fof(c_0_536,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_248 ).
fof(c_0_537,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
c_0_249 ).
fof(c_0_538,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_250 ).
fof(c_0_539,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_251 ).
fof(c_0_540,axiom,
empty(empty_set),
c_0_252 ).
fof(c_0_541,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_253 ).
fof(c_0_542,axiom,
? [X1] : latt_str(X1),
c_0_254 ).
fof(c_0_543,axiom,
? [X1] : join_semilatt_str(X1),
c_0_255 ).
fof(c_0_544,axiom,
? [X1] : one_sorted_str(X1),
c_0_256 ).
fof(c_0_545,axiom,
? [X1] : meet_semilatt_str(X1),
c_0_257 ).
fof(c_0_546,axiom,
$true,
c_0_258 ).
fof(c_0_547,axiom,
$true,
c_0_259 ).
fof(c_0_548,axiom,
$true,
c_0_260 ).
fof(c_0_549,axiom,
$true,
c_0_261 ).
fof(c_0_550,axiom,
$true,
c_0_262 ).
fof(c_0_551,axiom,
$true,
c_0_263 ).
fof(c_0_552,axiom,
$true,
c_0_264 ).
fof(c_0_553,axiom,
$true,
c_0_265 ).
fof(c_0_554,axiom,
$true,
c_0_266 ).
fof(c_0_555,axiom,
$true,
c_0_267 ).
fof(c_0_556,axiom,
$true,
c_0_268 ).
fof(c_0_557,axiom,
$true,
c_0_269 ).
fof(c_0_558,axiom,
$true,
c_0_270 ).
fof(c_0_559,axiom,
$true,
c_0_271 ).
fof(c_0_560,axiom,
$true,
c_0_272 ).
fof(c_0_561,axiom,
$true,
c_0_273 ).
fof(c_0_562,axiom,
$true,
c_0_274 ).
fof(c_0_563,axiom,
$true,
c_0_275 ).
fof(c_0_564,axiom,
$true,
c_0_276 ).
fof(c_0_565,axiom,
$true,
c_0_277 ).
fof(c_0_566,axiom,
$true,
c_0_278 ).
fof(c_0_567,axiom,
$true,
c_0_279 ).
fof(c_0_568,axiom,
$true,
c_0_280 ).
fof(c_0_569,axiom,
$true,
c_0_281 ).
fof(c_0_570,axiom,
$true,
c_0_282 ).
fof(c_0_571,axiom,
$true,
c_0_283 ).
fof(c_0_572,axiom,
$true,
c_0_284 ).
fof(c_0_573,axiom,
$true,
c_0_285 ).
fof(c_0_574,plain,
! [X19,X20,X27,X31,X32,X34,X39,X40,X41,X42,X43,X44] :
( ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| ordered_pair(esk138_2(X19,X20),esk139_2(X19,X20)) = esk136_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| in(esk138_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| esk138_2(X19,X20) = esk140_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| in(esk139_2(X19,X20),esk140_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| ~ in(X27,esk140_2(X19,X20))
| in(ordered_pair(esk139_2(X19,X20),X27),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| esk135_2(X19,X20) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| ordered_pair(esk141_2(X19,X20),esk142_2(X19,X20)) = esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| in(esk141_2(X19,X20),X19)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| esk141_2(X19,X20) = esk143_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| in(esk142_2(X19,X20),esk143_2(X19,X20))
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| ~ in(X31,esk143_2(X19,X20))
| in(ordered_pair(esk142_2(X19,X20),X31),X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk145_4(X19,X20,X32,X34),cartesian_product2(X19,X32))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk145_4(X19,X20,X32,X34) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ordered_pair(esk146_4(X19,X20,X32,X34),esk147_4(X19,X20,X32,X34)) = X34
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk146_4(X19,X20,X32,X34),X19)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( esk146_4(X19,X20,X32,X34) = esk148_4(X19,X20,X32,X34)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk147_4(X19,X20,X32,X34),esk148_4(X19,X20,X32,X34))
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(X39,esk148_4(X19,X20,X32,X34))
| in(ordered_pair(esk147_4(X19,X20,X32,X34),X39),X20)
| ~ in(X34,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( in(esk149_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,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_2(X19,X20)
| empty(X19)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X43,esk149_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,esk144_3(X19,X20,X32))
| esk136_2(X19,X20) != esk137_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_287])])])])])]) ).
fof(c_0_575,plain,
! [X7,X8,X9,X10,X11,X12] :
( empty(X7)
| empty(X8)
| ~ function(X10)
| ~ quasi_total(X10,cartesian_product2(X7,X8),X9)
| ~ relation_of2(X10,cartesian_product2(X7,X8),X9)
| ~ element(X11,X7)
| ~ element(X12,X8)
| element(apply_binary_as_element(X7,X8,X9,X10,X11,X12),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_288])]) ).
fof(c_0_576,plain,
! [X12,X13,X18,X20,X22,X25,X26,X27,X28] :
( ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk129_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk127_2(X12,X13),esk129_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| ~ in(X18,esk129_2(X12,X13))
| in(ordered_pair(esk127_2(X12,X13),X18),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk126_2(X12,X13),X12)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| esk126_2(X12,X13) = esk130_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| in(esk128_2(X12,X13),esk130_2(X12,X13))
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| ~ in(X20,esk130_2(X12,X13))
| in(ordered_pair(esk128_2(X12,X13),X20),X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk132_3(X12,X13,X22),X12)
| ~ in(X22,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( esk132_3(X12,X13,X22) = esk133_3(X12,X13,X22)
| ~ in(X22,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(X22,esk133_3(X12,X13,X22))
| ~ in(X22,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(X25,esk133_3(X12,X13,X22))
| in(ordered_pair(X22,X25),X13)
| ~ in(X22,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( in(esk134_5(X12,X13,X26,X27,X28),X28)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_2(X12,X13)
| empty(X12)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X26,esk134_5(X12,X13,X26,X27,X28)),X13)
| ~ in(X26,X28)
| X27 != X28
| ~ in(X27,X12)
| ~ in(X27,X12)
| in(X26,esk131_2(X12,X13))
| esk127_2(X12,X13) != esk128_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_289])])])])])]) ).
fof(c_0_577,plain,
! [X7,X8,X9,X10,X11,X12] :
( empty(X7)
| empty(X8)
| ~ function(X10)
| ~ quasi_total(X10,cartesian_product2(X7,X8),X9)
| ~ relation_of2(X10,cartesian_product2(X7,X8),X9)
| ~ element(X11,X7)
| ~ element(X12,X8)
| apply_binary_as_element(X7,X8,X9,X10,X11,X12) = apply_binary(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_290])]) ).
fof(c_0_578,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| meet(X4,X5,X6) = apply_binary_as_element(the_carrier(X4),the_carrier(X4),the_carrier(X4),the_L_meet(X4),X5,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_291])])]) ).
fof(c_0_579,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join(X4,X5,X6) = apply_binary_as_element(the_carrier(X4),the_carrier(X4),the_carrier(X4),the_L_join(X4),X5,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_292])])]) ).
fof(c_0_580,plain,
! [X13,X14,X15,X24,X28,X29,X30,X31] :
( ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk184_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk184_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk184_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk184_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,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk184_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) = ordered_pair(esk186_3(X13,X14,X15),esk187_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) = ordered_pair(esk186_3(X13,X14,X15),esk187_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) = ordered_pair(esk186_3(X13,X14,X15),esk187_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) = ordered_pair(esk186_3(X13,X14,X15),esk187_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,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) = ordered_pair(esk186_3(X13,X14,X15),esk187_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk186_3(X13,X14,X15)),apply(X15,esk187_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk186_3(X13,X14,X15)),apply(X15,esk187_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk186_3(X13,X14,X15)),apply(X15,esk187_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk186_3(X13,X14,X15)),apply(X15,esk187_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,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk186_3(X13,X14,X15)),apply(X15,esk187_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk185_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,esk190_3(X13,X14,X15))
| esk183_3(X13,X14,X15) = esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk185_3(X13,X14,X15) = ordered_pair(esk188_3(X13,X14,X15),esk189_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| esk185_3(X13,X14,X15) = ordered_pair(esk188_3(X13,X14,X15),esk189_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk185_3(X13,X14,X15) = ordered_pair(esk188_3(X13,X14,X15),esk189_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| esk185_3(X13,X14,X15) = ordered_pair(esk188_3(X13,X14,X15),esk189_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,esk190_3(X13,X14,X15))
| esk185_3(X13,X14,X15) = ordered_pair(esk188_3(X13,X14,X15),esk189_3(X13,X14,X15))
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk188_3(X13,X14,X15)),apply(X15,esk189_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk188_3(X13,X14,X15)),apply(X15,esk189_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk188_3(X13,X14,X15)),apply(X15,esk189_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk188_3(X13,X14,X15)),apply(X15,esk189_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,esk190_3(X13,X14,X15))
| in(ordered_pair(apply(X15,esk188_3(X13,X14,X15)),apply(X15,esk189_3(X13,X14,X15))),X14)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk191_4(X13,X14,X15,X24),cartesian_product2(X13,X13))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) != esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( esk191_4(X13,X14,X15,X24) = X24
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) != esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( X24 = ordered_pair(esk192_4(X13,X14,X15,X24),esk193_4(X13,X14,X15,X24))
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) != esk185_3(X13,X14,X15)
| ~ relation(X14)
| ~ relation(X15)
| ~ function(X15) )
& ( in(ordered_pair(apply(X15,esk192_4(X13,X14,X15,X24)),apply(X15,esk193_4(X13,X14,X15,X24))),X14)
| ~ in(X24,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) != esk185_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,esk190_3(X13,X14,X15))
| esk184_3(X13,X14,X15) != esk185_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_293])])])])])]) ).
fof(c_0_581,plain,
! [X7,X8,X9,X10,X11,X13,X14,X15,X18] :
( ( in(ordered_pair(X10,esk86_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(esk86_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(esk87_3(X7,X8,X9),esk88_3(X7,X8,X9)),X9)
| ~ in(ordered_pair(esk87_3(X7,X8,X9),X18),X7)
| ~ in(ordered_pair(X18,esk88_3(X7,X8,X9)),X8)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk87_3(X7,X8,X9),esk89_3(X7,X8,X9)),X7)
| in(ordered_pair(esk87_3(X7,X8,X9),esk88_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk89_3(X7,X8,X9),esk88_3(X7,X8,X9)),X8)
| in(ordered_pair(esk87_3(X7,X8,X9),esk88_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_294])])])])])]) ).
fof(c_0_582,plain,
! [X17,X22,X25,X27,X28,X29,X30,X32] :
( ( in(esk170_2(X17,X22),succ(X17))
| ~ in(X22,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( esk170_2(X17,X22) = X22
| ~ in(X22,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( ordinal(esk171_2(X17,X22))
| ~ in(X22,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( X22 = esk171_2(X17,X22)
| ~ in(X22,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( in(esk172_3(X17,X22,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(esk171_2(X17,X22))))
| ~ in(esk171_2(X17,X22),omega)
| ~ in(X22,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( ~ in(X27,X25)
| ~ subset(esk172_3(X17,X22,X25),X27)
| X27 = esk172_3(X17,X22,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(esk171_2(X17,X22))))
| ~ in(esk171_2(X17,X22),omega)
| ~ in(X22,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( in(X30,omega)
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( element(esk173_4(X17,X28,X29,X30),powerset(powerset(X30)))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( esk173_4(X17,X28,X29,X30) != empty_set
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( in(esk174_5(X17,X28,X29,X30,X32),esk173_4(X17,X28,X29,X30))
| ~ in(X32,esk173_4(X17,X28,X29,X30))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( subset(X32,esk174_5(X17,X28,X29,X30,X32))
| ~ in(X32,esk173_4(X17,X28,X29,X30))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( esk174_5(X17,X28,X29,X30,X32) != X32
| ~ in(X32,esk173_4(X17,X28,X29,X30))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| epred1_3(esk168_1(X17),esk167_1(X17),esk166_1(X17))
| ~ ordinal(X17) )
& ( in(esk170_2(X17,X22),succ(X17))
| ~ in(X22,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( esk170_2(X17,X22) = X22
| ~ in(X22,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( ordinal(esk171_2(X17,X22))
| ~ in(X22,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( X22 = esk171_2(X17,X22)
| ~ in(X22,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( in(esk172_3(X17,X22,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(esk171_2(X17,X22))))
| ~ in(esk171_2(X17,X22),omega)
| ~ in(X22,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( ~ in(X27,X25)
| ~ subset(esk172_3(X17,X22,X25),X27)
| X27 = esk172_3(X17,X22,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(esk171_2(X17,X22))))
| ~ in(esk171_2(X17,X22),omega)
| ~ in(X22,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( in(X30,omega)
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( element(esk173_4(X17,X28,X29,X30),powerset(powerset(X30)))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( esk173_4(X17,X28,X29,X30) != empty_set
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( in(esk174_5(X17,X28,X29,X30,X32),esk173_4(X17,X28,X29,X30))
| ~ in(X32,esk173_4(X17,X28,X29,X30))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( subset(X32,esk174_5(X17,X28,X29,X30,X32))
| ~ in(X32,esk173_4(X17,X28,X29,X30))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(X17) )
& ( esk174_5(X17,X28,X29,X30,X32) != X32
| ~ in(X32,esk173_4(X17,X28,X29,X30))
| X28 != X30
| ~ ordinal(X30)
| X29 != X28
| ~ in(X29,succ(X17))
| in(X28,esk169_1(X17))
| esk167_1(X17) != esk168_1(X17)
| ~ ordinal(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_295])])])])])]) ).
fof(c_0_583,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(esk80_3(X6,X7,X8),esk81_3(X6,X7,X8)),X6)
| ~ in(esk80_3(X6,X7,X8),relation_field(X6))
| ~ in(esk81_3(X6,X7,X8),relation_field(X6))
| ~ in(ordered_pair(apply(X8,esk80_3(X6,X7,X8)),apply(X8,esk81_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(esk80_3(X6,X7,X8),relation_field(X6))
| in(ordered_pair(esk80_3(X6,X7,X8),esk81_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(esk81_3(X6,X7,X8),relation_field(X6))
| in(ordered_pair(esk80_3(X6,X7,X8),esk81_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,esk80_3(X6,X7,X8)),apply(X8,esk81_3(X6,X7,X8))),X7)
| in(ordered_pair(esk80_3(X6,X7,X8),esk81_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_296])])])])])]) ).
fof(c_0_584,plain,
! [X13,X14,X15,X17,X19,X21,X23] :
( ( X13 = X14
| ~ epred1_3(X15,X14,X13) )
& ( ordinal(esk216_3(X13,X14,X15))
| ~ epred1_3(X15,X14,X13) )
& ( X14 = esk216_3(X13,X14,X15)
| ~ epred1_3(X15,X14,X13) )
& ( in(esk217_4(X13,X14,X15,X17),X17)
| X17 = empty_set
| ~ element(X17,powerset(powerset(esk216_3(X13,X14,X15))))
| ~ in(esk216_3(X13,X14,X15),omega)
| ~ epred1_3(X15,X14,X13) )
& ( ~ in(X19,X17)
| ~ subset(esk217_4(X13,X14,X15,X17),X19)
| X19 = esk217_4(X13,X14,X15,X17)
| X17 = empty_set
| ~ element(X17,powerset(powerset(esk216_3(X13,X14,X15))))
| ~ in(esk216_3(X13,X14,X15),omega)
| ~ epred1_3(X15,X14,X13) )
& ( X13 = X15
| ~ epred1_3(X15,X14,X13) )
& ( ordinal(esk218_3(X13,X14,X15))
| ~ epred1_3(X15,X14,X13) )
& ( X15 = esk218_3(X13,X14,X15)
| ~ epred1_3(X15,X14,X13) )
& ( in(esk219_4(X13,X14,X15,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(esk218_3(X13,X14,X15))))
| ~ in(esk218_3(X13,X14,X15),omega)
| ~ epred1_3(X15,X14,X13) )
& ( ~ in(X23,X21)
| ~ subset(esk219_4(X13,X14,X15,X21),X23)
| X23 = esk219_4(X13,X14,X15,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(esk218_3(X13,X14,X15))))
| ~ in(esk218_3(X13,X14,X15),omega)
| ~ epred1_3(X15,X14,X13) ) ),
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_297])])])])]) ).
fof(c_0_585,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_298])])])])])]) ).
fof(c_0_586,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_299])])])])])]) ).
fof(c_0_587,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_300])])])])])]) ).
fof(c_0_588,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_301])])])])])]) ).
fof(c_0_589,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_302])])])])])]) ).
fof(c_0_590,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk46_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk47_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk46_4(X7,X8,X9,X10),esk47_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(esk48_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk48_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk49_3(X16,X17,X18),X16)
| in(esk48_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk50_3(X16,X17,X18),X17)
| in(esk48_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk48_3(X16,X17,X18) = ordered_pair(esk49_3(X16,X17,X18),esk50_3(X16,X17,X18))
| in(esk48_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_303])])])])])]) ).
fof(c_0_591,plain,
! [X7,X8,X9,X14,X16,X17] :
( ( in(esk203_4(X7,X8,X9,X14),powerset(relation_dom(X9)))
| ~ in(X14,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk200_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( esk203_4(X7,X8,X9,X14) = X14
| ~ in(X14,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk200_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(relation_image(X9,X14),X8)
| ~ in(X14,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk200_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X17,powerset(relation_dom(X9)))
| X17 != X16
| ~ in(relation_image(X9,X16),X8)
| in(X16,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk200_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(esk203_4(X7,X8,X9,X14),powerset(relation_dom(X9)))
| ~ in(X14,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk200_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( esk203_4(X7,X8,X9,X14) = X14
| ~ in(X14,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk200_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(relation_image(X9,X14),X8)
| ~ in(X14,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk200_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X17,powerset(relation_dom(X9)))
| X17 != X16
| ~ in(relation_image(X9,X16),X8)
| in(X16,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk200_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(esk203_4(X7,X8,X9,X14),powerset(relation_dom(X9)))
| ~ in(X14,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( esk203_4(X7,X8,X9,X14) = X14
| ~ in(X14,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(relation_image(X9,X14),X8)
| ~ in(X14,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X17,powerset(relation_dom(X9)))
| X17 != X16
| ~ in(relation_image(X9,X16),X8)
| in(X16,esk202_3(X7,X8,X9))
| esk199_3(X7,X8,X9) = esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(esk203_4(X7,X8,X9,X14),powerset(relation_dom(X9)))
| ~ in(X14,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk201_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( esk203_4(X7,X8,X9,X14) = X14
| ~ in(X14,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk201_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(relation_image(X9,X14),X8)
| ~ in(X14,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk201_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X17,powerset(relation_dom(X9)))
| X17 != X16
| ~ in(relation_image(X9,X16),X8)
| in(X16,esk202_3(X7,X8,X9))
| in(relation_image(X9,esk201_3(X7,X8,X9)),X8)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(esk203_4(X7,X8,X9,X14),powerset(relation_dom(X9)))
| ~ in(X14,esk202_3(X7,X8,X9))
| esk200_3(X7,X8,X9) != esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( esk203_4(X7,X8,X9,X14) = X14
| ~ in(X14,esk202_3(X7,X8,X9))
| esk200_3(X7,X8,X9) != esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( in(relation_image(X9,X14),X8)
| ~ in(X14,esk202_3(X7,X8,X9))
| esk200_3(X7,X8,X9) != esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X17,powerset(relation_dom(X9)))
| X17 != X16
| ~ in(relation_image(X9,X16),X8)
| in(X16,esk202_3(X7,X8,X9))
| esk200_3(X7,X8,X9) != esk201_3(X7,X8,X9)
| ~ element(X8,powerset(powerset(X7)))
| ~ 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_304])])])])])]) ).
fof(c_0_592,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_305])])])])])]) ).
fof(c_0_593,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(esk93_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk93_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk93_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk93_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk93_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_306])])])])]) ).
fof(c_0_594,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(esk32_3(X5,X10,X11),X11)
| esk32_3(X5,X10,X11) = X10
| ~ in(ordered_pair(esk32_3(X5,X10,X11),X10),X5)
| X11 = fiber(X5,X10)
| ~ relation(X5) )
& ( esk32_3(X5,X10,X11) != X10
| in(esk32_3(X5,X10,X11),X11)
| X11 = fiber(X5,X10)
| ~ relation(X5) )
& ( in(ordered_pair(esk32_3(X5,X10,X11),X10),X5)
| in(esk32_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_307])])])])])]) ).
fof(c_0_595,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(esk58_3(X10,X11,X12),X12)
| ~ in(esk58_3(X10,X11,X12),X10)
| ~ in(esk58_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk58_3(X10,X11,X12),X10)
| in(esk58_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk58_3(X10,X11,X12),X11)
| in(esk58_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_308])])])])])]) ).
fof(c_0_596,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_309])])])])])]) ).
fof(c_0_597,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(esk68_3(X10,X11,X12),X12)
| ~ in(esk68_3(X10,X11,X12),X10)
| in(esk68_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk68_3(X10,X11,X12),X10)
| in(esk68_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk68_3(X10,X11,X12),X11)
| in(esk68_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_310])])])])])]) ).
fof(c_0_598,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(esk78_2(X5,X6),esk79_2(X5,X6)),X6)
| ~ in(ordered_pair(esk79_2(X5,X6),esk78_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk78_2(X5,X6),esk79_2(X5,X6)),X6)
| in(ordered_pair(esk79_2(X5,X6),esk78_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_311])])])])])]) ).
fof(c_0_599,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(esk40_2(X5,X6),esk41_2(X5,X6)),X5)
| ~ in(ordered_pair(esk40_2(X5,X6),esk41_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk40_2(X5,X6),esk41_2(X5,X6)),X5)
| in(ordered_pair(esk40_2(X5,X6),esk41_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_312])])])])])]) ).
fof(c_0_600,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(esk45_3(X10,X11,X12),X10)
| ~ in(esk45_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk45_3(X10,X11,X12),X11)
| ~ in(esk45_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk45_3(X10,X11,X12),X12)
| in(esk45_3(X10,X11,X12),X10)
| in(esk45_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_313])])])])])]) ).
fof(c_0_601,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(esk33_2(X5,X6),X5)
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( in(esk34_2(X5,X6),X5)
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk33_2(X5,X6),esk34_2(X5,X6)),X6)
| ~ subset(esk33_2(X5,X6),esk34_2(X5,X6))
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( in(ordered_pair(esk33_2(X5,X6),esk34_2(X5,X6)),X6)
| subset(esk33_2(X5,X6),esk34_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_314])])])])]) ).
fof(c_0_602,plain,
! [X9,X10,X17,X20,X21,X22] :
( ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk176_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk176_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk176_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk176_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk176_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| in(esk178_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| in(esk178_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| in(esk178_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| in(esk178_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| in(esk178_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) = set_difference(esk178_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) = set_difference(esk178_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) = set_difference(esk178_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) = set_difference(esk178_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| esk176_2(X9,X10) = set_difference(esk178_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| esk175_2(X9,X10) = esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| in(esk179_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| in(esk179_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| in(esk179_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| in(esk179_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| in(esk179_2(X9,X10),X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk177_2(X9,X10) = set_difference(esk179_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| esk177_2(X9,X10) = set_difference(esk179_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| esk177_2(X9,X10) = set_difference(esk179_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk177_2(X9,X10) = set_difference(esk179_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| esk177_2(X9,X10) = set_difference(esk179_2(X9,X10),singleton(X9))
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk181_3(X9,X10,X17),powerset(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) != esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( esk181_3(X9,X10,X17) = X17
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) != esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( in(esk182_3(X9,X10,X17),X10)
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) != esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( X17 = set_difference(esk182_3(X9,X10,X17),singleton(X9))
| ~ in(X17,esk180_2(X9,X10))
| esk176_2(X9,X10) != esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(X9)))) )
& ( ~ in(X21,powerset(X9))
| X21 != X20
| ~ in(X22,X10)
| X20 != set_difference(X22,singleton(X9))
| in(X20,esk180_2(X9,X10))
| esk176_2(X9,X10) != esk177_2(X9,X10)
| ~ ordinal(X9)
| ~ element(X10,powerset(powerset(succ(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_315])])])])])]) ).
fof(c_0_603,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_316])])])])])]) ).
fof(c_0_604,plain,
! [X4,X5,X6] :
( ( ~ meet_absorbing(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join(X4,meet(X4,X5,X6),X6) = X6
| empty_carrier(X4)
| ~ latt_str(X4) )
& ( element(esk84_1(X4),the_carrier(X4))
| meet_absorbing(X4)
| empty_carrier(X4)
| ~ latt_str(X4) )
& ( element(esk85_1(X4),the_carrier(X4))
| meet_absorbing(X4)
| empty_carrier(X4)
| ~ latt_str(X4) )
& ( join(X4,meet(X4,esk84_1(X4),esk85_1(X4)),esk85_1(X4)) != esk85_1(X4)
| meet_absorbing(X4)
| empty_carrier(X4)
| ~ latt_str(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_317])])])])]) ).
fof(c_0_605,plain,
! [X12,X20,X22,X26,X27,X28,X29] :
( ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk156_1(X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk156_1(X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk156_1(X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk156_1(X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk156_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| esk155_1(X12) = esk156_1(X12) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk158_1(X12),esk159_1(X12)) = esk156_1(X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk158_1(X12),esk159_1(X12)) = esk156_1(X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk158_1(X12),esk159_1(X12)) = esk156_1(X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk158_1(X12),esk159_1(X12)) = esk156_1(X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk158_1(X12),esk159_1(X12)) = esk156_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| ordered_pair(esk158_1(X12),esk159_1(X12)) = esk156_1(X12) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| in(esk158_1(X12),X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| in(esk158_1(X12),X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| in(esk158_1(X12),X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| in(esk158_1(X12),X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| in(esk158_1(X12),X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| in(esk158_1(X12),X12) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| esk159_1(X12) = singleton(esk158_1(X12)) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk159_1(X12) = singleton(esk158_1(X12)) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk159_1(X12) = singleton(esk158_1(X12)) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| esk159_1(X12) = singleton(esk158_1(X12)) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| esk159_1(X12) = singleton(esk158_1(X12)) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| esk159_1(X12) = singleton(esk158_1(X12)) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk157_1(X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk157_1(X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk157_1(X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk157_1(X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| esk155_1(X12) = esk157_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| esk155_1(X12) = esk157_1(X12) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk160_1(X12),esk161_1(X12)) = esk157_1(X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk160_1(X12),esk161_1(X12)) = esk157_1(X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk160_1(X12),esk161_1(X12)) = esk157_1(X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk160_1(X12),esk161_1(X12)) = esk157_1(X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| ordered_pair(esk160_1(X12),esk161_1(X12)) = esk157_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| ordered_pair(esk160_1(X12),esk161_1(X12)) = esk157_1(X12) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| in(esk160_1(X12),X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| in(esk160_1(X12),X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| in(esk160_1(X12),X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| in(esk160_1(X12),X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| in(esk160_1(X12),X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| in(esk160_1(X12),X12) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| esk161_1(X12) = singleton(esk160_1(X12)) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk161_1(X12) = singleton(esk160_1(X12)) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk161_1(X12) = singleton(esk160_1(X12)) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| esk161_1(X12) = singleton(esk160_1(X12)) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| esk161_1(X12) = singleton(esk160_1(X12)) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| esk161_1(X12) = singleton(esk160_1(X12)) )
& ( in(esk163_3(X12,X20,X22),cartesian_product2(X12,X20))
| ~ in(X22,esk162_2(X12,X20))
| esk156_1(X12) != esk157_1(X12) )
& ( esk163_3(X12,X20,X22) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk156_1(X12) != esk157_1(X12) )
& ( ordered_pair(esk164_3(X12,X20,X22),esk165_3(X12,X20,X22)) = X22
| ~ in(X22,esk162_2(X12,X20))
| esk156_1(X12) != esk157_1(X12) )
& ( in(esk164_3(X12,X20,X22),X12)
| ~ in(X22,esk162_2(X12,X20))
| esk156_1(X12) != esk157_1(X12) )
& ( esk165_3(X12,X20,X22) = singleton(esk164_3(X12,X20,X22))
| ~ in(X22,esk162_2(X12,X20))
| esk156_1(X12) != esk157_1(X12) )
& ( ~ in(X27,cartesian_product2(X12,X20))
| X27 != X26
| ordered_pair(X28,X29) != X26
| ~ in(X28,X12)
| X29 != singleton(X28)
| in(X26,esk162_2(X12,X20))
| esk156_1(X12) != esk157_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_318])])])])])]) ).
fof(c_0_606,plain,
! [X5,X6,X7,X9,X11] :
( ( in(esk56_3(X5,X6,X7),X7)
| X7 = empty_set
| ~ subset(X7,X6)
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( disjoint(fiber(X5,esk56_3(X5,X6,X7)),X7)
| X7 = empty_set
| ~ subset(X7,X6)
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( subset(esk57_2(X5,X9),X9)
| is_well_founded_in(X5,X9)
| ~ relation(X5) )
& ( esk57_2(X5,X9) != empty_set
| is_well_founded_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(X11,esk57_2(X5,X9))
| ~ disjoint(fiber(X5,X11),esk57_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_319])])])])])]) ).
fof(c_0_607,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) )
& ( esk42_3(X10,X11,X12) != X10
| ~ in(esk42_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk42_3(X10,X11,X12) != X11
| ~ in(esk42_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk42_3(X10,X11,X12),X12)
| esk42_3(X10,X11,X12) = X10
| esk42_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_320])])])])])]) ).
fof(c_0_608,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk73_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(esk74_2(X5,X11),X11)
| ~ in(ordered_pair(X13,esk74_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk74_2(X5,X11),X11)
| in(ordered_pair(esk75_2(X5,X11),esk74_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_321])])])])])]) ).
fof(c_0_609,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk59_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(esk60_2(X5,X11),X11)
| ~ in(ordered_pair(esk60_2(X5,X11),X13),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk60_2(X5,X11),X11)
| in(ordered_pair(esk60_2(X5,X11),esk61_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_322])])])])])]) ).
fof(c_0_610,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(esk90_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(esk91_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(esk92_2(X6,X11),X11)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(ordered_pair(esk90_2(X6,X11),esk91_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( in(ordered_pair(esk91_2(X6,X11),esk92_2(X6,X11)),X6)
| is_transitive_in(X6,X11)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk90_2(X6,X11),esk92_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_323])])])])])]) ).
fof(c_0_611,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(esk53_2(X5,X6),esk54_2(X5,X6)),X5)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk53_2(X5,X6),esk54_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_324])])])])]) ).
fof(c_0_612,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(esk76_2(X5,X9),X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( in(esk77_2(X5,X9),X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( esk76_2(X5,X9) != esk77_2(X5,X9)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk76_2(X5,X9),esk77_2(X5,X9)),X5)
| is_connected_in(X5,X9)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk77_2(X5,X9),esk76_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_325])])])])])]) ).
fof(c_0_613,plain,
! [X4,X5,X6,X7] :
( ( ~ is_reflexive_in(X4,X5)
| ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ relation(X4) )
& ( in(esk27_2(X4,X7),X7)
| is_reflexive_in(X4,X7)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk27_2(X4,X7),esk27_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_326])])])])])]) ).
fof(c_0_614,plain,
! [X9,X10,X17,X20,X21,X22] :
( ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk205_2(X9,X10)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk205_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk205_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk205_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk205_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk205_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk207_2(X9,X10))
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk207_2(X9,X10))
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk207_2(X9,X10))
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk207_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk207_2(X9,X10))
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| ordinal(esk207_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) = esk207_2(X9,X10)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) = esk207_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) = esk207_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) = esk207_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) = esk207_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| esk205_2(X9,X10) = esk207_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| in(esk207_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| in(esk207_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| in(esk207_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| in(esk207_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| in(esk207_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| in(esk207_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| esk204_2(X9,X10) = esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk208_2(X9,X10))
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk208_2(X9,X10))
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk208_2(X9,X10))
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk208_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| ordinal(esk208_2(X9,X10))
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| ordinal(esk208_2(X9,X10))
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| esk206_2(X9,X10) = esk208_2(X9,X10)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| esk206_2(X9,X10) = esk208_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| esk206_2(X9,X10) = esk208_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| esk206_2(X9,X10) = esk208_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| esk206_2(X9,X10) = esk208_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| esk206_2(X9,X10) = esk208_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| in(esk208_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| in(esk208_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| in(esk208_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| in(esk208_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| in(esk208_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| in(esk208_2(X9,X10),X9)
| ~ ordinal(X10) )
& ( in(esk210_3(X9,X10,X17),succ(X10))
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) != esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( esk210_3(X9,X10,X17) = X17
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) != esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( ordinal(esk211_3(X9,X10,X17))
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) != esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( X17 = esk211_3(X9,X10,X17)
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) != esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( in(esk211_3(X9,X10,X17),X9)
| ~ in(X17,esk209_2(X9,X10))
| esk205_2(X9,X10) != esk206_2(X9,X10)
| ~ ordinal(X10) )
& ( ~ in(X21,succ(X10))
| X21 != X20
| ~ ordinal(X22)
| X20 != X22
| ~ in(X22,X9)
| in(X20,esk209_2(X9,X10))
| esk205_2(X9,X10) != esk206_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_327])])])])])]) ).
fof(c_0_615,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_328])])]) ).
fof(c_0_616,plain,
! [X4,X5,X6] :
( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6)
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_329])])])]) ).
fof(c_0_617,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(esk28_3(X5,X6,X9),X5)
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( ~ in(X9,esk28_3(X5,X6,X9))
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk30_2(X5,X11),X5)
| ~ in(esk29_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( ~ in(esk29_2(X5,X11),esk30_2(X5,X11))
| ~ in(esk29_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( in(esk29_2(X5,X11),X11)
| ~ in(X14,X5)
| in(esk29_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_330])])])])])]) ).
fof(c_0_618,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_331])]) ).
fof(c_0_619,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_332])]) ).
fof(c_0_620,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| element(meet_commut(X4,X5,X6),the_carrier(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_333])]) ).
fof(c_0_621,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_commutative(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| element(join_commut(X4,X5,X6),the_carrier(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_334])]) ).
fof(c_0_622,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(esk62_2(X5,X9),X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(esk63_2(X5,X9),X9)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(ordered_pair(esk62_2(X5,X9),esk63_2(X5,X9)),X5)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( in(ordered_pair(esk63_2(X5,X9),esk62_2(X5,X9)),X5)
| is_antisymmetric_in(X5,X9)
| ~ relation(X5) )
& ( esk62_2(X5,X9) != esk63_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_335])])])])])]) ).
fof(c_0_623,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| element(meet(X4,X5,X6),the_carrier(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_336])]) ).
fof(c_0_624,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| element(join(X4,X5,X6),the_carrier(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_337])]) ).
fof(c_0_625,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| meet_commut(X4,X5,X6) = meet(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_338])]) ).
fof(c_0_626,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_commutative(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join_commut(X4,X5,X6) = join(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_339])]) ).
fof(c_0_627,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| meet_commut(X4,X5,X6) = meet_commut(X4,X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_340])]) ).
fof(c_0_628,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_commutative(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| join_commut(X4,X5,X6) = join_commut(X4,X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_341])]) ).
fof(c_0_629,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_342])]) ).
fof(c_0_630,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( in(esk69_3(X5,X6,X7),relation_dom(X5))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,esk69_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(esk70_2(X5,X11),X11)
| ~ in(X13,relation_dom(X5))
| esk70_2(X5,X11) != apply(X5,X13)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk71_2(X5,X11),relation_dom(X5))
| in(esk70_2(X5,X11),X11)
| X11 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk70_2(X5,X11) = apply(X5,esk71_2(X5,X11))
| in(esk70_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_343])])])])])]) ).
fof(c_0_631,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_344])]) ).
fof(c_0_632,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk64_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk64_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk65_2(X11,X12),X12)
| ~ in(esk65_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk65_2(X11,X12),esk66_2(X11,X12))
| in(esk65_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk66_2(X11,X12),X11)
| in(esk65_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_345])])])])])]) ).
fof(c_0_633,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_346])]) ).
fof(c_0_634,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_347])]) ).
fof(c_0_635,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_348])])])]) ).
fof(c_0_636,plain,
! [X4,X5,X8] :
( ( in(esk43_2(X4,X5),X5)
| X5 = empty_set
| ~ subset(X5,relation_field(X4))
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( disjoint(fiber(X4,esk43_2(X4,X5)),X5)
| X5 = empty_set
| ~ subset(X5,relation_field(X4))
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( subset(esk44_1(X4),relation_field(X4))
| well_founded_relation(X4)
| ~ relation(X4) )
& ( esk44_1(X4) != empty_set
| well_founded_relation(X4)
| ~ relation(X4) )
& ( ~ in(X8,esk44_1(X4))
| ~ disjoint(fiber(X4,X8),esk44_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_349])])])])]) ).
fof(c_0_637,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(esk19_1(X9),esk20_1(X9)),X9)
| function(X9) )
& ( in(ordered_pair(esk19_1(X9),esk21_1(X9)),X9)
| function(X9) )
& ( esk20_1(X9) != esk21_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_350])])])])])]) ).
fof(c_0_638,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_351])])])])]) ).
fof(c_0_639,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_352])]) ).
fof(c_0_640,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(esk82_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk83_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk82_1(X4)) = apply(X4,esk83_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk82_1(X4) != esk83_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_353])])])])]) ).
fof(c_0_641,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(esk36_2(X8,X9),X9)
| ~ subset(esk36_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk36_2(X8,X9),X9)
| subset(esk36_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_354])])])])])]) ).
fof(c_0_642,plain,
! [X4,X5] :
( ( ~ in(esk212_2(X4,X5),X4)
| ~ in(esk212_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk212_2(X4,X5),X4)
| in(esk212_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_355])])])]) ).
fof(c_0_643,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_356])])])]) ).
fof(c_0_644,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_357])])])])]) ).
fof(c_0_645,plain,
! [X2] :
( ( function(the_L_join(X2))
| ~ join_semilatt_str(X2) )
& ( quasi_total(the_L_join(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ join_semilatt_str(X2) )
& ( relation_of2_as_subset(the_L_join(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ join_semilatt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_358])])]) ).
fof(c_0_646,plain,
! [X2] :
( ( function(the_L_meet(X2))
| ~ meet_semilatt_str(X2) )
& ( quasi_total(the_L_meet(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ meet_semilatt_str(X2) )
& ( relation_of2_as_subset(the_L_meet(X2),cartesian_product2(the_carrier(X2),the_carrier(X2)),the_carrier(X2))
| ~ meet_semilatt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_359])])]) ).
fof(c_0_647,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_360])]) ).
fof(c_0_648,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_361])]) ).
fof(c_0_649,plain,
! [X5,X6,X8] :
( ( in(esk213_2(X5,X6),X6)
| ~ in(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,esk213_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_362])])])])]) ).
fof(c_0_650,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_363])]) ).
fof(c_0_651,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_364])]) ).
fof(c_0_652,plain,
! [X5,X6,X9,X11,X12] :
( ( ~ relation(X5)
| ~ in(X6,X5)
| X6 = ordered_pair(esk24_2(X5,X6),esk25_2(X5,X6)) )
& ( in(esk26_1(X9),X9)
| relation(X9) )
& ( esk26_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_365])])])])])]) ).
fof(c_0_653,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(esk37_2(X5,X11),esk38_2(X5,X11))
| X11 = pair_second(X5)
| X5 != ordered_pair(X6,X7) )
& ( X11 != esk38_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_366])])])])])]) ).
fof(c_0_654,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(esk22_2(X5,X11),esk23_2(X5,X11))
| X11 = pair_first(X5)
| X5 != ordered_pair(X6,X7) )
& ( X11 != esk22_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_367])])])])])]) ).
fof(c_0_655,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk214_1(X6))
& ( ~ in(X8,esk214_1(X6))
| ~ subset(X9,X8)
| in(X9,esk214_1(X6)) )
& ( in(esk215_2(X6,X10),esk214_1(X6))
| ~ in(X10,esk214_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk215_2(X6,X10))
| ~ in(X10,esk214_1(X6)) )
& ( ~ subset(X13,esk214_1(X6))
| are_equipotent(X13,esk214_1(X6))
| in(X13,esk214_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_368])])])])]) ).
fof(c_0_656,plain,
! [X5,X10,X12,X13] :
( ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( X10 = singleton(esk154_2(X5,X10))
| ~ in(X10,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| esk151_1(X5) = singleton(esk150_1(X5)) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| esk151_1(X5) = singleton(esk150_1(X5)) )
& ( X10 = singleton(esk154_2(X5,X10))
| ~ in(X10,esk153_1(X5))
| esk151_1(X5) = singleton(esk150_1(X5)) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk153_1(X5))
| esk151_1(X5) = singleton(esk150_1(X5)) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( X10 = singleton(esk154_2(X5,X10))
| ~ in(X10,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk153_1(X5))
| in(esk150_1(X5),X5) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| esk152_1(X5) = singleton(esk150_1(X5)) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| esk152_1(X5) = singleton(esk150_1(X5)) )
& ( X10 = singleton(esk154_2(X5,X10))
| ~ in(X10,esk153_1(X5))
| esk152_1(X5) = singleton(esk150_1(X5)) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk153_1(X5))
| esk152_1(X5) = singleton(esk150_1(X5)) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| esk151_1(X5) != esk152_1(X5) )
& ( in(esk154_2(X5,X10),X5)
| ~ in(X10,esk153_1(X5))
| esk151_1(X5) != esk152_1(X5) )
& ( X10 = singleton(esk154_2(X5,X10))
| ~ in(X10,esk153_1(X5))
| esk151_1(X5) != esk152_1(X5) )
& ( ~ in(X13,X5)
| ~ in(X13,X5)
| X12 != singleton(X13)
| in(X12,esk153_1(X5))
| esk151_1(X5) != esk152_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_369])])])])])]) ).
fof(c_0_657,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk31_2(X8,X9),X9)
| esk31_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk31_2(X8,X9),X9)
| esk31_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_370])])])])])]) ).
fof(c_0_658,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_371])]) ).
fof(c_0_659,plain,
! [X4,X5,X6,X7] :
( ( ~ epsilon_connected(X4)
| ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5) )
& ( in(esk51_1(X7),X7)
| epsilon_connected(X7) )
& ( in(esk52_1(X7),X7)
| epsilon_connected(X7) )
& ( ~ in(esk51_1(X7),esk52_1(X7))
| epsilon_connected(X7) )
& ( esk51_1(X7) != esk52_1(X7)
| epsilon_connected(X7) )
& ( ~ in(esk52_1(X7),esk51_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_372])])])])])]) ).
fof(c_0_660,plain,
! [X4,X5] :
( relation_of2(esk115_2(X4,X5),X4,X5)
& relation(esk115_2(X4,X5))
& function(esk115_2(X4,X5)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_373])]) ).
fof(c_0_661,plain,
! [X4,X5] :
( relation_of2(esk104_2(X4,X5),X4,X5)
& relation(esk104_2(X4,X5))
& function(esk104_2(X4,X5))
& quasi_total(esk104_2(X4,X5),X4,X5) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_374])]) ).
fof(c_0_662,plain,
! [X4,X5] : relation_of2_as_subset(esk100_2(X4,X5),X4,X5),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_375])]) ).
fof(c_0_663,plain,
! [X4,X5] : relation_of2(esk98_2(X4,X5),X4,X5),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_376])]) ).
fof(c_0_664,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_377])]) ).
fof(c_0_665,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk55_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk55_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_378])])])])])]) ).
fof(c_0_666,plain,
! [X8,X10,X12,X13] :
( ( in(esk198_2(X8,X10),X8)
| ~ in(X10,esk197_1(X8))
| esk194_0 = esk195_0 )
& ( esk198_2(X8,X10) = X10
| ~ in(X10,esk197_1(X8))
| esk194_0 = esk195_0 )
& ( ordinal(X10)
| ~ in(X10,esk197_1(X8))
| esk194_0 = esk195_0 )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk197_1(X8))
| esk194_0 = esk195_0 )
& ( in(esk198_2(X8,X10),X8)
| ~ in(X10,esk197_1(X8))
| ordinal(esk195_0) )
& ( esk198_2(X8,X10) = X10
| ~ in(X10,esk197_1(X8))
| ordinal(esk195_0) )
& ( ordinal(X10)
| ~ in(X10,esk197_1(X8))
| ordinal(esk195_0) )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk197_1(X8))
| ordinal(esk195_0) )
& ( in(esk198_2(X8,X10),X8)
| ~ in(X10,esk197_1(X8))
| esk194_0 = esk196_0 )
& ( esk198_2(X8,X10) = X10
| ~ in(X10,esk197_1(X8))
| esk194_0 = esk196_0 )
& ( ordinal(X10)
| ~ in(X10,esk197_1(X8))
| esk194_0 = esk196_0 )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk197_1(X8))
| esk194_0 = esk196_0 )
& ( in(esk198_2(X8,X10),X8)
| ~ in(X10,esk197_1(X8))
| ordinal(esk196_0) )
& ( esk198_2(X8,X10) = X10
| ~ in(X10,esk197_1(X8))
| ordinal(esk196_0) )
& ( ordinal(X10)
| ~ in(X10,esk197_1(X8))
| ordinal(esk196_0) )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk197_1(X8))
| ordinal(esk196_0) )
& ( in(esk198_2(X8,X10),X8)
| ~ in(X10,esk197_1(X8))
| esk195_0 != esk196_0 )
& ( esk198_2(X8,X10) = X10
| ~ in(X10,esk197_1(X8))
| esk195_0 != esk196_0 )
& ( ordinal(X10)
| ~ in(X10,esk197_1(X8))
| esk195_0 != esk196_0 )
& ( ~ in(X13,X8)
| X13 != X12
| ~ ordinal(X12)
| in(X12,esk197_1(X8))
| esk195_0 != esk196_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_379])])])])])]) ).
fof(c_0_667,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_380])]) ).
fof(c_0_668,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_381])]) ).
fof(c_0_669,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_382])]) ).
fof(c_0_670,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_383])]) ).
fof(c_0_671,plain,
! [X3,X4,X5] :
( ( in(empty_set,X3)
| X3 != omega )
& ( being_limit_ordinal(X3)
| X3 != omega )
& ( ordinal(X3)
| X3 != omega )
& ( ~ ordinal(X4)
| ~ in(empty_set,X4)
| ~ being_limit_ordinal(X4)
| subset(X3,X4)
| X3 != omega )
& ( ordinal(esk72_1(X5))
| ~ ordinal(X5)
| ~ being_limit_ordinal(X5)
| ~ in(empty_set,X5)
| X5 = omega )
& ( in(empty_set,esk72_1(X5))
| ~ ordinal(X5)
| ~ being_limit_ordinal(X5)
| ~ in(empty_set,X5)
| X5 = omega )
& ( being_limit_ordinal(esk72_1(X5))
| ~ ordinal(X5)
| ~ being_limit_ordinal(X5)
| ~ in(empty_set,X5)
| X5 = omega )
& ( ~ subset(X5,esk72_1(X5))
| ~ ordinal(X5)
| ~ being_limit_ordinal(X5)
| ~ in(empty_set,X5)
| X5 = omega ) ),
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_384])])])])])]) ).
fof(c_0_672,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_385])])])]) ).
fof(c_0_673,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_386])])]) ).
fof(c_0_674,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_387])]) ).
fof(c_0_675,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_388]) ).
fof(c_0_676,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_389])])]) ).
fof(c_0_677,plain,
! [X3,X5,X6] :
( ( relation(esk18_1(X3))
| ~ finite(X3) )
& ( function(esk18_1(X3))
| ~ finite(X3) )
& ( relation_rng(esk18_1(X3)) = X3
| ~ finite(X3) )
& ( in(relation_dom(esk18_1(X3)),omega)
| ~ finite(X3) )
& ( ~ relation(X6)
| ~ function(X6)
| relation_rng(X6) != X5
| ~ in(relation_dom(X6),omega)
| finite(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_390])])])])])]) ).
fof(c_0_678,plain,
! [X3,X4] :
( empty(X3)
| empty(X4)
| ~ empty(cartesian_product2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_391])]) ).
fof(c_0_679,plain,
! [X4,X5,X7,X8,X9] :
( ( relation(esk67_2(X4,X5))
| ~ equipotent(X4,X5) )
& ( function(esk67_2(X4,X5))
| ~ equipotent(X4,X5) )
& ( one_to_one(esk67_2(X4,X5))
| ~ equipotent(X4,X5) )
& ( relation_dom(esk67_2(X4,X5)) = X4
| ~ equipotent(X4,X5) )
& ( relation_rng(esk67_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_392])])])])])]) ).
fof(c_0_680,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_393])])])]) ).
fof(c_0_681,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_394])])])]) ).
fof(c_0_682,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ function(X3)
| ~ finite(X4)
| finite(relation_image(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_395])]) ).
fof(c_0_683,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_396])])]) ).
fof(c_0_684,plain,
! [X3] :
( ( element(esk125_1(X3),powerset(the_carrier(X3)))
| empty_carrier(X3)
| ~ one_sorted_str(X3) )
& ( ~ empty(esk125_1(X3))
| empty_carrier(X3)
| ~ one_sorted_str(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_397])])])]) ).
fof(c_0_685,plain,
! [X3,X4] : ~ empty(unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_398]) ).
fof(c_0_686,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_399]) ).
fof(c_0_687,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_400])])])])]) ).
fof(c_0_688,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_401])])]) ).
fof(c_0_689,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_402])])])]) ).
fof(c_0_690,plain,
! [X2] :
( ~ one_sorted_str(X2)
| element(cast_as_carrier_subset(X2),powerset(the_carrier(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_403])]) ).
fof(c_0_691,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_404])]) ).
fof(c_0_692,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_405])]) ).
fof(c_0_693,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_406])])]) ).
fof(c_0_694,plain,
! [X3,X4] :
( ~ finite(X3)
| ~ finite(X4)
| finite(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_407])]) ).
fof(c_0_695,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_408])])]) ).
fof(c_0_696,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_409])])])])]) ).
fof(c_0_697,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_difference(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_410])]) ).
fof(c_0_698,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_411])]) ).
fof(c_0_699,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_412])]) ).
fof(c_0_700,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_413])])])])]) ).
fof(c_0_701,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_414])])]) ).
fof(c_0_702,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(relation_composition(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_415])]) ).
fof(c_0_703,plain,
! [X3,X4,X5] :
( ( ~ epsilon_transitive(X3)
| ~ in(X4,X3)
| subset(X4,X3) )
& ( in(esk39_1(X5),X5)
| epsilon_transitive(X5) )
& ( ~ subset(esk39_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_416])])])])])]) ).
fof(c_0_704,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_417])])]) ).
fof(c_0_705,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_418])])]) ).
fof(c_0_706,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_419])])]) ).
fof(c_0_707,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_420])])]) ).
fof(c_0_708,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_421])])]) ).
fof(c_0_709,plain,
! [X3,X4] :
( ( v1_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v5_membered(X3) )
& ( v2_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v5_membered(X3) )
& ( v3_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v5_membered(X3) )
& ( v4_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v5_membered(X3) )
& ( v5_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v5_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_422])])])]) ).
fof(c_0_710,plain,
! [X3,X4] :
( ( v1_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v4_membered(X3) )
& ( v2_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v4_membered(X3) )
& ( v3_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v4_membered(X3) )
& ( v4_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v4_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_423])])])]) ).
fof(c_0_711,plain,
! [X3,X4] :
( ( v1_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v3_membered(X3) )
& ( v2_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v3_membered(X3) )
& ( v3_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v3_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_424])])])]) ).
fof(c_0_712,plain,
! [X3,X4] :
( ( v1_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v2_membered(X3) )
& ( v2_membered(X4)
| ~ element(X4,powerset(X3))
| ~ v2_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_425])])])]) ).
fof(c_0_713,plain,
! [X3,X4] :
( ~ v1_membered(X3)
| ~ element(X4,powerset(X3))
| v1_membered(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_426])])]) ).
fof(c_0_714,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_427])]) ).
fof(c_0_715,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_428])]) ).
fof(c_0_716,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_429])])])])]) ).
fof(c_0_717,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_430])])])])]) ).
fof(c_0_718,plain,
! [X3,X4] :
( ~ finite(X3)
| finite(set_difference(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_431])])])]) ).
fof(c_0_719,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_432])])])]) ).
fof(c_0_720,plain,
! [X3,X4] :
( ~ finite(X4)
| finite(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_433])]) ).
fof(c_0_721,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_434])]) ).
fof(c_0_722,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_435])])])]) ).
fof(c_0_723,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_436])])])]) ).
fof(c_0_724,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_437])]) ).
fof(c_0_725,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_438])]) ).
fof(c_0_726,plain,
! [X3,X4] :
( ~ equipotent(X3,X4)
| equipotent(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_439])]) ).
fof(c_0_727,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_440])]) ).
fof(c_0_728,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_441])])])]) ).
fof(c_0_729,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_442])])])]) ).
fof(c_0_730,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_443])])])]) ).
fof(c_0_731,plain,
! [X3,X4] :
( ( v1_xcmplx_0(X4)
| ~ element(X4,X3)
| ~ v5_membered(X3) )
& ( natural(X4)
| ~ element(X4,X3)
| ~ v5_membered(X3) )
& ( v1_xreal_0(X4)
| ~ element(X4,X3)
| ~ v5_membered(X3) )
& ( v1_int_1(X4)
| ~ element(X4,X3)
| ~ v5_membered(X3) )
& ( v1_rat_1(X4)
| ~ element(X4,X3)
| ~ v5_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_444])])])]) ).
fof(c_0_732,plain,
! [X3,X4] :
( ( v1_xcmplx_0(X4)
| ~ element(X4,X3)
| ~ v4_membered(X3) )
& ( v1_xreal_0(X4)
| ~ element(X4,X3)
| ~ v4_membered(X3) )
& ( v1_int_1(X4)
| ~ element(X4,X3)
| ~ v4_membered(X3) )
& ( v1_rat_1(X4)
| ~ element(X4,X3)
| ~ v4_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_445])])])]) ).
fof(c_0_733,plain,
! [X3,X4] :
( ( v1_xcmplx_0(X4)
| ~ element(X4,X3)
| ~ v3_membered(X3) )
& ( v1_xreal_0(X4)
| ~ element(X4,X3)
| ~ v3_membered(X3) )
& ( v1_rat_1(X4)
| ~ element(X4,X3)
| ~ v3_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_446])])])]) ).
fof(c_0_734,plain,
! [X3,X4] :
( ( v1_xcmplx_0(X4)
| ~ element(X4,X3)
| ~ v2_membered(X3) )
& ( v1_xreal_0(X4)
| ~ element(X4,X3)
| ~ v2_membered(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_447])])])]) ).
fof(c_0_735,plain,
! [X3,X4] :
( ~ v1_membered(X3)
| ~ element(X4,X3)
| v1_xcmplx_0(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_448])])]) ).
fof(c_0_736,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_449])])]) ).
fof(c_0_737,plain,
! [X3] :
( ( element(esk119_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk119_1(X3))
| empty(X3) )
& ( finite(esk119_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_450])])])]) ).
fof(c_0_738,plain,
! [X3] :
( ( element(esk110_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk110_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_451])])])]) ).
fof(c_0_739,plain,
! [X2] :
( ( ~ empty(succ(X2))
| ~ ordinal(X2)
| ~ natural(X2) )
& ( epsilon_transitive(succ(X2))
| ~ ordinal(X2)
| ~ natural(X2) )
& ( epsilon_connected(succ(X2))
| ~ ordinal(X2)
| ~ natural(X2) )
& ( ordinal(succ(X2))
| ~ ordinal(X2)
| ~ natural(X2) )
& ( natural(succ(X2))
| ~ ordinal(X2)
| ~ natural(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_452])])]) ).
fof(c_0_740,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_453])]) ).
fof(c_0_741,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_454])]) ).
fof(c_0_742,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_455])])])]) ).
fof(c_0_743,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_456])]) ).
fof(c_0_744,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_457])]) ).
fof(c_0_745,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_458])]) ).
fof(c_0_746,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_747,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_748,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_461]) ).
fof(c_0_749,plain,
! [X3] :
( element(esk117_1(X3),powerset(X3))
& empty(esk117_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_462])]) ).
fof(c_0_750,plain,
! [X3] :
( element(esk112_1(X3),powerset(X3))
& empty(esk112_1(X3))
& relation(esk112_1(X3))
& function(esk112_1(X3))
& one_to_one(esk112_1(X3))
& epsilon_transitive(esk112_1(X3))
& epsilon_connected(esk112_1(X3))
& ordinal(esk112_1(X3))
& natural(esk112_1(X3))
& finite(esk112_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_463])]) ).
fof(c_0_751,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_752,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_465])])]) ).
fof(c_0_753,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk35_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_466])])])])]) ).
fof(c_0_754,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_467])])]) ).
fof(c_0_755,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ element(X2,omega) )
& ( epsilon_connected(X2)
| ~ element(X2,omega) )
& ( ordinal(X2)
| ~ element(X2,omega) )
& ( natural(X2)
| ~ element(X2,omega) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_468])])]) ).
fof(c_0_756,plain,
! [X2] : succ(X2) = set_union2(X2,singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_469]) ).
fof(c_0_757,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_470])])]) ).
fof(c_0_758,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_759,plain,
! [X3] : element(esk99_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_472])]) ).
fof(c_0_760,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_473])])])])]) ).
fof(c_0_761,plain,
! [X2] :
( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_474])]) ).
fof(c_0_762,plain,
! [X2] :
( ~ cup_closed(X2)
| ~ diff_closed(X2)
| preboolean(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_475])]) ).
fof(c_0_763,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_476])])]) ).
fof(c_0_764,plain,
! [X2] :
( ~ relation(X2)
| relation_inverse(relation_inverse(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_477])]) ).
fof(c_0_765,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_478])])]) ).
fof(c_0_766,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_479])])]) ).
fof(c_0_767,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_480])])]) ).
fof(c_0_768,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_481])])]) ).
fof(c_0_769,plain,
! [X2] :
( ~ relation(X2)
| relation(relation_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_482])]) ).
fof(c_0_770,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_771,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_772,plain,
! [X2] : ~ empty(succ(X2)),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_773,plain,
! [X2,X3,X4,X5] :
( ~ empty(powerset(X2))
& cup_closed(powerset(X3))
& diff_closed(powerset(X4))
& preboolean(powerset(X5)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_486])])]) ).
fof(c_0_774,plain,
! [X2,X3] :
( ~ empty(singleton(X2))
& finite(singleton(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_487])])]) ).
fof(c_0_775,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_488])])])]) ).
fof(c_0_776,plain,
! [X2] :
( ~ one_sorted_str(X2)
| cast_as_carrier_subset(X2) = the_carrier(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_489])]) ).
fof(c_0_777,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_778,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_779,plain,
! [X3,X4] : equipotent(X3,X3),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_780,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_781,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_782,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_783,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_784,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_785,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_498])])])]) ).
fof(c_0_786,plain,
! [X2] :
( ( meet_semilatt_str(X2)
| ~ latt_str(X2) )
& ( join_semilatt_str(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_499])])]) ).
fof(c_0_787,plain,
! [X2] :
( ~ join_semilatt_str(X2)
| one_sorted_str(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_500])]) ).
fof(c_0_788,plain,
! [X2] :
( ~ meet_semilatt_str(X2)
| one_sorted_str(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_501])]) ).
fof(c_0_789,plain,
! [X2] :
( ~ v2_membered(X2)
| v1_membered(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_502])]) ).
fof(c_0_790,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_503])])]) ).
fof(c_0_791,plain,
! [X2] :
( ~ v3_membered(X2)
| v2_membered(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_504])]) ).
fof(c_0_792,plain,
! [X2] :
( ~ v4_membered(X2)
| v3_membered(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_505])]) ).
fof(c_0_793,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_506])]) ).
fof(c_0_794,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_507])])]) ).
fof(c_0_795,plain,
! [X2] :
( ~ v5_membered(X2)
| v4_membered(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_508])]) ).
fof(c_0_796,plain,
! [X2] :
( ~ empty(X2)
| function(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_509])]) ).
fof(c_0_797,plain,
! [X2] :
( ( cup_closed(X2)
| ~ preboolean(X2) )
& ( diff_closed(X2)
| ~ preboolean(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_510])])]) ).
fof(c_0_798,plain,
! [X2] :
( ~ empty(X2)
| finite(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_511])]) ).
fof(c_0_799,plain,
! [X2] :
( ( v1_membered(X2)
| ~ empty(X2) )
& ( v2_membered(X2)
| ~ empty(X2) )
& ( v3_membered(X2)
| ~ empty(X2) )
& ( v4_membered(X2)
| ~ empty(X2) )
& ( v5_membered(X2)
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_512])])]) ).
fof(c_0_800,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_513])])]) ).
fof(c_0_801,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_802,plain,
! [X2] : relation(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_803,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_516])]) ).
fof(c_0_804,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_805,plain,
( one_sorted_str(esk123_0)
& ~ empty_carrier(esk123_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_518])]) ).
fof(c_0_806,plain,
( ~ empty(esk121_0)
& epsilon_transitive(esk121_0)
& epsilon_connected(esk121_0)
& ordinal(esk121_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_519])]) ).
fof(c_0_807,plain,
~ empty(esk118_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_520])]) ).
fof(c_0_808,plain,
( ~ empty(esk116_0)
& relation(esk116_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_521])]) ).
fof(c_0_809,plain,
( ~ empty(esk105_0)
& v1_membered(esk105_0)
& v2_membered(esk105_0)
& v3_membered(esk105_0)
& v4_membered(esk105_0)
& v5_membered(esk105_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_522])]) ).
fof(c_0_810,plain,
( ~ empty(esk102_0)
& finite(esk102_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_523])]) ).
fof(c_0_811,plain,
( ~ empty(esk101_0)
& epsilon_transitive(esk101_0)
& epsilon_connected(esk101_0)
& ordinal(esk101_0)
& natural(esk101_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_524])]) ).
fof(c_0_812,plain,
( epsilon_transitive(omega)
& epsilon_connected(omega)
& ordinal(omega)
& ~ empty(omega) ),
c_0_525 ).
fof(c_0_813,plain,
( relation(esk124_0)
& relation_empty_yielding(esk124_0)
& function(esk124_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_526])]) ).
fof(c_0_814,plain,
( relation(esk122_0)
& relation_empty_yielding(esk122_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_527])]) ).
fof(c_0_815,plain,
( relation(esk120_0)
& function(esk120_0)
& one_to_one(esk120_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_528])]) ).
fof(c_0_816,plain,
( relation(esk114_0)
& function(esk114_0)
& one_to_one(esk114_0)
& empty(esk114_0)
& epsilon_transitive(esk114_0)
& epsilon_connected(esk114_0)
& ordinal(esk114_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_529])]) ).
fof(c_0_817,plain,
( relation(esk113_0)
& empty(esk113_0)
& function(esk113_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_530])]) ).
fof(c_0_818,plain,
empty(esk111_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_531])]) ).
fof(c_0_819,plain,
( empty(esk109_0)
& relation(esk109_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_532])]) ).
fof(c_0_820,plain,
( relation(esk108_0)
& function(esk108_0)
& one_to_one(esk108_0)
& empty(esk108_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_533])]) ).
fof(c_0_821,plain,
( epsilon_transitive(esk107_0)
& epsilon_connected(esk107_0)
& ordinal(esk107_0)
& being_limit_ordinal(esk107_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_534])]) ).
fof(c_0_822,plain,
( epsilon_transitive(esk106_0)
& epsilon_connected(esk106_0)
& ordinal(esk106_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_535])]) ).
fof(c_0_823,plain,
( relation(esk103_0)
& function(esk103_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_536])]) ).
fof(c_0_824,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
c_0_537 ).
fof(c_0_825,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_538 ).
fof(c_0_826,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_539 ).
fof(c_0_827,axiom,
empty(empty_set),
c_0_540 ).
fof(c_0_828,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_541 ).
fof(c_0_829,plain,
latt_str(esk97_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_542])]) ).
fof(c_0_830,plain,
join_semilatt_str(esk96_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_543])]) ).
fof(c_0_831,plain,
one_sorted_str(esk95_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_544])]) ).
fof(c_0_832,plain,
meet_semilatt_str(esk94_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_545])]) ).
fof(c_0_833,axiom,
$true,
c_0_546 ).
fof(c_0_834,axiom,
$true,
c_0_547 ).
fof(c_0_835,axiom,
$true,
c_0_548 ).
fof(c_0_836,axiom,
$true,
c_0_549 ).
fof(c_0_837,axiom,
$true,
c_0_550 ).
fof(c_0_838,axiom,
$true,
c_0_551 ).
fof(c_0_839,axiom,
$true,
c_0_552 ).
fof(c_0_840,axiom,
$true,
c_0_553 ).
fof(c_0_841,axiom,
$true,
c_0_554 ).
fof(c_0_842,axiom,
$true,
c_0_555 ).
fof(c_0_843,axiom,
$true,
c_0_556 ).
fof(c_0_844,axiom,
$true,
c_0_557 ).
fof(c_0_845,axiom,
$true,
c_0_558 ).
fof(c_0_846,axiom,
$true,
c_0_559 ).
fof(c_0_847,axiom,
$true,
c_0_560 ).
fof(c_0_848,axiom,
$true,
c_0_561 ).
fof(c_0_849,axiom,
$true,
c_0_562 ).
fof(c_0_850,axiom,
$true,
c_0_563 ).
fof(c_0_851,axiom,
$true,
c_0_564 ).
fof(c_0_852,axiom,
$true,
c_0_565 ).
fof(c_0_853,axiom,
$true,
c_0_566 ).
fof(c_0_854,axiom,
$true,
c_0_567 ).
fof(c_0_855,axiom,
$true,
c_0_568 ).
fof(c_0_856,axiom,
$true,
c_0_569 ).
fof(c_0_857,axiom,
$true,
c_0_570 ).
fof(c_0_858,axiom,
$true,
c_0_571 ).
fof(c_0_859,axiom,
$true,
c_0_572 ).
fof(c_0_860,axiom,
$true,
c_0_573 ).
cnf(c_0_861,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk140_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,esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_862,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk143_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,esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_863,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_864,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_865,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_866,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_867,plain,
( empty(X2)
| in(X3,esk144_3(X2,X1,X4))
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_868,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_869,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_870,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_871,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_872,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_873,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_874,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| in(esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk140_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_574]) ).
cnf(c_0_875,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| in(esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk143_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_574]) ).
cnf(c_0_876,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_877,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_878,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_879,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_880,plain,
( empty(X2)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_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_574]) ).
cnf(c_0_881,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_882,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_883,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_884,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_885,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_886,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_574]) ).
cnf(c_0_887,plain,
( element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_575]) ).
cnf(c_0_888,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_889,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_890,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_891,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_892,plain,
( empty(X2)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_893,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_894,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_895,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_896,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_897,plain,
( apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_577]) ).
cnf(c_0_898,plain,
( meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_578]) ).
cnf(c_0_899,plain,
( join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_900,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_901,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_902,plain,
( in(ordered_pair(X4,esk86_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_581]) ).
cnf(c_0_903,plain,
( in(ordered_pair(esk86_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_581]) ).
cnf(c_0_904,plain,
( esk184_3(X3,X2,X1) = ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1))
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_905,plain,
( esk185_3(X3,X2,X1) = ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1))
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_906,plain,
( in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk184_3(X3,X2,X1) != esk185_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_907,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_908,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_909,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| in(esk174_5(X1,X2,X3,X4,X5),esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_910,plain,
( in(X2,esk169_1(X1))
| in(esk174_5(X1,X2,X3,X4,X5),esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_911,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| subset(X5,esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_912,plain,
( in(X2,esk169_1(X1))
| subset(X5,esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_913,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4))
| esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_914,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,esk80_3(X1,X2,X3)),apply(X3,esk81_3(X1,X2,X3))),X2)
| ~ in(esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_915,plain,
( in(X2,esk169_1(X1))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4))
| esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_916,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_917,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_918,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| in(esk134_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_576]) ).
cnf(c_0_919,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| in(esk134_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_576]) ).
cnf(c_0_920,plain,
( empty(X2)
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_921,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| in(esk134_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_576]) ).
cnf(c_0_922,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| in(esk134_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_576]) ).
cnf(c_0_923,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| in(esk134_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_576]) ).
cnf(c_0_924,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| in(esk134_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_576]) ).
cnf(c_0_925,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_926,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_927,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(ordered_pair(esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5))
| ~ in(X6,esk148_4(X2,X1,X5,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_928,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(ordered_pair(esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5))
| ~ in(X6,esk148_4(X2,X1,X5,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_929,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_930,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_931,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_932,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_933,plain,
( empty(X2)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_934,plain,
( X4 = empty_set
| X5 = esk217_4(X3,X2,X1,X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk216_3(X3,X2,X1))))
| ~ subset(esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_935,plain,
( X4 = empty_set
| X5 = esk219_4(X3,X2,X1,X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk218_3(X3,X2,X1))))
| ~ subset(esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_936,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_937,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_938,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_939,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_940,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_941,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_942,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_943,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_944,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_585]) ).
cnf(c_0_945,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_586]) ).
cnf(c_0_946,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1)
| in(ordered_pair(apply(X3,esk80_3(X1,X2,X3)),apply(X3,esk81_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_583]) ).
cnf(c_0_947,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk88_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk87_3(X1,X2,X3),esk88_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_948,plain,
( X4 = empty_set
| in(esk217_4(X3,X2,X1,X4),X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk216_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_949,plain,
( X4 = empty_set
| in(esk219_4(X3,X2,X1,X4),X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk218_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_950,plain,
( esk184_3(X3,X2,X1) = ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1))
| X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_951,plain,
( esk185_3(X3,X2,X1) = ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1))
| X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_952,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_953,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_954,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| in(X4,esk190_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_580]) ).
cnf(c_0_955,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| in(X4,esk190_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_580]) ).
cnf(c_0_956,plain,
( X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk184_3(X3,X2,X1) != esk185_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_957,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| ordered_pair(esk146_4(X2,X1,X5,X4),esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_958,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| ordered_pair(esk146_4(X2,X1,X5,X4),esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_959,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(esk147_4(X2,X1,X5,X4),esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_960,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(esk147_4(X2,X1,X5,X4),esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_961,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_962,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| X4 = ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_963,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_587]) ).
cnf(c_0_964,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_965,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_966,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_967,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_968,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_969,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_970,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_971,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_972,plain,
( empty(X2)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_973,plain,
( empty(X2)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_974,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_975,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_976,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_587]) ).
cnf(c_0_977,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_587]) ).
cnf(c_0_978,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_587]) ).
cnf(c_0_979,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_980,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_981,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_982,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_983,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_984,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_985,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_986,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_987,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_988,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_989,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_588]) ).
cnf(c_0_990,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_589]) ).
cnf(c_0_991,plain,
( X4 = ordered_pair(esk46_4(X2,X3,X1,X4),esk47_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_992,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_993,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_994,plain,
( esk184_3(X3,X2,X1) = ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1))
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_995,plain,
( esk185_3(X3,X2,X1) = ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1))
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_996,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk87_3(X1,X2,X3),esk88_3(X1,X2,X3)),X3)
| in(ordered_pair(esk87_3(X1,X2,X3),esk89_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_997,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk87_3(X1,X2,X3),esk88_3(X1,X2,X3)),X3)
| in(ordered_pair(esk89_3(X1,X2,X3),esk88_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_998,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_585]) ).
cnf(c_0_999,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_586]) ).
cnf(c_0_1000,plain,
( in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk200_3(X3,X2,X1) != esk201_3(X3,X2,X1)
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1001,plain,
( in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk184_3(X3,X2,X1) != esk185_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1002,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1003,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1004,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1005,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1006,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1007,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1008,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1009,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1010,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| esk146_4(X2,X1,X5,X4) = esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1011,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| esk146_4(X2,X1,X5,X4) = esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1012,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_592]) ).
cnf(c_0_1013,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1014,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1015,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1016,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1017,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1018,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1019,plain,
( empty(X2)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1020,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1021,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1022,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1023,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1024,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1025,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1026,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1027,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1028,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1029,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1030,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1031,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1032,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1033,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1034,plain,
( empty(X2)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1035,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1036,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1037,plain,
( esk184_3(X3,X2,X1) = ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1))
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1038,plain,
( esk185_3(X3,X2,X1) = ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1))
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1039,plain,
( esk184_3(X3,X2,X1) = ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1))
| in(X4,esk190_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_580]) ).
cnf(c_0_1040,plain,
( esk185_3(X3,X2,X1) = ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1))
| in(X4,esk190_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_580]) ).
cnf(c_0_1041,plain,
( empty(X2)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1042,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1043,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1044,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1045,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1046,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1047,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1048,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1049,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1050,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1051,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1052,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1)
| in(esk80_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_583]) ).
cnf(c_0_1053,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1)
| in(esk81_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_583]) ).
cnf(c_0_1054,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk93_3(X2,X1,X3)),X1)
| ~ in(esk93_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_1055,plain,
( esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk200_3(X3,X2,X1) != esk201_3(X3,X2,X1)
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1056,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| element(esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1057,plain,
( X2 = fiber(X1,X3)
| esk32_3(X1,X3,X2) = X3
| ~ relation(X1)
| ~ in(ordered_pair(esk32_3(X1,X3,X2),X3),X1)
| ~ in(esk32_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1058,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| X3 = empty_set
| X4 = esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2))))
| ~ subset(esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1059,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_588]) ).
cnf(c_0_1060,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_589]) ).
cnf(c_0_1061,plain,
( esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk184_3(X3,X2,X1) != esk185_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1062,plain,
( in(X4,esk190_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk184_3(X3,X2,X1) != esk185_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_580]) ).
cnf(c_0_1063,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_585]) ).
cnf(c_0_1064,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_586]) ).
cnf(c_0_1065,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1066,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1067,plain,
( in(X2,esk169_1(X1))
| element(esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1068,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_588]) ).
cnf(c_0_1069,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_589]) ).
cnf(c_0_1070,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1071,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1072,plain,
( X3 = empty_set
| X4 = esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2))))
| ~ subset(esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1073,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk58_3(X2,X3,X1),X3)
| ~ in(esk58_3(X2,X3,X1),X2)
| ~ in(esk58_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1074,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_596]) ).
cnf(c_0_1075,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1076,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_1077,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| in(X4,esk190_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_580]) ).
cnf(c_0_1078,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| in(X4,esk190_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_580]) ).
cnf(c_0_1079,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_596]) ).
cnf(c_0_1080,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_596]) ).
cnf(c_0_1081,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_588]) ).
cnf(c_0_1082,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_589]) ).
cnf(c_0_1083,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1084,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1085,plain,
( in(esk46_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1086,plain,
( in(esk47_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1087,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1088,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1089,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| esk173_4(X1,X2,X3,X4) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1090,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1091,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1092,plain,
( X1 = set_difference(X2,X3)
| in(esk68_3(X2,X3,X1),X3)
| ~ in(esk68_3(X2,X3,X1),X2)
| ~ in(esk68_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1093,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1094,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1095,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| X3 = empty_set
| in(esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1096,plain,
( empty(X2)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| esk136_2(X2,X1) != esk137_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1097,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk93_3(X2,X1,X3)),X1)
| in(esk93_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_1098,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1099,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1100,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1101,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1102,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1103,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_1104,plain,
( in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk200_3(X3,X2,X1) != esk201_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1105,plain,
( in(X2,esk169_1(X1))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| esk173_4(X1,X2,X3,X4) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1106,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk79_2(X1,X2),esk78_2(X1,X2)),X1)
| ~ in(ordered_pair(esk78_2(X1,X2),esk79_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_598]) ).
cnf(c_0_1107,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X2)
| ~ in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_599]) ).
cnf(c_0_1108,plain,
( in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk200_3(X3,X2,X1) != esk201_3(X3,X2,X1)
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1109,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1))
| ~ in(X5,esk133_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1110,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1))
| ~ in(X5,esk133_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1111,plain,
( X3 = empty_set
| in(esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1112,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_583]) ).
cnf(c_0_1113,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk48_3(X2,X3,X1),X1)
| esk48_3(X2,X3,X1) = ordered_pair(esk49_3(X2,X3,X1),esk50_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1114,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1115,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1116,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1117,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_1118,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_592]) ).
cnf(c_0_1119,plain,
( X2 = fiber(X1,X3)
| in(esk32_3(X1,X3,X2),X2)
| in(ordered_pair(esk32_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1120,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk45_3(X2,X3,X1),X1)
| ~ in(esk45_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1121,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk45_3(X2,X3,X1),X1)
| ~ in(esk45_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1122,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_596]) ).
cnf(c_0_1123,plain,
( X1 = set_union2(X2,X3)
| in(esk45_3(X2,X3,X1),X3)
| in(esk45_3(X2,X3,X1),X2)
| in(esk45_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1124,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1125,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1126,plain,
( X1 = cartesian_product2(X2,X3)
| esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk48_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1127,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1128,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1129,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1130,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1131,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1132,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(X4,esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1133,plain,
( X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2
| ~ subset(esk33_2(X2,X1),esk34_2(X2,X1))
| ~ in(ordered_pair(esk33_2(X2,X1),esk34_2(X2,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_1134,plain,
( empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1135,plain,
( esk176_2(X2,X1) = set_difference(esk178_2(X2,X1),singleton(X2))
| X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1136,plain,
( esk177_2(X2,X1) = set_difference(esk179_2(X2,X1),singleton(X2))
| X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1137,plain,
( esk176_2(X2,X1) = set_difference(esk178_2(X2,X1),singleton(X2))
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1138,plain,
( esk177_2(X2,X1) = set_difference(esk179_2(X2,X1),singleton(X2))
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1139,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_603]) ).
cnf(c_0_1140,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1141,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1142,plain,
( esk176_2(X2,X1) = set_difference(esk178_2(X2,X1),singleton(X2))
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1143,plain,
( esk177_2(X2,X1) = set_difference(esk179_2(X2,X1),singleton(X2))
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1144,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| esk132_3(X2,X1,X4) = esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1145,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| esk132_3(X2,X1,X4) = esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1146,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1147,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1148,plain,
( X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk176_2(X2,X1) != esk177_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1149,plain,
( in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk176_2(X2,X1) != esk177_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1150,plain,
( in(esk178_2(X2,X1),X1)
| X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1151,plain,
( in(esk179_2(X2,X1),X1)
| X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1152,plain,
( in(esk178_2(X2,X1),X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1153,plain,
( in(esk179_2(X2,X1),X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1154,plain,
( X1 = set_difference(X2,X3)
| in(esk68_3(X2,X3,X1),X1)
| ~ in(esk68_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1155,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_596]) ).
cnf(c_0_1156,plain,
( in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk176_2(X2,X1) != esk177_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1157,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| ~ latt_str(X1)
| join(X1,meet(X1,esk84_1(X1),esk85_1(X1)),esk85_1(X1)) != esk85_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_1158,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1159,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1160,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_583]) ).
cnf(c_0_1161,plain,
( in(esk178_2(X2,X1),X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1162,plain,
( in(esk179_2(X2,X1),X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1163,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1164,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| X3 = set_difference(esk182_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1165,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1166,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1167,plain,
( in(esk158_1(X1),X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1168,plain,
( in(esk160_1(X1),X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1169,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1170,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1171,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk56_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_1172,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk79_2(X1,X2),esk78_2(X1,X2)),X1)
| in(ordered_pair(esk78_2(X1,X2),esk79_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_598]) ).
cnf(c_0_1173,plain,
( esk159_1(X1) = singleton(esk158_1(X1))
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1174,plain,
( esk161_1(X1) = singleton(esk160_1(X1))
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1175,plain,
( ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| esk156_1(X1) != esk157_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1176,plain,
( X1 = X2
| in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X2)
| in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_599]) ).
cnf(c_0_1177,plain,
( esk155_1(X1) = esk156_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1178,plain,
( esk155_1(X1) = esk157_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1179,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk42_3(X2,X3,X1),X1)
| esk42_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1180,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk42_3(X2,X3,X1),X1)
| esk42_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1181,plain,
( in(ordered_pair(esk73_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_1182,plain,
( in(ordered_pair(X3,esk59_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_1183,plain,
( esk176_2(X2,X1) = set_difference(esk178_2(X2,X1),singleton(X2))
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1184,plain,
( esk177_2(X2,X1) = set_difference(esk179_2(X2,X1),singleton(X2))
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1185,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_592]) ).
cnf(c_0_1186,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_596]) ).
cnf(c_0_1187,plain,
( esk176_2(X2,X1) = set_difference(esk178_2(X2,X1),singleton(X2))
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1188,plain,
( esk177_2(X2,X1) = set_difference(esk179_2(X2,X1),singleton(X2))
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1189,plain,
( in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk176_2(X2,X1) != esk177_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1190,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_596]) ).
cnf(c_0_1191,plain,
( in(esk178_2(X2,X1),X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1192,plain,
( in(esk179_2(X2,X1),X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1193,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_610]) ).
cnf(c_0_1194,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_588]) ).
cnf(c_0_1195,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_589]) ).
cnf(c_0_1196,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1197,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1198,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1199,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1200,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1201,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1202,plain,
( esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk176_2(X2,X1) != esk177_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1203,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1204,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1205,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1206,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1207,plain,
( X1 = set_difference(X2,X3)
| in(esk68_3(X2,X3,X1),X1)
| in(esk68_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1208,plain,
( X1 = set_intersection2(X2,X3)
| in(esk58_3(X2,X3,X1),X1)
| in(esk58_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1209,plain,
( X1 = set_intersection2(X2,X3)
| in(esk58_3(X2,X3,X1),X1)
| in(esk58_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1210,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk48_3(X2,X3,X1),X1)
| in(esk49_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1211,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk48_3(X2,X3,X1),X1)
| in(esk50_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_1212,plain,
( in(esk178_2(X2,X1),X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1213,plain,
( in(esk179_2(X2,X1),X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1214,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_611]) ).
cnf(c_0_1215,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1216,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1217,plain,
( in(esk158_1(X1),X1)
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1218,plain,
( in(esk160_1(X1),X1)
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1219,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk90_2(X1,X2),esk92_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1220,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk76_2(X1,X2),esk77_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1221,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk77_2(X1,X2),esk76_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1222,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk27_2(X1,X2),esk27_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_613]) ).
cnf(c_0_1223,plain,
( X1 = unordered_pair(X2,X3)
| esk42_3(X2,X3,X1) = X3
| esk42_3(X2,X3,X1) = X2
| in(esk42_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1224,plain,
( empty_carrier(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| ~ latt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1) ),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_1225,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk93_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_1226,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1227,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_1228,plain,
( esk159_1(X1) = singleton(esk158_1(X1))
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1229,plain,
( esk161_1(X1) = singleton(esk160_1(X1))
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1230,plain,
( in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| esk205_2(X2,X1) != esk206_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1231,plain,
( esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| esk156_1(X1) != esk157_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1232,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1233,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1234,plain,
( empty(X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1235,plain,
( empty(X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1236,plain,
( empty(X2)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1237,plain,
( in(esk207_2(X2,X1),X2)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1238,plain,
( in(esk208_2(X2,X1),X2)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1239,plain,
( esk155_1(X1) = esk156_1(X1)
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1240,plain,
( esk155_1(X1) = esk157_1(X1)
| esk165_3(X1,X3,X2) = singleton(esk164_3(X1,X3,X2))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1241,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_593]) ).
cnf(c_0_1242,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1243,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1244,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1245,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1246,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1247,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1248,plain,
( in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| esk205_2(X2,X1) != esk206_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1249,plain,
( in(esk207_2(X2,X1),X2)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1250,plain,
( in(esk208_2(X2,X1),X2)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1251,plain,
( X1 = inclusion_relation(X2)
| subset(esk33_2(X2,X1),esk34_2(X2,X1))
| in(ordered_pair(esk33_2(X2,X1),esk34_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_1252,plain,
( in(esk158_1(X1),X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1253,plain,
( in(esk160_1(X1),X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1254,plain,
( X2 = fiber(X1,X3)
| in(esk32_3(X1,X3,X2),X2)
| ~ relation(X1)
| esk32_3(X1,X3,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1255,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_615]) ).
cnf(c_0_1256,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_615]) ).
cnf(c_0_1257,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_615]) ).
cnf(c_0_1258,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_615]) ).
cnf(c_0_1259,plain,
( empty(X2)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| esk127_2(X2,X1) != esk128_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1260,plain,
( ordinal(esk207_2(X2,X1))
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1261,plain,
( ordinal(esk208_2(X2,X1))
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1262,plain,
( ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| esk205_2(X2,X1) != esk206_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1263,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1264,plain,
( esk205_2(X2,X1) = esk207_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1265,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1266,plain,
( esk206_2(X2,X1) = esk208_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1267,plain,
( esk159_1(X1) = singleton(esk158_1(X1))
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1268,plain,
( esk161_1(X1) = singleton(esk160_1(X1))
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1269,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1270,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1271,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1272,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1273,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1274,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1275,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1276,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1277,plain,
( in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| esk156_1(X1) != esk157_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1278,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_593]) ).
cnf(c_0_1279,plain,
( ordinal(esk207_2(X2,X1))
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1280,plain,
( in(esk207_2(X2,X1),X2)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1281,plain,
( ordinal(esk208_2(X2,X1))
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1282,plain,
( in(esk208_2(X2,X1),X2)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1283,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk74_2(X1,X2)),X1)
| ~ in(esk74_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_1284,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk60_2(X1,X2),X3),X1)
| ~ in(esk60_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_1285,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1286,plain,
( esk205_2(X2,X1) = esk207_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1287,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1288,plain,
( esk206_2(X2,X1) = esk208_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1289,plain,
( esk155_1(X1) = esk156_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1290,plain,
( esk155_1(X1) = esk157_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1291,plain,
( empty_carrier(X1)
| below(X1,X2,X3)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_616]) ).
cnf(c_0_1292,plain,
( empty_carrier(X1)
| join(X1,X2,X3) = X3
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_616]) ).
cnf(c_0_1293,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1294,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1295,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk28_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1296,plain,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_618]) ).
cnf(c_0_1297,plain,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_619]) ).
cnf(c_0_1298,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_581]) ).
cnf(c_0_1299,plain,
( ordinal(esk207_2(X2,X1))
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1300,plain,
( ordinal(esk208_2(X2,X1))
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1301,plain,
( empty(X2)
| esk126_2(X2,X1) = esk129_2(X2,X1)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1302,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_1303,plain,
( element(meet_commut(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_1304,plain,
( element(join_commut(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_621]) ).
cnf(c_0_1305,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1306,plain,
( esk205_2(X2,X1) = esk207_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1307,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1308,plain,
( esk206_2(X2,X1) = esk208_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1309,plain,
( in(esk158_1(X1),X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1310,plain,
( in(esk160_1(X1),X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1311,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_622]) ).
cnf(c_0_1312,plain,
( element(meet(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_623]) ).
cnf(c_0_1313,plain,
( element(join(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_1314,plain,
( esk159_1(X1) = singleton(esk158_1(X1))
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1315,plain,
( esk161_1(X1) = singleton(esk160_1(X1))
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1316,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_583]) ).
cnf(c_0_1317,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_583]) ).
cnf(c_0_1318,plain,
( in(esk164_3(X1,X3,X2),X1)
| esk156_1(X1) != esk157_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1319,plain,
( ordinal(esk216_3(X3,X2,X1))
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1320,plain,
( ordinal(esk218_3(X3,X2,X1))
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1321,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk75_2(X1,X2),esk74_2(X1,X2)),X1)
| in(esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_1322,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk60_2(X1,X2),esk61_2(X1,X2)),X1)
| in(esk60_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_1323,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_603]) ).
cnf(c_0_1324,plain,
( esk155_1(X1) = esk156_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1325,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| in(X2,esk162_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_605]) ).
cnf(c_0_1326,plain,
( esk155_1(X1) = esk157_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1327,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| in(X2,esk162_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_605]) ).
cnf(c_0_1328,plain,
( meet_commut(X1,X2,X3) = meet(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_625]) ).
cnf(c_0_1329,plain,
( join_commut(X1,X2,X3) = join(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_626]) ).
cnf(c_0_1330,plain,
( meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_627]) ).
cnf(c_0_1331,plain,
( join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_1332,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_629]) ).
cnf(c_0_1333,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk57_2(X1,X2))
| ~ in(X3,esk57_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_1334,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_603]) ).
cnf(c_0_1335,plain,
( in(esk158_1(X1),X1)
| in(X2,esk162_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_605]) ).
cnf(c_0_1336,plain,
( in(esk160_1(X1),X1)
| in(X2,esk162_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_605]) ).
cnf(c_0_1337,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_615]) ).
cnf(c_0_1338,plain,
( esk159_1(X1) = singleton(esk158_1(X1))
| in(X2,esk162_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_605]) ).
cnf(c_0_1339,plain,
( esk161_1(X1) = singleton(esk160_1(X1))
| in(X2,esk162_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_605]) ).
cnf(c_0_1340,plain,
( in(X2,esk162_2(X1,X3))
| esk156_1(X1) != esk157_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_605]) ).
cnf(c_0_1341,plain,
( X3 = empty_set
| in(esk56_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_1342,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk29_2(X1,X2),X2)
| ~ in(esk29_2(X1,X2),esk30_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1343,plain,
( subset(X1,X2)
| in(ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_611]) ).
cnf(c_0_1344,plain,
( in(esk69_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_630]) ).
cnf(c_0_1345,plain,
( esk155_1(X1) = esk156_1(X1)
| in(X2,esk162_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_605]) ).
cnf(c_0_1346,plain,
( esk155_1(X1) = esk157_1(X1)
| in(X2,esk162_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_605]) ).
cnf(c_0_1347,plain,
( esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| esk205_2(X2,X1) != esk206_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1348,plain,
( X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| esk205_2(X2,X1) != esk206_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1349,plain,
( X3 = apply(X1,esk69_3(X1,X2,X3))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_1350,plain,
( in(esk207_2(X2,X1),X2)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1351,plain,
( in(esk207_2(X2,X1),X2)
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1352,plain,
( in(esk208_2(X2,X1),X2)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1353,plain,
( in(esk208_2(X2,X1),X2)
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1354,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk90_2(X1,X2),esk91_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1355,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk91_2(X1,X2),esk92_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1356,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk62_2(X1,X2),esk63_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1357,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk63_2(X1,X2),esk62_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1358,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_585]) ).
cnf(c_0_1359,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_586]) ).
cnf(c_0_1360,plain,
( in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| esk205_2(X2,X1) != esk206_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1361,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1362,plain,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| esk70_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(esk70_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_1363,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(esk170_2(X1,X2),succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1364,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_631]) ).
cnf(c_0_1365,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_612]) ).
cnf(c_0_1366,plain,
( in(esk207_2(X2,X1),X2)
| in(X3,esk209_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_614]) ).
cnf(c_0_1367,plain,
( in(esk208_2(X2,X1),X2)
| in(X3,esk209_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_614]) ).
cnf(c_0_1368,plain,
( ordinal(esk207_2(X2,X1))
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1369,plain,
( ordinal(esk207_2(X2,X1))
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1370,plain,
( ordinal(esk208_2(X2,X1))
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1371,plain,
( ordinal(esk208_2(X2,X1))
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1372,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk65_2(X2,X1),X3)
| ~ in(esk65_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1373,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1374,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1375,plain,
( esk205_2(X2,X1) = esk207_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1376,plain,
( esk205_2(X2,X1) = esk207_2(X2,X1)
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1377,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1378,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1379,plain,
( esk206_2(X2,X1) = esk208_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1380,plain,
( esk206_2(X2,X1) = esk208_2(X2,X1)
| X3 = esk211_3(X2,X1,X3)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_1381,plain,
( in(X3,esk64_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1382,plain,
( in(esk64_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1383,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1384,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1385,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_592]) ).
cnf(c_0_1386,plain,
( ordinal(esk207_2(X2,X1))
| in(X3,esk209_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_614]) ).
cnf(c_0_1387,plain,
( ordinal(esk208_2(X2,X1))
| in(X3,esk209_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_614]) ).
cnf(c_0_1388,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_615]) ).
cnf(c_0_1389,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk28_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1390,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| in(X3,esk209_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_614]) ).
cnf(c_0_1391,plain,
( esk205_2(X2,X1) = esk207_2(X2,X1)
| in(X3,esk209_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_614]) ).
cnf(c_0_1392,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| in(X3,esk209_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_614]) ).
cnf(c_0_1393,plain,
( esk206_2(X2,X1) = esk208_2(X2,X1)
| in(X3,esk209_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_614]) ).
cnf(c_0_1394,plain,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_633]) ).
cnf(c_0_1395,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_634]) ).
cnf(c_0_1396,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| ordinal(esk171_2(X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1397,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_585]) ).
cnf(c_0_1398,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_586]) ).
cnf(c_0_1399,plain,
( X2 = esk216_3(X3,X2,X1)
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1400,plain,
( X1 = esk218_3(X3,X2,X1)
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1401,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_635]) ).
cnf(c_0_1402,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_635]) ).
cnf(c_0_1403,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_611]) ).
cnf(c_0_1404,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1405,plain,
( in(esk158_1(X1),X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1406,plain,
( in(esk160_1(X1),X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1407,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_601]) ).
cnf(c_0_1408,plain,
( X1 = X2
| ~ in(ordered_pair(X3,X2),X4)
| ~ in(ordered_pair(X3,X1),X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_1409,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_638]) ).
cnf(c_0_1410,plain,
( esk159_1(X1) = singleton(esk158_1(X1))
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1411,plain,
( esk161_1(X1) = singleton(esk160_1(X1))
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1412,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_639]) ).
cnf(c_0_1413,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_640]) ).
cnf(c_0_1414,plain,
( esk163_3(X1,X3,X2) = X2
| esk156_1(X1) != esk157_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1415,plain,
( X1 = powerset(X2)
| ~ subset(esk36_2(X2,X1),X2)
| ~ in(esk36_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_1416,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_588]) ).
cnf(c_0_1417,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_589]) ).
cnf(c_0_1418,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_596]) ).
cnf(c_0_1419,plain,
( X1 = X2
| ~ in(esk212_2(X1,X2),X2)
| ~ in(esk212_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_642]) ).
cnf(c_0_1420,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| esk170_2(X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1421,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| X2 = esk171_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1422,plain,
( esk155_1(X1) = esk156_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1423,plain,
( esk155_1(X1) = esk157_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_1424,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_598]) ).
cnf(c_0_1425,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_598]) ).
cnf(c_0_1426,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_643]) ).
cnf(c_0_1427,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_644]) ).
cnf(c_0_1428,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_645]) ).
cnf(c_0_1429,plain,
( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_645]) ).
cnf(c_0_1430,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_646]) ).
cnf(c_0_1431,plain,
( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_646]) ).
cnf(c_0_1432,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_601]) ).
cnf(c_0_1433,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_583]) ).
cnf(c_0_1434,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_583]) ).
cnf(c_0_1435,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_599]) ).
cnf(c_0_1436,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_599]) ).
cnf(c_0_1437,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_583]) ).
cnf(c_0_1438,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_643]) ).
cnf(c_0_1439,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_647]) ).
cnf(c_0_1440,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk44_1(X1))
| ~ in(X2,esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1441,plain,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_1442,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_585]) ).
cnf(c_0_1443,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_586]) ).
cnf(c_0_1444,plain,
( X2 = relation_rng(X1)
| in(esk70_2(X1,X2),X2)
| esk70_2(X1,X2) = apply(X1,esk71_2(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_1445,plain,
( X1 = union(X2)
| in(esk65_2(X2,X1),X1)
| in(esk65_2(X2,X1),esk66_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1446,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_594]) ).
cnf(c_0_1447,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_644]) ).
cnf(c_0_1448,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk30_2(X1,X2),X1)
| ~ in(esk29_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1449,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk29_2(X1,X2),X3)
| in(esk29_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1450,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_648]) ).
cnf(c_0_1451,plain,
( ~ in(X1,X2)
| ~ in(X3,esk213_2(X1,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_649]) ).
cnf(c_0_1452,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_590]) ).
cnf(c_0_1453,plain,
( X2 = relation_rng(X1)
| in(esk70_2(X1,X2),X2)
| in(esk71_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_1454,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_1455,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_1456,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_1457,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_592]) ).
cnf(c_0_1458,plain,
( in(X2,esk169_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1459,plain,
( in(esk170_2(X1,X2),succ(X1))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1460,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_650]) ).
cnf(c_0_1461,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_651]) ).
cnf(c_0_1462,plain,
( X1 = ordered_pair(esk24_2(X2,X1),esk25_2(X2,X1))
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_652]) ).
cnf(c_0_1463,plain,
( X4 = pair_second(X1)
| X1 = ordered_pair(esk37_2(X1,X4),esk38_2(X1,X4))
| X1 != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_653]) ).
cnf(c_0_1464,plain,
( X4 = pair_first(X1)
| X1 = ordered_pair(esk22_2(X1,X4),esk23_2(X1,X4))
| X1 != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_654]) ).
cnf(c_0_1465,plain,
( in(X3,esk215_2(X2,X1))
| ~ in(X1,esk214_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_1466,plain,
( in(esk150_1(X1),X1)
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1467,plain,
( in(esk150_1(X1),X1)
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1468,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1469,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_1470,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_630]) ).
cnf(c_0_1471,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_1472,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_603]) ).
cnf(c_0_1473,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1474,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1475,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1476,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1477,plain,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_613]) ).
cnf(c_0_1478,plain,
( X1 = singleton(X2)
| esk31_2(X2,X1) != X2
| ~ in(esk31_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_1479,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_658]) ).
cnf(c_0_1480,plain,
( esk151_1(X1) = singleton(esk150_1(X1))
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1481,plain,
( esk152_1(X1) = singleton(esk150_1(X1))
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1482,plain,
( X2 = empty_set
| in(esk43_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1483,plain,
( X3 = X2
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1484,plain,
( X3 = X1
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_1485,plain,
( in(X2,esk153_1(X1))
| esk151_1(X1) != esk152_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1486,plain,
( esk151_1(X1) = singleton(esk150_1(X1))
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1487,plain,
( esk151_1(X1) = singleton(esk150_1(X1))
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1488,plain,
( esk152_1(X1) = singleton(esk150_1(X1))
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1489,plain,
( esk152_1(X1) = singleton(esk150_1(X1))
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1490,plain,
( X1 = union(X2)
| in(esk65_2(X2,X1),X1)
| in(esk66_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1491,plain,
( X1 = powerset(X2)
| subset(esk36_2(X2,X1),X2)
| in(esk36_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_1492,plain,
( in(esk154_2(X1,X2),X1)
| esk151_1(X1) != esk152_1(X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1493,plain,
( in(esk154_2(X1,X2),X1)
| esk151_1(X1) != esk152_1(X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1494,plain,
( in(esk150_1(X1),X1)
| X2 = singleton(esk154_2(X1,X2))
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1495,plain,
( in(esk150_1(X1),X1)
| X2 = singleton(esk154_2(X1,X2))
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1496,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1497,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_659]) ).
cnf(c_0_1498,plain,
( ordinal(esk171_2(X1,X2))
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1499,plain,
( X1 = X2
| in(esk212_2(X1,X2),X2)
| in(esk212_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_642]) ).
cnf(c_0_1500,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_603]) ).
cnf(c_0_1501,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_592]) ).
cnf(c_0_1502,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_603]) ).
cnf(c_0_1503,plain,
relation_of2(esk115_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_660]) ).
cnf(c_0_1504,plain,
relation_of2(esk104_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_1505,plain,
quasi_total(esk104_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_1506,plain,
relation_of2_as_subset(esk100_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_662]) ).
cnf(c_0_1507,plain,
relation_of2(esk98_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_663]) ).
cnf(c_0_1508,plain,
( in(esk215_2(X2,X1),esk214_1(X2))
| ~ in(X1,esk214_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_1509,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_664]) ).
cnf(c_0_1510,plain,
( esk151_1(X1) = singleton(esk150_1(X1))
| X2 = singleton(esk154_2(X1,X2))
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1511,plain,
( esk152_1(X1) = singleton(esk150_1(X1))
| X2 = singleton(esk154_2(X1,X2))
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1512,plain,
( subset(X1,X2)
| ~ in(esk55_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_665]) ).
cnf(c_0_1513,plain,
( X2 = singleton(esk154_2(X1,X2))
| esk151_1(X1) != esk152_1(X1)
| ~ in(X2,esk153_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_1514,plain,
( ordinal(esk195_0)
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1515,plain,
( ordinal(esk196_0)
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1516,plain,
( in(X1,esk214_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk214_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_1517,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1518,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1519,plain,
( in(esk198_2(X2,X1),X2)
| esk195_0 != esk196_0
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1520,plain,
( in(X1,esk214_1(X2))
| are_equipotent(X1,esk214_1(X2))
| ~ subset(X1,esk214_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_1521,plain,
( esk194_0 = esk195_0
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1522,plain,
( esk194_0 = esk196_0
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1523,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_667]) ).
cnf(c_0_1524,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1525,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_668]) ).
cnf(c_0_1526,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_669]) ).
cnf(c_0_1527,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_670]) ).
cnf(c_0_1528,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1529,plain,
( function(X1)
| in(ordered_pair(esk19_1(X1),esk20_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_1530,plain,
( function(X1)
| in(ordered_pair(esk19_1(X1),esk21_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_1531,plain,
( X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ subset(X1,esk72_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1532,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_1533,plain,
( esk170_2(X1,X2) = X2
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1534,plain,
( X2 = esk171_2(X1,X2)
| ~ ordinal(X1)
| esk167_1(X1) != esk168_1(X1)
| ~ in(X2,esk169_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_1535,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| esk76_2(X1,X2) != esk77_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1536,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| esk62_2(X1,X2) != esk63_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1537,plain,
( in(esk213_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_649]) ).
cnf(c_0_1538,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_672]) ).
cnf(c_0_1539,plain,
( is_transitive_in(X1,X2)
| in(esk90_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1540,plain,
( is_transitive_in(X1,X2)
| in(esk91_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1541,plain,
( is_transitive_in(X1,X2)
| in(esk92_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_1542,plain,
( is_connected_in(X1,X2)
| in(esk76_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1543,plain,
( is_connected_in(X1,X2)
| in(esk77_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_1544,plain,
( is_antisymmetric_in(X1,X2)
| in(esk62_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1545,plain,
( is_antisymmetric_in(X1,X2)
| in(esk63_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_1546,plain,
( is_well_founded_in(X1,X2)
| subset(esk57_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_1547,plain,
( is_reflexive_in(X1,X2)
| in(esk27_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_613]) ).
cnf(c_0_1548,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_673]) ).
cnf(c_0_1549,plain,
( X1 = inclusion_relation(X2)
| in(esk33_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_1550,plain,
( X1 = inclusion_relation(X2)
| in(esk34_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_1551,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_1552,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1553,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_1554,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1555,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_1556,plain,
( X1 = singleton(X2)
| esk31_2(X2,X1) = X2
| in(esk31_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_1557,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_674]) ).
cnf(c_0_1558,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_644]) ).
cnf(c_0_1559,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_675]) ).
cnf(c_0_1560,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_665]) ).
cnf(c_0_1561,plain,
( one_to_one(X1)
| apply(X1,esk82_1(X1)) = apply(X1,esk83_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_1562,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_676]) ).
cnf(c_0_1563,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_676]) ).
cnf(c_0_1564,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X6,X5)
| X4 != pair_second(X1) ),
inference(split_conjunct,[status(thm)],[c_0_653]) ).
cnf(c_0_1565,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X5,X6)
| X4 != pair_first(X1) ),
inference(split_conjunct,[status(thm)],[c_0_654]) ).
cnf(c_0_1566,plain,
( ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_1567,plain,
( finite(X1)
| ~ in(relation_dom(X2),omega)
| relation_rng(X2) != X1
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_1568,plain,
( ordinal(esk195_0)
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1569,plain,
( ordinal(esk196_0)
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1570,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_678]) ).
cnf(c_0_1571,plain,
( in(X1,esk197_1(X2))
| esk195_0 != esk196_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1572,plain,
( X1 = omega
| in(empty_set,esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1573,plain,
( esk194_0 = esk195_0
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1574,plain,
( esk194_0 = esk196_0
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1575,plain,
( subset(X1,X2)
| in(esk55_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_665]) ).
cnf(c_0_1576,plain,
( relation_dom(esk67_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_1577,plain,
( relation_rng(esk67_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_1578,plain,
( relation(esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_1579,plain,
( function(esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_1580,plain,
( one_to_one(esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_1581,plain,
( X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3)
| X4 != esk38_2(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_653]) ).
cnf(c_0_1582,plain,
( X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3)
| X4 != esk22_2(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_654]) ).
cnf(c_0_1583,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_679]) ).
cnf(c_0_1584,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_644]) ).
cnf(c_0_1585,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_680]) ).
cnf(c_0_1586,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_681]) ).
cnf(c_0_1587,plain,
( finite(relation_image(X1,X2))
| ~ finite(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_682]) ).
cnf(c_0_1588,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_683]) ).
cnf(c_0_1589,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_683]) ).
cnf(c_0_1590,plain,
( subset(X1,X2)
| X1 != omega
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1591,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1592,plain,
( ordinal(esk195_0)
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1593,plain,
( ordinal(esk196_0)
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1594,plain,
( empty_carrier(X1)
| element(esk125_1(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_684]) ).
cnf(c_0_1595,plain,
( esk198_2(X2,X1) = X1
| esk195_0 != esk196_0
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1596,plain,
( esk194_0 = esk195_0
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1597,plain,
( esk194_0 = esk196_0
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1598,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_685]) ).
cnf(c_0_1599,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_686]) ).
cnf(c_0_1600,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_687]) ).
cnf(c_0_1601,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_688]) ).
cnf(c_0_1602,plain,
( X1 = omega
| ordinal(esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1603,plain,
( X1 = omega
| being_limit_ordinal(esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1604,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_689]) ).
cnf(c_0_1605,plain,
( epsilon_connected(X1)
| ~ in(esk51_1(X1),esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_1606,plain,
( epsilon_connected(X1)
| ~ in(esk52_1(X1),esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_1607,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_690]) ).
cnf(c_0_1608,plain,
( one_to_one(X1)
| in(esk82_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_1609,plain,
( one_to_one(X1)
| in(esk83_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_1610,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_1611,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_1612,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_691]) ).
cnf(c_0_1613,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_692]) ).
cnf(c_0_1614,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_693]) ).
cnf(c_0_1615,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_693]) ).
cnf(c_0_1616,plain,
( finite(set_union2(X1,X2))
| ~ finite(X2)
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_694]) ).
cnf(c_0_1617,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_695]) ).
cnf(c_0_1618,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_695]) ).
cnf(c_0_1619,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_696]) ).
cnf(c_0_1620,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_696]) ).
cnf(c_0_1621,plain,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_697]) ).
cnf(c_0_1622,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_698]) ).
cnf(c_0_1623,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_699]) ).
cnf(c_0_1624,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_700]) ).
cnf(c_0_1625,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_700]) ).
cnf(c_0_1626,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_701]) ).
cnf(c_0_1627,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_701]) ).
cnf(c_0_1628,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_702]) ).
cnf(c_0_1629,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1630,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1631,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1632,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1633,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_1634,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk57_2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_1635,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_703]) ).
cnf(c_0_1636,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_704]) ).
cnf(c_0_1637,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_705]) ).
cnf(c_0_1638,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_706]) ).
cnf(c_0_1639,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_707]) ).
cnf(c_0_1640,plain,
( finite(X1)
| ~ element(X1,powerset(X2))
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_708]) ).
cnf(c_0_1641,plain,
( v1_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1642,plain,
( v2_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1643,plain,
( v3_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1644,plain,
( v4_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1645,plain,
( v5_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1646,plain,
( v1_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_1647,plain,
( v2_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_1648,plain,
( v3_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_1649,plain,
( v4_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_1650,plain,
( v1_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_711]) ).
cnf(c_0_1651,plain,
( v2_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_711]) ).
cnf(c_0_1652,plain,
( v3_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_711]) ).
cnf(c_0_1653,plain,
( v1_membered(X2)
| ~ v2_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_712]) ).
cnf(c_0_1654,plain,
( v2_membered(X2)
| ~ v2_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_712]) ).
cnf(c_0_1655,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v1_membered(X2) ),
inference(split_conjunct,[status(thm)],[c_0_713]) ).
cnf(c_0_1656,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_689]) ).
cnf(c_0_1657,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_714]) ).
cnf(c_0_1658,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| element(esk84_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_1659,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| element(esk85_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_1660,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1661,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_1662,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_715]) ).
cnf(c_0_1663,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_1664,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_1665,plain,
( ordinal(esk195_0)
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1666,plain,
( ordinal(esk196_0)
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1667,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_717]) ).
cnf(c_0_1668,plain,
( well_founded_relation(X1)
| subset(esk44_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1669,plain,
( in(relation_dom(esk18_1(X1)),omega)
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_1670,plain,
( ordinal(X1)
| esk195_0 != esk196_0
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1671,plain,
( esk194_0 = esk195_0
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1672,plain,
( esk194_0 = esk196_0
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_1673,plain,
( finite(set_difference(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_718]) ).
cnf(c_0_1674,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_719]) ).
cnf(c_0_1675,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_720]) ).
cnf(c_0_1676,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_721]) ).
cnf(c_0_1677,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_722]) ).
cnf(c_0_1678,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_723]) ).
cnf(c_0_1679,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_724]) ).
cnf(c_0_1680,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_725]) ).
cnf(c_0_1681,plain,
( equipotent(X1,X2)
| ~ equipotent(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_726]) ).
cnf(c_0_1682,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_727]) ).
cnf(c_0_1683,plain,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_728]) ).
cnf(c_0_1684,plain,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_728]) ).
cnf(c_0_1685,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_717]) ).
cnf(c_0_1686,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_729]) ).
cnf(c_0_1687,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_729]) ).
cnf(c_0_1688,plain,
( epsilon_transitive(X1)
| ~ subset(esk39_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_703]) ).
cnf(c_0_1689,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_704]) ).
cnf(c_0_1690,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_705]) ).
cnf(c_0_1691,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_706]) ).
cnf(c_0_1692,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_707]) ).
cnf(c_0_1693,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_1694,plain,
( epsilon_transitive(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_730]) ).
cnf(c_0_1695,plain,
( epsilon_connected(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_730]) ).
cnf(c_0_1696,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_730]) ).
cnf(c_0_1697,plain,
( v1_xcmplx_0(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1698,plain,
( natural(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1699,plain,
( v1_xreal_0(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1700,plain,
( v1_int_1(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1701,plain,
( v1_rat_1(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1702,plain,
( v1_xcmplx_0(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1703,plain,
( v1_xreal_0(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1704,plain,
( v1_int_1(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1705,plain,
( v1_rat_1(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1706,plain,
( v1_xcmplx_0(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_733]) ).
cnf(c_0_1707,plain,
( v1_xreal_0(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_733]) ).
cnf(c_0_1708,plain,
( v1_rat_1(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_733]) ).
cnf(c_0_1709,plain,
( v1_xcmplx_0(X2)
| ~ v2_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_734]) ).
cnf(c_0_1710,plain,
( v1_xreal_0(X2)
| ~ v2_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_734]) ).
cnf(c_0_1711,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v1_membered(X2) ),
inference(split_conjunct,[status(thm)],[c_0_735]) ).
cnf(c_0_1712,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_1713,plain,
( relation(X1)
| esk26_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_652]) ).
cnf(c_0_1714,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_736]) ).
cnf(c_0_1715,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_736]) ).
cnf(c_0_1716,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk82_1(X1) != esk83_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_1717,plain,
( empty(X1)
| element(esk119_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_737]) ).
cnf(c_0_1718,plain,
( empty(X1)
| element(esk110_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_738]) ).
cnf(c_0_1719,plain,
( ~ natural(X1)
| ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1720,plain,
relation(esk115_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_660]) ).
cnf(c_0_1721,plain,
function(esk115_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_660]) ).
cnf(c_0_1722,plain,
relation(esk104_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_1723,plain,
function(esk104_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_1724,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_740]) ).
cnf(c_0_1725,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_741]) ).
cnf(c_0_1726,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_742]) ).
cnf(c_0_1727,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_1728,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(esk125_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_684]) ).
cnf(c_0_1729,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_743]) ).
cnf(c_0_1730,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_744]) ).
cnf(c_0_1731,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_745]) ).
cnf(c_0_1732,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_746]) ).
cnf(c_0_1733,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_747]) ).
cnf(c_0_1734,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_748]) ).
cnf(c_0_1735,plain,
element(esk117_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_749]) ).
cnf(c_0_1736,plain,
element(esk112_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1737,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_751]) ).
cnf(c_0_1738,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_1739,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_717]) ).
cnf(c_0_1740,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_752]) ).
cnf(c_0_1741,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_752]) ).
cnf(c_0_1742,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_752]) ).
cnf(c_0_1743,plain,
( epsilon_connected(X1)
| in(esk51_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_1744,plain,
( epsilon_connected(X1)
| in(esk52_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_1745,plain,
( epsilon_transitive(X1)
| in(esk39_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_703]) ).
cnf(c_0_1746,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_753]) ).
cnf(c_0_1747,plain,
( relation(X1)
| in(esk26_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_652]) ).
cnf(c_0_1748,plain,
( epsilon_transitive(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1749,plain,
( epsilon_connected(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1750,plain,
( ordinal(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1751,plain,
( natural(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1752,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_754]) ).
cnf(c_0_1753,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_754]) ).
cnf(c_0_1754,plain,
( epsilon_transitive(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1755,plain,
( epsilon_connected(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1756,plain,
( ordinal(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1757,plain,
( natural(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1758,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_756]) ).
cnf(c_0_1759,plain,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1760,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_758]) ).
cnf(c_0_1761,plain,
( X1 = empty_set
| in(esk35_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_753]) ).
cnf(c_0_1762,plain,
( empty(X1)
| ~ empty(esk119_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_737]) ).
cnf(c_0_1763,plain,
( empty(X1)
| ~ empty(esk110_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_738]) ).
cnf(c_0_1764,plain,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_1765,plain,
in(X1,esk214_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_1766,plain,
element(esk99_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_759]) ).
cnf(c_0_1767,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_1768,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_1769,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_1770,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_1771,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_1772,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1773,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk44_1(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_1774,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_761]) ).
cnf(c_0_1775,plain,
( preboolean(X1)
| ~ diff_closed(X1)
| ~ cup_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_762]) ).
cnf(c_0_1776,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1777,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1778,plain,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1779,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1780,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_764]) ).
cnf(c_0_1781,plain,
( relation_rng(esk18_1(X1)) = X1
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_1782,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_687]) ).
cnf(c_0_1783,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_687]) ).
cnf(c_0_1784,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_765]) ).
cnf(c_0_1785,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_765]) ).
cnf(c_0_1786,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_766]) ).
cnf(c_0_1787,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_766]) ).
cnf(c_0_1788,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1789,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1790,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1791,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1792,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1793,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1794,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_768]) ).
cnf(c_0_1795,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_768]) ).
cnf(c_0_1796,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_645]) ).
cnf(c_0_1797,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_646]) ).
cnf(c_0_1798,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_769]) ).
cnf(c_0_1799,plain,
( relation(esk18_1(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_1800,plain,
( function(esk18_1(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_1801,plain,
( epsilon_connected(X1)
| esk51_1(X1) != esk52_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_1802,plain,
( function(X1)
| esk20_1(X1) != esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_1803,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_770]) ).
cnf(c_0_1804,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_771]) ).
cnf(c_0_1805,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_772]) ).
cnf(c_0_1806,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1807,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1808,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_775]) ).
cnf(c_0_1809,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_776]) ).
cnf(c_0_1810,plain,
( in(empty_set,X1)
| X1 != omega ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1811,plain,
( empty(X1)
| finite(esk119_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_737]) ).
cnf(c_0_1812,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_777]) ).
cnf(c_0_1813,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_778]) ).
cnf(c_0_1814,plain,
equipotent(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_779]) ).
cnf(c_0_1815,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_780]) ).
cnf(c_0_1816,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_781]) ).
cnf(c_0_1817,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_782]) ).
cnf(c_0_1818,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_783]) ).
cnf(c_0_1819,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_784]) ).
cnf(c_0_1820,plain,
( being_limit_ordinal(X1)
| X1 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1821,plain,
( X1 = union(X1)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1822,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1823,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1824,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1825,plain,
( one_sorted_str(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_787]) ).
cnf(c_0_1826,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_788]) ).
cnf(c_0_1827,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1828,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1829,plain,
( v1_membered(X1)
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[c_0_789]) ).
cnf(c_0_1830,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1831,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1832,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1833,plain,
( v2_membered(X1)
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[c_0_791]) ).
cnf(c_0_1834,plain,
( v3_membered(X1)
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[c_0_792]) ).
cnf(c_0_1835,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_793]) ).
cnf(c_0_1836,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1837,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1838,plain,
( v4_membered(X1)
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[c_0_795]) ).
cnf(c_0_1839,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_796]) ).
cnf(c_0_1840,plain,
( cup_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1841,plain,
( diff_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1842,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_798]) ).
cnf(c_0_1843,plain,
( v1_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1844,plain,
( v2_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1845,plain,
( v3_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1846,plain,
( v4_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1847,plain,
( v5_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1848,plain,
empty(esk117_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_749]) ).
cnf(c_0_1849,plain,
empty(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1850,plain,
relation(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1851,plain,
function(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1852,plain,
one_to_one(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1853,plain,
epsilon_transitive(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1854,plain,
epsilon_connected(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1855,plain,
ordinal(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1856,plain,
natural(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1857,plain,
finite(esk112_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1858,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1859,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1860,plain,
cup_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1861,plain,
diff_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1862,plain,
preboolean(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1863,plain,
finite(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1864,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_801]) ).
cnf(c_0_1865,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_802]) ).
cnf(c_0_1866,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_1867,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_803]) ).
cnf(c_0_1868,plain,
( being_limit_ordinal(X1)
| X1 != omega ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1869,plain,
( ordinal(X1)
| X1 != omega ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_1870,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_804]) ).
cnf(c_0_1871,plain,
~ empty_carrier(esk123_0),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1872,plain,
~ empty(esk121_0),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1873,plain,
~ empty(esk118_0),
inference(split_conjunct,[status(thm)],[c_0_807]) ).
cnf(c_0_1874,plain,
~ empty(esk116_0),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1875,plain,
~ empty(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1876,plain,
~ empty(esk102_0),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1877,plain,
~ empty(esk101_0),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1878,plain,
~ empty(omega),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1879,plain,
relation(esk124_0),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1880,plain,
relation_empty_yielding(esk124_0),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1881,plain,
function(esk124_0),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1882,plain,
one_sorted_str(esk123_0),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1883,plain,
relation(esk122_0),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1884,plain,
relation_empty_yielding(esk122_0),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1885,plain,
epsilon_transitive(esk121_0),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1886,plain,
epsilon_connected(esk121_0),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1887,plain,
ordinal(esk121_0),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1888,plain,
relation(esk120_0),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1889,plain,
function(esk120_0),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1890,plain,
one_to_one(esk120_0),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1891,plain,
relation(esk116_0),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1892,plain,
relation(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1893,plain,
function(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1894,plain,
one_to_one(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1895,plain,
empty(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1896,plain,
epsilon_transitive(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1897,plain,
epsilon_connected(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1898,plain,
ordinal(esk114_0),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1899,plain,
relation(esk113_0),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1900,plain,
empty(esk113_0),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1901,plain,
function(esk113_0),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1902,plain,
empty(esk111_0),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1903,plain,
empty(esk109_0),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1904,plain,
relation(esk109_0),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1905,plain,
relation(esk108_0),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1906,plain,
function(esk108_0),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1907,plain,
one_to_one(esk108_0),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1908,plain,
empty(esk108_0),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1909,plain,
epsilon_transitive(esk107_0),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1910,plain,
epsilon_connected(esk107_0),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1911,plain,
ordinal(esk107_0),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1912,plain,
being_limit_ordinal(esk107_0),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1913,plain,
epsilon_transitive(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1914,plain,
epsilon_connected(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1915,plain,
ordinal(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1916,plain,
v1_membered(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1917,plain,
v2_membered(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1918,plain,
v3_membered(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1919,plain,
v4_membered(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1920,plain,
v5_membered(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1921,plain,
relation(esk103_0),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1922,plain,
function(esk103_0),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1923,plain,
finite(esk102_0),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1924,plain,
epsilon_transitive(esk101_0),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1925,plain,
epsilon_connected(esk101_0),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1926,plain,
ordinal(esk101_0),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1927,plain,
natural(esk101_0),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1928,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1929,plain,
v1_membered(empty_set),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1930,plain,
v2_membered(empty_set),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1931,plain,
v3_membered(empty_set),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1932,plain,
v4_membered(empty_set),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1933,plain,
v5_membered(empty_set),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1934,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1935,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1936,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1937,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1938,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1939,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1940,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1941,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1942,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1943,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1944,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1945,plain,
epsilon_transitive(omega),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1946,plain,
epsilon_connected(omega),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1947,plain,
ordinal(omega),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1948,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1949,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1950,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1951,plain,
latt_str(esk97_0),
inference(split_conjunct,[status(thm)],[c_0_829]) ).
cnf(c_0_1952,plain,
join_semilatt_str(esk96_0),
inference(split_conjunct,[status(thm)],[c_0_830]) ).
cnf(c_0_1953,plain,
one_sorted_str(esk95_0),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1954,plain,
meet_semilatt_str(esk94_0),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1955,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_833]) ).
cnf(c_0_1956,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1957,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1958,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1959,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1960,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1961,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1962,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1963,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1964,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1965,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1966,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1967,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_845]) ).
cnf(c_0_1968,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1969,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1970,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1971,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1972,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1973,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1974,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1975,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1976,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1977,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1978,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1979,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1980,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1981,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1982,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1983,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk140_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,esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
c_0_861,
[final] ).
cnf(c_0_1984,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,esk143_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,esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
c_0_862,
[final] ).
cnf(c_0_1985,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_863,
[final] ).
cnf(c_0_1986,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_864,
[final] ).
cnf(c_0_1987,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_865,
[final] ).
cnf(c_0_1988,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_866,
[final] ).
cnf(c_0_1989,plain,
( empty(X2)
| in(X3,esk144_3(X2,X1,X4))
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_867,
[final] ).
cnf(c_0_1990,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_868,
[final] ).
cnf(c_0_1991,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_869,
[final] ).
cnf(c_0_1992,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_870,
[final] ).
cnf(c_0_1993,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_871,
[final] ).
cnf(c_0_1994,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_872,
[final] ).
cnf(c_0_1995,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(X3,esk144_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,esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
c_0_873,
[final] ).
cnf(c_0_1996,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| in(esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk140_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_874,
[final] ).
cnf(c_0_1997,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(X4,esk144_3(X2,X1,X5))
| in(esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,esk143_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_875,
[final] ).
cnf(c_0_1998,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_876,
[final] ).
cnf(c_0_1999,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_877,
[final] ).
cnf(c_0_2000,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_878,
[final] ).
cnf(c_0_2001,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_879,
[final] ).
cnf(c_0_2002,plain,
( empty(X2)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_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_880,
[final] ).
cnf(c_0_2003,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_881,
[final] ).
cnf(c_0_2004,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_882,
[final] ).
cnf(c_0_2005,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_883,
[final] ).
cnf(c_0_2006,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_884,
[final] ).
cnf(c_0_2007,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_885,
[final] ).
cnf(c_0_2008,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(X3,esk144_3(X2,X1,X4))
| in(esk149_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_886,
[final] ).
cnf(c_0_2009,plain,
( element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
c_0_887,
[final] ).
cnf(c_0_2010,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk134_5(X2,X1,X4,X5,X6)),X1) ),
c_0_888,
[final] ).
cnf(c_0_2011,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,esk134_5(X2,X1,X4,X5,X6)),X1) ),
c_0_889,
[final] ).
cnf(c_0_2012,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_890,
[final] ).
cnf(c_0_2013,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_891,
[final] ).
cnf(c_0_2014,plain,
( empty(X2)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_892,
[final] ).
cnf(c_0_2015,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_893,
[final] ).
cnf(c_0_2016,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_894,
[final] ).
cnf(c_0_2017,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_895,
[final] ).
cnf(c_0_2018,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,esk134_5(X2,X1,X3,X4,X5)),X1) ),
c_0_896,
[final] ).
cnf(c_0_2019,plain,
( apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
c_0_897,
[final] ).
cnf(c_0_2020,plain,
( apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) = meet(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
c_0_898,
[final] ).
cnf(c_0_2021,plain,
( apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) = join(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
c_0_899,
[final] ).
cnf(c_0_2022,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_900,
[final] ).
cnf(c_0_2023,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_901,
[final] ).
cnf(c_0_2024,plain,
( in(ordered_pair(X4,esk86_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_902,
[final] ).
cnf(c_0_2025,plain,
( in(ordered_pair(esk86_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_903,
[final] ).
cnf(c_0_2026,plain,
( ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1)) = esk184_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_904,
[final] ).
cnf(c_0_2027,plain,
( ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1)) = esk185_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_905,
[final] ).
cnf(c_0_2028,plain,
( in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk185_3(X3,X2,X1) != esk184_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_906,
[final] ).
cnf(c_0_2029,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_907,
[final] ).
cnf(c_0_2030,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| in(ordered_pair(apply(X1,esk192_4(X3,X2,X1,X4)),apply(X1,esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_908,
[final] ).
cnf(c_0_2031,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| in(esk174_5(X1,X2,X3,X4,X5),esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
c_0_909,
[final] ).
cnf(c_0_2032,plain,
( in(X2,esk169_1(X1))
| in(esk174_5(X1,X2,X3,X4,X5),esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
c_0_910,
[final] ).
cnf(c_0_2033,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| subset(X5,esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
c_0_911,
[final] ).
cnf(c_0_2034,plain,
( in(X2,esk169_1(X1))
| subset(X5,esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4)) ),
c_0_912,
[final] ).
cnf(c_0_2035,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4))
| esk174_5(X1,X2,X3,X4,X5) != X5 ),
c_0_913,
[final] ).
cnf(c_0_2036,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,esk80_3(X1,X2,X3)),apply(X3,esk81_3(X1,X2,X3))),X2)
| ~ in(esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1) ),
c_0_914,
[final] ).
cnf(c_0_2037,plain,
( in(X2,esk169_1(X1))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,esk173_4(X1,X2,X3,X4))
| esk174_5(X1,X2,X3,X4,X5) != X5 ),
c_0_915,
[final] ).
cnf(c_0_2038,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
c_0_916,
[final] ).
cnf(c_0_2039,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(X4,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
c_0_917,
[final] ).
cnf(c_0_2040,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_918,
[final] ).
cnf(c_0_2041,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_919,
[final] ).
cnf(c_0_2042,plain,
( empty(X2)
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_920,
[final] ).
cnf(c_0_2043,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_921,
[final] ).
cnf(c_0_2044,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_922,
[final] ).
cnf(c_0_2045,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_923,
[final] ).
cnf(c_0_2046,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(X3,esk131_2(X2,X1))
| in(esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
c_0_924,
[final] ).
cnf(c_0_2047,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_925,
[final] ).
cnf(c_0_2048,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_926,
[final] ).
cnf(c_0_2049,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(ordered_pair(esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5))
| ~ in(X6,esk148_4(X2,X1,X5,X4)) ),
c_0_927,
[final] ).
cnf(c_0_2050,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(ordered_pair(esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5))
| ~ in(X6,esk148_4(X2,X1,X5,X4)) ),
c_0_928,
[final] ).
cnf(c_0_2051,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_929,
[final] ).
cnf(c_0_2052,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_930,
[final] ).
cnf(c_0_2053,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_931,
[final] ).
cnf(c_0_2054,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_932,
[final] ).
cnf(c_0_2055,plain,
( empty(X2)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_933,
[final] ).
cnf(c_0_2056,plain,
( X4 = empty_set
| X5 = esk217_4(X3,X2,X1,X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk216_3(X3,X2,X1))))
| ~ subset(esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
c_0_934,
[final] ).
cnf(c_0_2057,plain,
( X4 = empty_set
| X5 = esk219_4(X3,X2,X1,X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk218_3(X3,X2,X1))))
| ~ subset(esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
c_0_935,
[final] ).
cnf(c_0_2058,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_936,
[final] ).
cnf(c_0_2059,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_937,
[final] ).
cnf(c_0_2060,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_938,
[final] ).
cnf(c_0_2061,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_939,
[final] ).
cnf(c_0_2062,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_940,
[final] ).
cnf(c_0_2063,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(ordered_pair(esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4))
| ~ in(X5,esk148_4(X2,X1,X4,X3)) ),
c_0_941,
[final] ).
cnf(c_0_2064,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_942,
[final] ).
cnf(c_0_2065,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_943,
[final] ).
cnf(c_0_2066,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_944,
[final] ).
cnf(c_0_2067,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_945,
[final] ).
cnf(c_0_2068,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1)
| in(ordered_pair(apply(X3,esk80_3(X1,X2,X3)),apply(X3,esk81_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_946,
[final] ).
cnf(c_0_2069,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk88_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk87_3(X1,X2,X3),esk88_3(X1,X2,X3)),X3) ),
c_0_947,
[final] ).
cnf(c_0_2070,plain,
( X4 = empty_set
| in(esk217_4(X3,X2,X1,X4),X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk216_3(X3,X2,X1)))) ),
c_0_948,
[final] ).
cnf(c_0_2071,plain,
( X4 = empty_set
| in(esk219_4(X3,X2,X1,X4),X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(esk218_3(X3,X2,X1)))) ),
c_0_949,
[final] ).
cnf(c_0_2072,plain,
( ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1)) = esk184_3(X3,X2,X1)
| ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_950,
[final] ).
cnf(c_0_2073,plain,
( ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1)) = esk185_3(X3,X2,X1)
| ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_951,
[final] ).
cnf(c_0_2074,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_952,
[final] ).
cnf(c_0_2075,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_953,
[final] ).
cnf(c_0_2076,plain,
( in(ordered_pair(apply(X1,esk186_3(X3,X2,X1)),apply(X1,esk187_3(X3,X2,X1))),X2)
| in(X4,esk190_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_954,
[final] ).
cnf(c_0_2077,plain,
( in(ordered_pair(apply(X1,esk188_3(X3,X2,X1)),apply(X1,esk189_3(X3,X2,X1))),X2)
| in(X4,esk190_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_955,
[final] ).
cnf(c_0_2078,plain,
( ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk185_3(X3,X2,X1) != esk184_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_956,
[final] ).
cnf(c_0_2079,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| ordered_pair(esk146_4(X2,X1,X5,X4),esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_957,
[final] ).
cnf(c_0_2080,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| ordered_pair(esk146_4(X2,X1,X5,X4),esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_958,
[final] ).
cnf(c_0_2081,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(esk147_4(X2,X1,X5,X4),esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_959,
[final] ).
cnf(c_0_2082,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(esk147_4(X2,X1,X5,X4),esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_960,
[final] ).
cnf(c_0_2083,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_961,
[final] ).
cnf(c_0_2084,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| ordered_pair(esk192_4(X3,X2,X1,X4),esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_962,
[final] ).
cnf(c_0_2085,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_963,
[final] ).
cnf(c_0_2086,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_964,
[final] ).
cnf(c_0_2087,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_965,
[final] ).
cnf(c_0_2088,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_966,
[final] ).
cnf(c_0_2089,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_967,
[final] ).
cnf(c_0_2090,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_968,
[final] ).
cnf(c_0_2091,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_969,
[final] ).
cnf(c_0_2092,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_970,
[final] ).
cnf(c_0_2093,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_971,
[final] ).
cnf(c_0_2094,plain,
( empty(X2)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_972,
[final] ).
cnf(c_0_2095,plain,
( empty(X2)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_973,
[final] ).
cnf(c_0_2096,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_974,
[final] ).
cnf(c_0_2097,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_975,
[final] ).
cnf(c_0_2098,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X2 ),
c_0_976,
[final] ).
cnf(c_0_2099,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X3 ),
c_0_977,
[final] ).
cnf(c_0_2100,plain,
( X1 = unordered_triple(X2,X3,X4)
| ~ in(esk17_4(X2,X3,X4,X1),X1)
| esk17_4(X2,X3,X4,X1) != X4 ),
c_0_978,
[final] ).
cnf(c_0_2101,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_979,
[final] ).
cnf(c_0_2102,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_980,
[final] ).
cnf(c_0_2103,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_981,
[final] ).
cnf(c_0_2104,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_982,
[final] ).
cnf(c_0_2105,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_983,
[final] ).
cnf(c_0_2106,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| ordered_pair(esk146_4(X2,X1,X4,X3),esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_984,
[final] ).
cnf(c_0_2107,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_985,
[final] ).
cnf(c_0_2108,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_986,
[final] ).
cnf(c_0_2109,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_987,
[final] ).
cnf(c_0_2110,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(esk147_4(X2,X1,X4,X3),esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_988,
[final] ).
cnf(c_0_2111,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_989,
[final] ).
cnf(c_0_2112,plain,
( in(ordered_pair(esk11_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_990,
[final] ).
cnf(c_0_2113,plain,
( ordered_pair(esk46_4(X2,X3,X1,X4),esk47_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_991,
[final] ).
cnf(c_0_2114,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_992,
[final] ).
cnf(c_0_2115,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_993,
[final] ).
cnf(c_0_2116,plain,
( ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1)) = esk184_3(X3,X2,X1)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_994,
[final] ).
cnf(c_0_2117,plain,
( ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1)) = esk185_3(X3,X2,X1)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_995,
[final] ).
cnf(c_0_2118,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk87_3(X1,X2,X3),esk88_3(X1,X2,X3)),X3)
| in(ordered_pair(esk87_3(X1,X2,X3),esk89_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_996,
[final] ).
cnf(c_0_2119,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk87_3(X1,X2,X3),esk88_3(X1,X2,X3)),X3)
| in(ordered_pair(esk89_3(X1,X2,X3),esk88_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_997,
[final] ).
cnf(c_0_2120,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_998,
[final] ).
cnf(c_0_2121,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_999,
[final] ).
cnf(c_0_2122,plain,
( in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk201_3(X3,X2,X1) != esk200_3(X3,X2,X1)
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1000,
[final] ).
cnf(c_0_2123,plain,
( in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk185_3(X3,X2,X1) != esk184_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1001,
[final] ).
cnf(c_0_2124,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1002,
[final] ).
cnf(c_0_2125,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1003,
[final] ).
cnf(c_0_2126,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1004,
[final] ).
cnf(c_0_2127,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| in(esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1005,
[final] ).
cnf(c_0_2128,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| in(esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1006,
[final] ).
cnf(c_0_2129,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| in(esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1007,
[final] ).
cnf(c_0_2130,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1008,
[final] ).
cnf(c_0_2131,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| in(esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1009,
[final] ).
cnf(c_0_2132,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| esk146_4(X2,X1,X5,X4) = esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1010,
[final] ).
cnf(c_0_2133,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| esk146_4(X2,X1,X5,X4) = esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1011,
[final] ).
cnf(c_0_2134,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_1012,
[final] ).
cnf(c_0_2135,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1013,
[final] ).
cnf(c_0_2136,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1014,
[final] ).
cnf(c_0_2137,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1015,
[final] ).
cnf(c_0_2138,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1016,
[final] ).
cnf(c_0_2139,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1017,
[final] ).
cnf(c_0_2140,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1018,
[final] ).
cnf(c_0_2141,plain,
( empty(X2)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1019,
[final] ).
cnf(c_0_2142,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1020,
[final] ).
cnf(c_0_2143,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1021,
[final] ).
cnf(c_0_2144,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1022,
[final] ).
cnf(c_0_2145,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1023,
[final] ).
cnf(c_0_2146,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1024,
[final] ).
cnf(c_0_2147,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1025,
[final] ).
cnf(c_0_2148,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1026,
[final] ).
cnf(c_0_2149,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1027,
[final] ).
cnf(c_0_2150,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1028,
[final] ).
cnf(c_0_2151,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1029,
[final] ).
cnf(c_0_2152,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1030,
[final] ).
cnf(c_0_2153,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1031,
[final] ).
cnf(c_0_2154,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1032,
[final] ).
cnf(c_0_2155,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1033,
[final] ).
cnf(c_0_2156,plain,
( empty(X2)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1034,
[final] ).
cnf(c_0_2157,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1035,
[final] ).
cnf(c_0_2158,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1036,
[final] ).
cnf(c_0_2159,plain,
( ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1)) = esk184_3(X3,X2,X1)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1037,
[final] ).
cnf(c_0_2160,plain,
( ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1)) = esk185_3(X3,X2,X1)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1038,
[final] ).
cnf(c_0_2161,plain,
( ordered_pair(esk186_3(X3,X2,X1),esk187_3(X3,X2,X1)) = esk184_3(X3,X2,X1)
| in(X4,esk190_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_1039,
[final] ).
cnf(c_0_2162,plain,
( ordered_pair(esk188_3(X3,X2,X1),esk189_3(X3,X2,X1)) = esk185_3(X3,X2,X1)
| in(X4,esk190_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_1040,
[final] ).
cnf(c_0_2163,plain,
( empty(X2)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1041,
[final] ).
cnf(c_0_2164,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1042,
[final] ).
cnf(c_0_2165,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1043,
[final] ).
cnf(c_0_2166,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1044,
[final] ).
cnf(c_0_2167,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1045,
[final] ).
cnf(c_0_2168,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1046,
[final] ).
cnf(c_0_2169,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| in(esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1047,
[final] ).
cnf(c_0_2170,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1048,
[final] ).
cnf(c_0_2171,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1049,
[final] ).
cnf(c_0_2172,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1050,
[final] ).
cnf(c_0_2173,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| esk146_4(X2,X1,X4,X3) = esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1051,
[final] ).
cnf(c_0_2174,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1)
| in(esk80_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_1052,
[final] ).
cnf(c_0_2175,plain,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(esk80_3(X1,X2,X3),esk81_3(X1,X2,X3)),X1)
| in(esk81_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_1053,
[final] ).
cnf(c_0_2176,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk93_3(X2,X1,X3)),X1)
| ~ in(esk93_3(X2,X1,X3),X3) ),
c_0_1054,
[final] ).
cnf(c_0_2177,plain,
( esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk201_3(X3,X2,X1) != esk200_3(X3,X2,X1)
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1055,
[final] ).
cnf(c_0_2178,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| element(esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
c_0_1056,
[final] ).
cnf(c_0_2179,plain,
( X2 = fiber(X1,X3)
| esk32_3(X1,X3,X2) = X3
| ~ relation(X1)
| ~ in(ordered_pair(esk32_3(X1,X3,X2),X3),X1)
| ~ in(esk32_3(X1,X3,X2),X2) ),
c_0_1057,
[final] ).
cnf(c_0_2180,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| X3 = empty_set
| X4 = esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2))))
| ~ subset(esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
c_0_1058,
[final] ).
cnf(c_0_2181,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_1059,
[final] ).
cnf(c_0_2182,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_1060,
[final] ).
cnf(c_0_2183,plain,
( esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk185_3(X3,X2,X1) != esk184_3(X3,X2,X1)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1061,
[final] ).
cnf(c_0_2184,plain,
( in(X4,esk190_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| esk185_3(X3,X2,X1) != esk184_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_1062,
[final] ).
cnf(c_0_2185,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_1063,
[final] ).
cnf(c_0_2186,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_1064,
[final] ).
cnf(c_0_2187,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1065,
[final] ).
cnf(c_0_2188,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1066,
[final] ).
cnf(c_0_2189,plain,
( in(X2,esk169_1(X1))
| element(esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
c_0_1067,
[final] ).
cnf(c_0_2190,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_1068,
[final] ).
cnf(c_0_2191,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_1069,
[final] ).
cnf(c_0_2192,plain,
( empty(X2)
| in(ordered_pair(esk139_2(X2,X1),X3),X1)
| esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk140_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1070,
[final] ).
cnf(c_0_2193,plain,
( empty(X2)
| in(ordered_pair(esk142_2(X2,X1),X3),X1)
| esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk143_2(X2,X1))
| ~ in(X4,esk144_3(X2,X1,X5)) ),
c_0_1071,
[final] ).
cnf(c_0_2194,plain,
( X3 = empty_set
| X4 = esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2))))
| ~ subset(esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
c_0_1072,
[final] ).
cnf(c_0_2195,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk58_3(X2,X3,X1),X3)
| ~ in(esk58_3(X2,X3,X1),X2)
| ~ in(esk58_3(X2,X3,X1),X1) ),
c_0_1073,
[final] ).
cnf(c_0_2196,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_1074,
[final] ).
cnf(c_0_2197,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1075,
[final] ).
cnf(c_0_2198,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,esk190_3(X3,X2,X1)) ),
c_0_1076,
[final] ).
cnf(c_0_2199,plain,
( esk183_3(X3,X2,X1) = esk184_3(X3,X2,X1)
| in(X4,esk190_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_1077,
[final] ).
cnf(c_0_2200,plain,
( esk183_3(X3,X2,X1) = esk185_3(X3,X2,X1)
| in(X4,esk190_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_1078,
[final] ).
cnf(c_0_2201,plain,
( apply(X1,esk5_4(X1,X3,X2,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1079,
[final] ).
cnf(c_0_2202,plain,
( in(esk5_4(X1,X3,X2,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1080,
[final] ).
cnf(c_0_2203,plain,
( in(esk14_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1081,
[final] ).
cnf(c_0_2204,plain,
( in(esk11_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1082,
[final] ).
cnf(c_0_2205,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
c_0_1083,
[final] ).
cnf(c_0_2206,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
c_0_1084,
[final] ).
cnf(c_0_2207,plain,
( in(esk46_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_1085,
[final] ).
cnf(c_0_2208,plain,
( in(esk47_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_1086,
[final] ).
cnf(c_0_2209,plain,
( in(relation_image(X1,esk200_3(X3,X2,X1)),X2)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1087,
[final] ).
cnf(c_0_2210,plain,
( in(relation_image(X1,esk201_3(X3,X2,X1)),X2)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1088,
[final] ).
cnf(c_0_2211,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| esk173_4(X1,X2,X3,X4) != empty_set ),
c_0_1089,
[final] ).
cnf(c_0_2212,plain,
( empty(X2)
| ordered_pair(esk138_2(X2,X1),esk139_2(X2,X1)) = esk136_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1090,
[final] ).
cnf(c_0_2213,plain,
( empty(X2)
| ordered_pair(esk141_2(X2,X1),esk142_2(X2,X1)) = esk137_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1091,
[final] ).
cnf(c_0_2214,plain,
( X1 = set_difference(X2,X3)
| in(esk68_3(X2,X3,X1),X3)
| ~ in(esk68_3(X2,X3,X1),X2)
| ~ in(esk68_3(X2,X3,X1),X1) ),
c_0_1092,
[final] ).
cnf(c_0_2215,plain,
( empty(X2)
| in(esk139_2(X2,X1),esk140_2(X2,X1))
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1093,
[final] ).
cnf(c_0_2216,plain,
( empty(X2)
| in(esk142_2(X2,X1),esk143_2(X2,X1))
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1094,
[final] ).
cnf(c_0_2217,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| X3 = empty_set
| in(esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2)))) ),
c_0_1095,
[final] ).
cnf(c_0_2218,plain,
( empty(X2)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| esk137_2(X2,X1) != esk136_2(X2,X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1096,
[final] ).
cnf(c_0_2219,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk93_3(X2,X1,X3)),X1)
| in(esk93_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_1097,
[final] ).
cnf(c_0_2220,plain,
( empty(X2)
| in(esk138_2(X2,X1),X2)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1098,
[final] ).
cnf(c_0_2221,plain,
( empty(X2)
| in(esk141_2(X2,X1),X2)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1099,
[final] ).
cnf(c_0_2222,plain,
( empty(X2)
| esk135_2(X2,X1) = esk136_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1100,
[final] ).
cnf(c_0_2223,plain,
( empty(X2)
| esk138_2(X2,X1) = esk140_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1101,
[final] ).
cnf(c_0_2224,plain,
( empty(X2)
| esk135_2(X2,X1) = esk137_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1102,
[final] ).
cnf(c_0_2225,plain,
( empty(X2)
| esk141_2(X2,X1) = esk143_2(X2,X1)
| esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,esk144_3(X2,X1,X4)) ),
c_0_1103,
[final] ).
cnf(c_0_2226,plain,
( in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk201_3(X3,X2,X1) != esk200_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
c_0_1104,
[final] ).
cnf(c_0_2227,plain,
( in(X2,esk169_1(X1))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| esk173_4(X1,X2,X3,X4) != empty_set ),
c_0_1105,
[final] ).
cnf(c_0_2228,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk79_2(X1,X2),esk78_2(X1,X2)),X1)
| ~ in(ordered_pair(esk78_2(X1,X2),esk79_2(X1,X2)),X2) ),
c_0_1106,
[final] ).
cnf(c_0_2229,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X2)
| ~ in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X1) ),
c_0_1107,
[final] ).
cnf(c_0_2230,plain,
( in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| esk201_3(X3,X2,X1) != esk200_3(X3,X2,X1)
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1108,
[final] ).
cnf(c_0_2231,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1))
| ~ in(X5,esk133_3(X2,X1,X4)) ),
c_0_1109,
[final] ).
cnf(c_0_2232,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1))
| ~ in(X5,esk133_3(X2,X1,X4)) ),
c_0_1110,
[final] ).
cnf(c_0_2233,plain,
( X3 = empty_set
| in(esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X2,esk169_1(X1))
| ~ in(esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk171_2(X1,X2)))) ),
c_0_1111,
[final] ).
cnf(c_0_2234,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_1112,
[final] ).
cnf(c_0_2235,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk48_3(X2,X3,X1),X1)
| ordered_pair(esk49_3(X2,X3,X1),esk50_3(X2,X3,X1)) = esk48_3(X2,X3,X1) ),
c_0_1113,
[final] ).
cnf(c_0_2236,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
c_0_1114,
[final] ).
cnf(c_0_2237,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| in(X4,esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
c_0_1115,
[final] ).
cnf(c_0_2238,plain,
( esk199_3(X3,X2,X1) = esk200_3(X3,X2,X1)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1116,
[final] ).
cnf(c_0_2239,plain,
( esk199_3(X3,X2,X1) = esk201_3(X3,X2,X1)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk202_3(X3,X2,X1)) ),
c_0_1117,
[final] ).
cnf(c_0_2240,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_1118,
[final] ).
cnf(c_0_2241,plain,
( X2 = fiber(X1,X3)
| in(esk32_3(X1,X3,X2),X2)
| in(ordered_pair(esk32_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
c_0_1119,
[final] ).
cnf(c_0_2242,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk45_3(X2,X3,X1),X1)
| ~ in(esk45_3(X2,X3,X1),X2) ),
c_0_1120,
[final] ).
cnf(c_0_2243,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk45_3(X2,X3,X1),X1)
| ~ in(esk45_3(X2,X3,X1),X3) ),
c_0_1121,
[final] ).
cnf(c_0_2244,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_1122,
[final] ).
cnf(c_0_2245,plain,
( X1 = set_union2(X2,X3)
| in(esk45_3(X2,X3,X1),X3)
| in(esk45_3(X2,X3,X1),X2)
| in(esk45_3(X2,X3,X1),X1) ),
c_0_1123,
[final] ).
cnf(c_0_2246,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1124,
[final] ).
cnf(c_0_2247,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1125,
[final] ).
cnf(c_0_2248,plain,
( X1 = cartesian_product2(X2,X3)
| esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk48_3(X2,X3,X1),X1) ),
c_0_1126,
[final] ).
cnf(c_0_2249,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1127,
[final] ).
cnf(c_0_2250,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1128,
[final] ).
cnf(c_0_2251,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| in(X4,esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1129,
[final] ).
cnf(c_0_2252,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1130,
[final] ).
cnf(c_0_2253,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1131,
[final] ).
cnf(c_0_2254,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| in(X4,esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1132,
[final] ).
cnf(c_0_2255,plain,
( X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2
| ~ subset(esk33_2(X2,X1),esk34_2(X2,X1))
| ~ in(ordered_pair(esk33_2(X2,X1),esk34_2(X2,X1)),X1) ),
c_0_1133,
[final] ).
cnf(c_0_2256,plain,
( empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1134,
[final] ).
cnf(c_0_2257,plain,
( set_difference(esk178_2(X2,X1),singleton(X2)) = esk176_2(X2,X1)
| set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1135,
[final] ).
cnf(c_0_2258,plain,
( set_difference(esk179_2(X2,X1),singleton(X2)) = esk177_2(X2,X1)
| set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1136,
[final] ).
cnf(c_0_2259,plain,
( set_difference(esk178_2(X2,X1),singleton(X2)) = esk176_2(X2,X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1137,
[final] ).
cnf(c_0_2260,plain,
( set_difference(esk179_2(X2,X1),singleton(X2)) = esk177_2(X2,X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1138,
[final] ).
cnf(c_0_2261,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_1139,
[final] ).
cnf(c_0_2262,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1140,
[final] ).
cnf(c_0_2263,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1141,
[final] ).
cnf(c_0_2264,plain,
( set_difference(esk178_2(X2,X1),singleton(X2)) = esk176_2(X2,X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1142,
[final] ).
cnf(c_0_2265,plain,
( set_difference(esk179_2(X2,X1),singleton(X2)) = esk177_2(X2,X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1143,
[final] ).
cnf(c_0_2266,plain,
( empty(X2)
| in(ordered_pair(esk127_2(X2,X1),X3),X1)
| esk132_3(X2,X1,X4) = esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk129_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1144,
[final] ).
cnf(c_0_2267,plain,
( empty(X2)
| in(ordered_pair(esk128_2(X2,X1),X3),X1)
| esk132_3(X2,X1,X4) = esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk130_2(X2,X1))
| ~ in(X4,esk131_2(X2,X1)) ),
c_0_1145,
[final] ).
cnf(c_0_2268,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1146,
[final] ).
cnf(c_0_2269,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1))
| ~ in(X4,esk133_3(X2,X1,X3)) ),
c_0_1147,
[final] ).
cnf(c_0_2270,plain,
( set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk177_2(X2,X1) != esk176_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1148,
[final] ).
cnf(c_0_2271,plain,
( in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk177_2(X2,X1) != esk176_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1149,
[final] ).
cnf(c_0_2272,plain,
( in(esk178_2(X2,X1),X1)
| set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1150,
[final] ).
cnf(c_0_2273,plain,
( in(esk179_2(X2,X1),X1)
| set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1151,
[final] ).
cnf(c_0_2274,plain,
( in(esk178_2(X2,X1),X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1152,
[final] ).
cnf(c_0_2275,plain,
( in(esk179_2(X2,X1),X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1153,
[final] ).
cnf(c_0_2276,plain,
( X1 = set_difference(X2,X3)
| in(esk68_3(X2,X3,X1),X1)
| ~ in(esk68_3(X2,X3,X1),X3) ),
c_0_1154,
[final] ).
cnf(c_0_2277,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_1155,
[final] ).
cnf(c_0_2278,plain,
( in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk177_2(X2,X1) != esk176_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1156,
[final] ).
cnf(c_0_2279,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| ~ latt_str(X1)
| join(X1,meet(X1,esk84_1(X1),esk85_1(X1)),esk85_1(X1)) != esk85_1(X1) ),
c_0_1157,
[final] ).
cnf(c_0_2280,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1158,
[final] ).
cnf(c_0_2281,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1159,
[final] ).
cnf(c_0_2282,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_1160,
[final] ).
cnf(c_0_2283,plain,
( in(esk178_2(X2,X1),X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1161,
[final] ).
cnf(c_0_2284,plain,
( in(esk179_2(X2,X1),X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1162,
[final] ).
cnf(c_0_2285,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1163,
[final] ).
cnf(c_0_2286,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| set_difference(esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1164,
[final] ).
cnf(c_0_2287,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1165,
[final] ).
cnf(c_0_2288,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| in(esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1166,
[final] ).
cnf(c_0_2289,plain,
( in(esk158_1(X1),X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1167,
[final] ).
cnf(c_0_2290,plain,
( in(esk160_1(X1),X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1168,
[final] ).
cnf(c_0_2291,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1169,
[final] ).
cnf(c_0_2292,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| in(esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1170,
[final] ).
cnf(c_0_2293,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk56_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
c_0_1171,
[final] ).
cnf(c_0_2294,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk79_2(X1,X2),esk78_2(X1,X2)),X1)
| in(ordered_pair(esk78_2(X1,X2),esk79_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_1172,
[final] ).
cnf(c_0_2295,plain,
( singleton(esk158_1(X1)) = esk159_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1173,
[final] ).
cnf(c_0_2296,plain,
( singleton(esk160_1(X1)) = esk161_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1174,
[final] ).
cnf(c_0_2297,plain,
( ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| esk157_1(X1) != esk156_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1175,
[final] ).
cnf(c_0_2298,plain,
( X1 = X2
| in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X2)
| in(ordered_pair(esk40_2(X1,X2),esk41_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_1176,
[final] ).
cnf(c_0_2299,plain,
( esk155_1(X1) = esk156_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1177,
[final] ).
cnf(c_0_2300,plain,
( esk155_1(X1) = esk157_1(X1)
| ordered_pair(esk164_3(X1,X3,X2),esk165_3(X1,X3,X2)) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1178,
[final] ).
cnf(c_0_2301,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk42_3(X2,X3,X1),X1)
| esk42_3(X2,X3,X1) != X2 ),
c_0_1179,
[final] ).
cnf(c_0_2302,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk42_3(X2,X3,X1),X1)
| esk42_3(X2,X3,X1) != X3 ),
c_0_1180,
[final] ).
cnf(c_0_2303,plain,
( in(ordered_pair(esk73_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_1181,
[final] ).
cnf(c_0_2304,plain,
( in(ordered_pair(X3,esk59_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
c_0_1182,
[final] ).
cnf(c_0_2305,plain,
( set_difference(esk178_2(X2,X1),singleton(X2)) = esk176_2(X2,X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1183,
[final] ).
cnf(c_0_2306,plain,
( set_difference(esk179_2(X2,X1),singleton(X2)) = esk177_2(X2,X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1184,
[final] ).
cnf(c_0_2307,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_1185,
[final] ).
cnf(c_0_2308,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_1186,
[final] ).
cnf(c_0_2309,plain,
( set_difference(esk178_2(X2,X1),singleton(X2)) = esk176_2(X2,X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1187,
[final] ).
cnf(c_0_2310,plain,
( set_difference(esk179_2(X2,X1),singleton(X2)) = esk177_2(X2,X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1188,
[final] ).
cnf(c_0_2311,plain,
( in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk177_2(X2,X1) != esk176_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1189,
[final] ).
cnf(c_0_2312,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_1190,
[final] ).
cnf(c_0_2313,plain,
( in(esk178_2(X2,X1),X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1191,
[final] ).
cnf(c_0_2314,plain,
( in(esk179_2(X2,X1),X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1192,
[final] ).
cnf(c_0_2315,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_1193,
[final] ).
cnf(c_0_2316,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_1194,
[final] ).
cnf(c_0_2317,plain,
( X2 = relation_image(X1,X3)
| in(esk12_3(X1,X3,X2),X2)
| in(esk13_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_1195,
[final] ).
cnf(c_0_2318,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1196,
[final] ).
cnf(c_0_2319,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1197,
[final] ).
cnf(c_0_2320,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1198,
[final] ).
cnf(c_0_2321,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1199,
[final] ).
cnf(c_0_2322,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1200,
[final] ).
cnf(c_0_2323,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1201,
[final] ).
cnf(c_0_2324,plain,
( esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| esk177_2(X2,X1) != esk176_2(X2,X1)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1202,
[final] ).
cnf(c_0_2325,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1203,
[final] ).
cnf(c_0_2326,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1204,
[final] ).
cnf(c_0_2327,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1205,
[final] ).
cnf(c_0_2328,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| in(X3,esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
c_0_1206,
[final] ).
cnf(c_0_2329,plain,
( X1 = set_difference(X2,X3)
| in(esk68_3(X2,X3,X1),X1)
| in(esk68_3(X2,X3,X1),X2) ),
c_0_1207,
[final] ).
cnf(c_0_2330,plain,
( X1 = set_intersection2(X2,X3)
| in(esk58_3(X2,X3,X1),X1)
| in(esk58_3(X2,X3,X1),X2) ),
c_0_1208,
[final] ).
cnf(c_0_2331,plain,
( X1 = set_intersection2(X2,X3)
| in(esk58_3(X2,X3,X1),X1)
| in(esk58_3(X2,X3,X1),X3) ),
c_0_1209,
[final] ).
cnf(c_0_2332,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk48_3(X2,X3,X1),X1)
| in(esk49_3(X2,X3,X1),X2) ),
c_0_1210,
[final] ).
cnf(c_0_2333,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk48_3(X2,X3,X1),X1)
| in(esk50_3(X2,X3,X1),X3) ),
c_0_1211,
[final] ).
cnf(c_0_2334,plain,
( in(esk178_2(X2,X1),X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1212,
[final] ).
cnf(c_0_2335,plain,
( in(esk179_2(X2,X1),X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1213,
[final] ).
cnf(c_0_2336,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),X2) ),
c_0_1214,
[final] ).
cnf(c_0_2337,plain,
( empty(X2)
| in(esk127_2(X2,X1),esk129_2(X2,X1))
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1215,
[final] ).
cnf(c_0_2338,plain,
( empty(X2)
| in(esk128_2(X2,X1),esk130_2(X2,X1))
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1216,
[final] ).
cnf(c_0_2339,plain,
( in(esk158_1(X1),X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1217,
[final] ).
cnf(c_0_2340,plain,
( in(esk160_1(X1),X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1218,
[final] ).
cnf(c_0_2341,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk90_2(X1,X2),esk92_2(X1,X2)),X1) ),
c_0_1219,
[final] ).
cnf(c_0_2342,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk76_2(X1,X2),esk77_2(X1,X2)),X1) ),
c_0_1220,
[final] ).
cnf(c_0_2343,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk77_2(X1,X2),esk76_2(X1,X2)),X1) ),
c_0_1221,
[final] ).
cnf(c_0_2344,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk27_2(X1,X2),esk27_2(X1,X2)),X1) ),
c_0_1222,
[final] ).
cnf(c_0_2345,plain,
( X1 = unordered_pair(X2,X3)
| esk42_3(X2,X3,X1) = X3
| esk42_3(X2,X3,X1) = X2
| in(esk42_3(X2,X3,X1),X1) ),
c_0_1223,
[final] ).
cnf(c_0_2346,plain,
( empty_carrier(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| ~ latt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1) ),
c_0_1224,
[final] ).
cnf(c_0_2347,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk93_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_1225,
[final] ).
cnf(c_0_2348,plain,
( esk175_2(X2,X1) = esk176_2(X2,X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1226,
[final] ).
cnf(c_0_2349,plain,
( esk175_2(X2,X1) = esk177_2(X2,X1)
| esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk180_2(X2,X1)) ),
c_0_1227,
[final] ).
cnf(c_0_2350,plain,
( singleton(esk158_1(X1)) = esk159_1(X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1228,
[final] ).
cnf(c_0_2351,plain,
( singleton(esk160_1(X1)) = esk161_1(X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1229,
[final] ).
cnf(c_0_2352,plain,
( in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| esk206_2(X2,X1) != esk205_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1230,
[final] ).
cnf(c_0_2353,plain,
( singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| esk157_1(X1) != esk156_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1231,
[final] ).
cnf(c_0_2354,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1232,
[final] ).
cnf(c_0_2355,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1233,
[final] ).
cnf(c_0_2356,plain,
( empty(X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1234,
[final] ).
cnf(c_0_2357,plain,
( empty(X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1235,
[final] ).
cnf(c_0_2358,plain,
( empty(X2)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1236,
[final] ).
cnf(c_0_2359,plain,
( in(esk207_2(X2,X1),X2)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1237,
[final] ).
cnf(c_0_2360,plain,
( in(esk208_2(X2,X1),X2)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1238,
[final] ).
cnf(c_0_2361,plain,
( esk155_1(X1) = esk156_1(X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1239,
[final] ).
cnf(c_0_2362,plain,
( esk155_1(X1) = esk157_1(X1)
| singleton(esk164_3(X1,X3,X2)) = esk165_3(X1,X3,X2)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1240,
[final] ).
cnf(c_0_2363,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_1241,
[final] ).
cnf(c_0_2364,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1242,
[final] ).
cnf(c_0_2365,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1243,
[final] ).
cnf(c_0_2366,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1244,
[final] ).
cnf(c_0_2367,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1245,
[final] ).
cnf(c_0_2368,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1246,
[final] ).
cnf(c_0_2369,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1247,
[final] ).
cnf(c_0_2370,plain,
( in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| esk206_2(X2,X1) != esk205_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1248,
[final] ).
cnf(c_0_2371,plain,
( in(esk207_2(X2,X1),X2)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1249,
[final] ).
cnf(c_0_2372,plain,
( in(esk208_2(X2,X1),X2)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1250,
[final] ).
cnf(c_0_2373,plain,
( X1 = inclusion_relation(X2)
| subset(esk33_2(X2,X1),esk34_2(X2,X1))
| in(ordered_pair(esk33_2(X2,X1),esk34_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
c_0_1251,
[final] ).
cnf(c_0_2374,plain,
( in(esk158_1(X1),X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1252,
[final] ).
cnf(c_0_2375,plain,
( in(esk160_1(X1),X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1253,
[final] ).
cnf(c_0_2376,plain,
( X2 = fiber(X1,X3)
| in(esk32_3(X1,X3,X2),X2)
| ~ relation(X1)
| esk32_3(X1,X3,X2) != X3 ),
c_0_1254,
[final] ).
cnf(c_0_2377,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_1255,
[final] ).
cnf(c_0_2378,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_1256,
[final] ).
cnf(c_0_2379,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_1257,
[final] ).
cnf(c_0_2380,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_1258,
[final] ).
cnf(c_0_2381,plain,
( empty(X2)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| esk128_2(X2,X1) != esk127_2(X2,X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1259,
[final] ).
cnf(c_0_2382,plain,
( ordinal(esk207_2(X2,X1))
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1260,
[final] ).
cnf(c_0_2383,plain,
( ordinal(esk208_2(X2,X1))
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1261,
[final] ).
cnf(c_0_2384,plain,
( ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| esk206_2(X2,X1) != esk205_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1262,
[final] ).
cnf(c_0_2385,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1263,
[final] ).
cnf(c_0_2386,plain,
( esk207_2(X2,X1) = esk205_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1264,
[final] ).
cnf(c_0_2387,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1265,
[final] ).
cnf(c_0_2388,plain,
( esk208_2(X2,X1) = esk206_2(X2,X1)
| in(esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1266,
[final] ).
cnf(c_0_2389,plain,
( singleton(esk158_1(X1)) = esk159_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1267,
[final] ).
cnf(c_0_2390,plain,
( singleton(esk160_1(X1)) = esk161_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1268,
[final] ).
cnf(c_0_2391,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1269,
[final] ).
cnf(c_0_2392,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1270,
[final] ).
cnf(c_0_2393,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1271,
[final] ).
cnf(c_0_2394,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1272,
[final] ).
cnf(c_0_2395,plain,
( empty(X2)
| in(esk126_2(X2,X1),X2)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1273,
[final] ).
cnf(c_0_2396,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1274,
[final] ).
cnf(c_0_2397,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1275,
[final] ).
cnf(c_0_2398,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| in(X3,esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1276,
[final] ).
cnf(c_0_2399,plain,
( in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| esk157_1(X1) != esk156_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1277,
[final] ).
cnf(c_0_2400,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_1278,
[final] ).
cnf(c_0_2401,plain,
( ordinal(esk207_2(X2,X1))
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1279,
[final] ).
cnf(c_0_2402,plain,
( in(esk207_2(X2,X1),X2)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1280,
[final] ).
cnf(c_0_2403,plain,
( ordinal(esk208_2(X2,X1))
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1281,
[final] ).
cnf(c_0_2404,plain,
( in(esk208_2(X2,X1),X2)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1282,
[final] ).
cnf(c_0_2405,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk74_2(X1,X2)),X1)
| ~ in(esk74_2(X1,X2),X2) ),
c_0_1283,
[final] ).
cnf(c_0_2406,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk60_2(X1,X2),X3),X1)
| ~ in(esk60_2(X1,X2),X2) ),
c_0_1284,
[final] ).
cnf(c_0_2407,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1285,
[final] ).
cnf(c_0_2408,plain,
( esk207_2(X2,X1) = esk205_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1286,
[final] ).
cnf(c_0_2409,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1287,
[final] ).
cnf(c_0_2410,plain,
( esk208_2(X2,X1) = esk206_2(X2,X1)
| in(esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1288,
[final] ).
cnf(c_0_2411,plain,
( esk155_1(X1) = esk156_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1289,
[final] ).
cnf(c_0_2412,plain,
( esk155_1(X1) = esk157_1(X1)
| in(esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1290,
[final] ).
cnf(c_0_2413,plain,
( empty_carrier(X1)
| below(X1,X2,X3)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
c_0_1291,
[final] ).
cnf(c_0_2414,plain,
( empty_carrier(X1)
| join(X1,X2,X3) = X3
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
c_0_1292,
[final] ).
cnf(c_0_2415,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1293,
[final] ).
cnf(c_0_2416,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1294,
[final] ).
cnf(c_0_2417,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk28_3(X1,X2,X3)) ),
c_0_1295,
[final] ).
cnf(c_0_2418,plain,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
c_0_1296,
[final] ).
cnf(c_0_2419,plain,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
c_0_1297,
[final] ).
cnf(c_0_2420,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_1298,
[final] ).
cnf(c_0_2421,plain,
( ordinal(esk207_2(X2,X1))
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1299,
[final] ).
cnf(c_0_2422,plain,
( ordinal(esk208_2(X2,X1))
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1300,
[final] ).
cnf(c_0_2423,plain,
( empty(X2)
| esk129_2(X2,X1) = esk126_2(X2,X1)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1301,
[final] ).
cnf(c_0_2424,plain,
( empty(X2)
| esk126_2(X2,X1) = esk130_2(X2,X1)
| esk132_3(X2,X1,X3) = esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,esk131_2(X2,X1)) ),
c_0_1302,
[final] ).
cnf(c_0_2425,plain,
( element(meet_commut(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
c_0_1303,
[final] ).
cnf(c_0_2426,plain,
( element(join_commut(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
c_0_1304,
[final] ).
cnf(c_0_2427,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1305,
[final] ).
cnf(c_0_2428,plain,
( esk207_2(X2,X1) = esk205_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1306,
[final] ).
cnf(c_0_2429,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1307,
[final] ).
cnf(c_0_2430,plain,
( esk208_2(X2,X1) = esk206_2(X2,X1)
| ordinal(esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1308,
[final] ).
cnf(c_0_2431,plain,
( in(esk158_1(X1),X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1309,
[final] ).
cnf(c_0_2432,plain,
( in(esk160_1(X1),X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1310,
[final] ).
cnf(c_0_2433,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_1311,
[final] ).
cnf(c_0_2434,plain,
( element(meet(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
c_0_1312,
[final] ).
cnf(c_0_2435,plain,
( element(join(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
c_0_1313,
[final] ).
cnf(c_0_2436,plain,
( singleton(esk158_1(X1)) = esk159_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1314,
[final] ).
cnf(c_0_2437,plain,
( singleton(esk160_1(X1)) = esk161_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1315,
[final] ).
cnf(c_0_2438,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_1316,
[final] ).
cnf(c_0_2439,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_1317,
[final] ).
cnf(c_0_2440,plain,
( in(esk164_3(X1,X3,X2),X1)
| esk157_1(X1) != esk156_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1318,
[final] ).
cnf(c_0_2441,plain,
( ordinal(esk216_3(X3,X2,X1))
| ~ epred1_3(X1,X2,X3) ),
c_0_1319,
[final] ).
cnf(c_0_2442,plain,
( ordinal(esk218_3(X3,X2,X1))
| ~ epred1_3(X1,X2,X3) ),
c_0_1320,
[final] ).
cnf(c_0_2443,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk75_2(X1,X2),esk74_2(X1,X2)),X1)
| in(esk74_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1321,
[final] ).
cnf(c_0_2444,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk60_2(X1,X2),esk61_2(X1,X2)),X1)
| in(esk60_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1322,
[final] ).
cnf(c_0_2445,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_1323,
[final] ).
cnf(c_0_2446,plain,
( esk155_1(X1) = esk156_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1324,
[final] ).
cnf(c_0_2447,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1325,
[final] ).
cnf(c_0_2448,plain,
( esk155_1(X1) = esk157_1(X1)
| in(esk164_3(X1,X3,X2),X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1326,
[final] ).
cnf(c_0_2449,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1327,
[final] ).
cnf(c_0_2450,plain,
( meet(X1,X2,X3) = meet_commut(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
c_0_1328,
[final] ).
cnf(c_0_2451,plain,
( join(X1,X2,X3) = join_commut(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
c_0_1329,
[final] ).
cnf(c_0_2452,plain,
( meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
c_0_1330,
[final] ).
cnf(c_0_2453,plain,
( join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
c_0_1331,
[final] ).
cnf(c_0_2454,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_1332,
[final] ).
cnf(c_0_2455,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk57_2(X1,X2))
| ~ in(X3,esk57_2(X1,X2)) ),
c_0_1333,
[final] ).
cnf(c_0_2456,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_1334,
[final] ).
cnf(c_0_2457,plain,
( in(esk158_1(X1),X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1335,
[final] ).
cnf(c_0_2458,plain,
( in(esk160_1(X1),X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1336,
[final] ).
cnf(c_0_2459,plain,
( X2 = empty_set
| X1 = empty_set
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| ~ quasi_total(X1,X2,X3) ),
c_0_1337,
[final] ).
cnf(c_0_2460,plain,
( singleton(esk158_1(X1)) = esk159_1(X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1338,
[final] ).
cnf(c_0_2461,plain,
( singleton(esk160_1(X1)) = esk161_1(X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1339,
[final] ).
cnf(c_0_2462,plain,
( in(X2,esk162_2(X1,X3))
| esk157_1(X1) != esk156_1(X1)
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1340,
[final] ).
cnf(c_0_2463,plain,
( X3 = empty_set
| in(esk56_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
c_0_1341,
[final] ).
cnf(c_0_2464,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk29_2(X1,X2),X2)
| ~ in(esk29_2(X1,X2),esk30_2(X1,X2)) ),
c_0_1342,
[final] ).
cnf(c_0_2465,plain,
( subset(X1,X2)
| in(ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_1343,
[final] ).
cnf(c_0_2466,plain,
( in(esk69_3(X1,X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_1344,
[final] ).
cnf(c_0_2467,plain,
( esk155_1(X1) = esk156_1(X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1345,
[final] ).
cnf(c_0_2468,plain,
( esk155_1(X1) = esk157_1(X1)
| in(X2,esk162_2(X1,X3))
| X4 != singleton(X5)
| ~ in(X5,X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
c_0_1346,
[final] ).
cnf(c_0_2469,plain,
( esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| esk206_2(X2,X1) != esk205_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1347,
[final] ).
cnf(c_0_2470,plain,
( esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| esk206_2(X2,X1) != esk205_2(X2,X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1348,
[final] ).
cnf(c_0_2471,plain,
( apply(X1,esk69_3(X1,X2,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_1349,
[final] ).
cnf(c_0_2472,plain,
( in(esk207_2(X2,X1),X2)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1350,
[final] ).
cnf(c_0_2473,plain,
( in(esk207_2(X2,X1),X2)
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1351,
[final] ).
cnf(c_0_2474,plain,
( in(esk208_2(X2,X1),X2)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1352,
[final] ).
cnf(c_0_2475,plain,
( in(esk208_2(X2,X1),X2)
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1353,
[final] ).
cnf(c_0_2476,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk90_2(X1,X2),esk91_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1354,
[final] ).
cnf(c_0_2477,plain,
( is_transitive_in(X1,X2)
| in(ordered_pair(esk91_2(X1,X2),esk92_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1355,
[final] ).
cnf(c_0_2478,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk62_2(X1,X2),esk63_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1356,
[final] ).
cnf(c_0_2479,plain,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(esk63_2(X1,X2),esk62_2(X1,X2)),X1)
| ~ relation(X1) ),
c_0_1357,
[final] ).
cnf(c_0_2480,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_1358,
[final] ).
cnf(c_0_2481,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_1359,
[final] ).
cnf(c_0_2482,plain,
( in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| esk206_2(X2,X1) != esk205_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1360,
[final] ).
cnf(c_0_2483,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(X2,esk169_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
c_0_1361,
[final] ).
cnf(c_0_2484,plain,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| esk70_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(esk70_2(X1,X2),X2) ),
c_0_1362,
[final] ).
cnf(c_0_2485,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| in(esk170_2(X1,X2),succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1363,
[final] ).
cnf(c_0_2486,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_1364,
[final] ).
cnf(c_0_2487,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_1365,
[final] ).
cnf(c_0_2488,plain,
( in(esk207_2(X2,X1),X2)
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1366,
[final] ).
cnf(c_0_2489,plain,
( in(esk208_2(X2,X1),X2)
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1367,
[final] ).
cnf(c_0_2490,plain,
( ordinal(esk207_2(X2,X1))
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1368,
[final] ).
cnf(c_0_2491,plain,
( ordinal(esk207_2(X2,X1))
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1369,
[final] ).
cnf(c_0_2492,plain,
( ordinal(esk208_2(X2,X1))
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1370,
[final] ).
cnf(c_0_2493,plain,
( ordinal(esk208_2(X2,X1))
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1371,
[final] ).
cnf(c_0_2494,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk65_2(X2,X1),X3)
| ~ in(esk65_2(X2,X1),X1) ),
c_0_1372,
[final] ).
cnf(c_0_2495,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1373,
[final] ).
cnf(c_0_2496,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1374,
[final] ).
cnf(c_0_2497,plain,
( esk207_2(X2,X1) = esk205_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1375,
[final] ).
cnf(c_0_2498,plain,
( esk207_2(X2,X1) = esk205_2(X2,X1)
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1376,
[final] ).
cnf(c_0_2499,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1377,
[final] ).
cnf(c_0_2500,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1378,
[final] ).
cnf(c_0_2501,plain,
( esk208_2(X2,X1) = esk206_2(X2,X1)
| esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1379,
[final] ).
cnf(c_0_2502,plain,
( esk208_2(X2,X1) = esk206_2(X2,X1)
| esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,esk209_2(X2,X1)) ),
c_0_1380,
[final] ).
cnf(c_0_2503,plain,
( in(X3,esk64_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_1381,
[final] ).
cnf(c_0_2504,plain,
( in(esk64_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_1382,
[final] ).
cnf(c_0_2505,plain,
( ordered_pair(esk158_1(X1),esk159_1(X1)) = esk156_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1383,
[final] ).
cnf(c_0_2506,plain,
( ordered_pair(esk160_1(X1),esk161_1(X1)) = esk157_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1384,
[final] ).
cnf(c_0_2507,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_1385,
[final] ).
cnf(c_0_2508,plain,
( ordinal(esk207_2(X2,X1))
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1386,
[final] ).
cnf(c_0_2509,plain,
( ordinal(esk208_2(X2,X1))
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1387,
[final] ).
cnf(c_0_2510,plain,
( X2 = empty_set
| quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| X3 != empty_set
| X1 != empty_set ),
c_0_1388,
[final] ).
cnf(c_0_2511,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk28_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
c_0_1389,
[final] ).
cnf(c_0_2512,plain,
( esk204_2(X2,X1) = esk205_2(X2,X1)
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1390,
[final] ).
cnf(c_0_2513,plain,
( esk207_2(X2,X1) = esk205_2(X2,X1)
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1391,
[final] ).
cnf(c_0_2514,plain,
( esk204_2(X2,X1) = esk206_2(X2,X1)
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1392,
[final] ).
cnf(c_0_2515,plain,
( esk208_2(X2,X1) = esk206_2(X2,X1)
| in(X3,esk209_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
c_0_1393,
[final] ).
cnf(c_0_2516,plain,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
c_0_1394,
[final] ).
cnf(c_0_2517,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
c_0_1395,
[final] ).
cnf(c_0_2518,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| ordinal(esk171_2(X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1396,
[final] ).
cnf(c_0_2519,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_1397,
[final] ).
cnf(c_0_2520,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_1398,
[final] ).
cnf(c_0_2521,plain,
( esk216_3(X3,X2,X1) = X2
| ~ epred1_3(X1,X2,X3) ),
c_0_1399,
[final] ).
cnf(c_0_2522,plain,
( esk218_3(X3,X2,X1) = X1
| ~ epred1_3(X1,X2,X3) ),
c_0_1400,
[final] ).
cnf(c_0_2523,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_1401,
[final] ).
cnf(c_0_2524,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
c_0_1402,
[final] ).
cnf(c_0_2525,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
c_0_1403,
[final] ).
cnf(c_0_2526,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
c_0_1404,
[final] ).
cnf(c_0_2527,plain,
( in(esk158_1(X1),X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1405,
[final] ).
cnf(c_0_2528,plain,
( in(esk160_1(X1),X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1406,
[final] ).
cnf(c_0_2529,plain,
( subset(X4,X3)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1407,
[final] ).
cnf(c_0_2530,plain,
( X1 = X2
| ~ in(ordered_pair(X3,X2),X4)
| ~ in(ordered_pair(X3,X1),X4)
| ~ function(X4) ),
c_0_1408,
[final] ).
cnf(c_0_2531,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_1409,
[final] ).
cnf(c_0_2532,plain,
( singleton(esk158_1(X1)) = esk159_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1410,
[final] ).
cnf(c_0_2533,plain,
( singleton(esk160_1(X1)) = esk161_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1411,
[final] ).
cnf(c_0_2534,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_1412,
[final] ).
cnf(c_0_2535,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_1413,
[final] ).
cnf(c_0_2536,plain,
( esk163_3(X1,X3,X2) = X2
| esk157_1(X1) != esk156_1(X1)
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1414,
[final] ).
cnf(c_0_2537,plain,
( X1 = powerset(X2)
| ~ subset(esk36_2(X2,X1),X2)
| ~ in(esk36_2(X2,X1),X1) ),
c_0_1415,
[final] ).
cnf(c_0_2538,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_1416,
[final] ).
cnf(c_0_2539,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
c_0_1417,
[final] ).
cnf(c_0_2540,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_1418,
[final] ).
cnf(c_0_2541,plain,
( X1 = X2
| ~ in(esk212_2(X1,X2),X2)
| ~ in(esk212_2(X1,X2),X1) ),
c_0_1419,
[final] ).
cnf(c_0_2542,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| esk170_2(X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1420,
[final] ).
cnf(c_0_2543,plain,
( epred1_3(esk168_1(X1),esk167_1(X1),esk166_1(X1))
| esk171_2(X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1421,
[final] ).
cnf(c_0_2544,plain,
( esk155_1(X1) = esk156_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1422,
[final] ).
cnf(c_0_2545,plain,
( esk155_1(X1) = esk157_1(X1)
| esk163_3(X1,X3,X2) = X2
| ~ in(X2,esk162_2(X1,X3)) ),
c_0_1423,
[final] ).
cnf(c_0_2546,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
c_0_1424,
[final] ).
cnf(c_0_2547,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1425,
[final] ).
cnf(c_0_2548,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
c_0_1426,
[final] ).
cnf(c_0_2549,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1427,
[final] ).
cnf(c_0_2550,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
c_0_1428,
[final] ).
cnf(c_0_2551,plain,
( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
c_0_1429,
[final] ).
cnf(c_0_2552,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
c_0_1430,
[final] ).
cnf(c_0_2553,plain,
( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
c_0_1431,
[final] ).
cnf(c_0_2554,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
c_0_1432,
[final] ).
cnf(c_0_2555,plain,
( relation_dom(X3) = relation_field(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
c_0_1433,
[final] ).
cnf(c_0_2556,plain,
( relation_rng(X3) = relation_field(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
c_0_1434,
[final] ).
cnf(c_0_2557,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1435,
[final] ).
cnf(c_0_2558,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
c_0_1436,
[final] ).
cnf(c_0_2559,plain,
( one_to_one(X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
c_0_1437,
[final] ).
cnf(c_0_2560,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
c_0_1438,
[final] ).
cnf(c_0_2561,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
c_0_1439,
[final] ).
cnf(c_0_2562,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk44_1(X1))
| ~ in(X2,esk44_1(X1)) ),
c_0_1440,
[final] ).
cnf(c_0_2563,plain,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
c_0_1441,
[final] ).
cnf(c_0_2564,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_1442,
[final] ).
cnf(c_0_2565,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_1443,
[final] ).
cnf(c_0_2566,plain,
( X2 = relation_rng(X1)
| in(esk70_2(X1,X2),X2)
| apply(X1,esk71_2(X1,X2)) = esk70_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1444,
[final] ).
cnf(c_0_2567,plain,
( X1 = union(X2)
| in(esk65_2(X2,X1),X1)
| in(esk65_2(X2,X1),esk66_2(X2,X1)) ),
c_0_1445,
[final] ).
cnf(c_0_2568,plain,
( in(X4,X2)
| X4 = X3
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1446,
[final] ).
cnf(c_0_2569,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
c_0_1447,
[final] ).
cnf(c_0_2570,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk30_2(X1,X2),X1)
| ~ in(esk29_2(X1,X2),X2) ),
c_0_1448,
[final] ).
cnf(c_0_2571,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk29_2(X1,X2),X3)
| in(esk29_2(X1,X2),X2)
| ~ in(X3,X1) ),
c_0_1449,
[final] ).
cnf(c_0_2572,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1450,
[final] ).
cnf(c_0_2573,plain,
( ~ in(X1,X2)
| ~ in(X3,esk213_2(X1,X2))
| ~ in(X3,X2) ),
c_0_1451,
[final] ).
cnf(c_0_2574,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_1452,
[final] ).
cnf(c_0_2575,plain,
( X2 = relation_rng(X1)
| in(esk70_2(X1,X2),X2)
| in(esk71_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1453,
[final] ).
cnf(c_0_2576,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
c_0_1454,
[final] ).
cnf(c_0_2577,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
c_0_1455,
[final] ).
cnf(c_0_2578,plain,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
c_0_1456,
[final] ).
cnf(c_0_2579,plain,
( in(apply(X1,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1457,
[final] ).
cnf(c_0_2580,plain,
( in(X2,esk169_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
c_0_1458,
[final] ).
cnf(c_0_2581,plain,
( in(esk170_2(X1,X2),succ(X1))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1459,
[final] ).
cnf(c_0_2582,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1460,
[final] ).
cnf(c_0_2583,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1461,
[final] ).
cnf(c_0_2584,plain,
( ordered_pair(esk24_2(X2,X1),esk25_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
c_0_1462,
[final] ).
cnf(c_0_2585,plain,
( X4 = pair_second(X1)
| ordered_pair(esk37_2(X1,X4),esk38_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
c_0_1463,
[final] ).
cnf(c_0_2586,plain,
( X4 = pair_first(X1)
| ordered_pair(esk22_2(X1,X4),esk23_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
c_0_1464,
[final] ).
cnf(c_0_2587,plain,
( in(X3,esk215_2(X2,X1))
| ~ in(X1,esk214_1(X2))
| ~ subset(X3,X1) ),
c_0_1465,
[final] ).
cnf(c_0_2588,plain,
( in(esk150_1(X1),X1)
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1466,
[final] ).
cnf(c_0_2589,plain,
( in(esk150_1(X1),X1)
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1467,
[final] ).
cnf(c_0_2590,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
c_0_1468,
[final] ).
cnf(c_0_2591,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_1469,
[final] ).
cnf(c_0_2592,plain,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_1470,
[final] ).
cnf(c_0_2593,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1471,
[final] ).
cnf(c_0_2594,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1472,
[final] ).
cnf(c_0_2595,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1473,
[final] ).
cnf(c_0_2596,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1474,
[final] ).
cnf(c_0_2597,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1475,
[final] ).
cnf(c_0_2598,plain,
( in(esk150_1(X1),X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1476,
[final] ).
cnf(c_0_2599,plain,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ is_reflexive_in(X1,X3) ),
c_0_1477,
[final] ).
cnf(c_0_2600,plain,
( X1 = singleton(X2)
| esk31_2(X2,X1) != X2
| ~ in(esk31_2(X2,X1),X1) ),
c_0_1478,
[final] ).
cnf(c_0_2601,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1479,
[final] ).
cnf(c_0_2602,plain,
( singleton(esk150_1(X1)) = esk151_1(X1)
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1480,
[final] ).
cnf(c_0_2603,plain,
( singleton(esk150_1(X1)) = esk152_1(X1)
| in(X2,esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1481,
[final] ).
cnf(c_0_2604,plain,
( X2 = empty_set
| in(esk43_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
c_0_1482,
[final] ).
cnf(c_0_2605,plain,
( X3 = X2
| ~ epred1_3(X1,X2,X3) ),
c_0_1483,
[final] ).
cnf(c_0_2606,plain,
( X3 = X1
| ~ epred1_3(X1,X2,X3) ),
c_0_1484,
[final] ).
cnf(c_0_2607,plain,
( in(X2,esk153_1(X1))
| esk152_1(X1) != esk151_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
c_0_1485,
[final] ).
cnf(c_0_2608,plain,
( singleton(esk150_1(X1)) = esk151_1(X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1486,
[final] ).
cnf(c_0_2609,plain,
( singleton(esk150_1(X1)) = esk151_1(X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1487,
[final] ).
cnf(c_0_2610,plain,
( singleton(esk150_1(X1)) = esk152_1(X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1488,
[final] ).
cnf(c_0_2611,plain,
( singleton(esk150_1(X1)) = esk152_1(X1)
| in(esk154_2(X1,X2),X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1489,
[final] ).
cnf(c_0_2612,plain,
( X1 = union(X2)
| in(esk65_2(X2,X1),X1)
| in(esk66_2(X2,X1),X2) ),
c_0_1490,
[final] ).
cnf(c_0_2613,plain,
( X1 = powerset(X2)
| subset(esk36_2(X2,X1),X2)
| in(esk36_2(X2,X1),X1) ),
c_0_1491,
[final] ).
cnf(c_0_2614,plain,
( in(esk154_2(X1,X2),X1)
| esk152_1(X1) != esk151_1(X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1492,
[final] ).
cnf(c_0_2615,plain,
( in(esk154_2(X1,X2),X1)
| esk152_1(X1) != esk151_1(X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1493,
[final] ).
cnf(c_0_2616,plain,
( in(esk150_1(X1),X1)
| singleton(esk154_2(X1,X2)) = X2
| ~ in(X2,esk153_1(X1)) ),
c_0_1494,
[final] ).
cnf(c_0_2617,plain,
( in(esk150_1(X1),X1)
| singleton(esk154_2(X1,X2)) = X2
| ~ in(X2,esk153_1(X1)) ),
c_0_1495,
[final] ).
cnf(c_0_2618,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_1496,
[final] ).
cnf(c_0_2619,plain,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ in(X1,X3)
| ~ in(X2,X3)
| ~ epsilon_connected(X3) ),
c_0_1497,
[final] ).
cnf(c_0_2620,plain,
( ordinal(esk171_2(X1,X2))
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1498,
[final] ).
cnf(c_0_2621,plain,
( X1 = X2
| in(esk212_2(X1,X2),X2)
| in(esk212_2(X1,X2),X1) ),
c_0_1499,
[final] ).
cnf(c_0_2622,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
c_0_1500,
[final] ).
cnf(c_0_2623,plain,
( in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_1501,
[final] ).
cnf(c_0_2624,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_1502,
[final] ).
cnf(c_0_2625,plain,
relation_of2(esk115_2(X1,X2),X1,X2),
c_0_1503,
[final] ).
cnf(c_0_2626,plain,
relation_of2(esk104_2(X1,X2),X1,X2),
c_0_1504,
[final] ).
cnf(c_0_2627,plain,
quasi_total(esk104_2(X1,X2),X1,X2),
c_0_1505,
[final] ).
cnf(c_0_2628,plain,
relation_of2_as_subset(esk100_2(X1,X2),X1,X2),
c_0_1506,
[final] ).
cnf(c_0_2629,plain,
relation_of2(esk98_2(X1,X2),X1,X2),
c_0_1507,
[final] ).
cnf(c_0_2630,plain,
( in(esk215_2(X2,X1),esk214_1(X2))
| ~ in(X1,esk214_1(X2)) ),
c_0_1508,
[final] ).
cnf(c_0_2631,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_1509,
[final] ).
cnf(c_0_2632,plain,
( singleton(esk150_1(X1)) = esk151_1(X1)
| singleton(esk154_2(X1,X2)) = X2
| ~ in(X2,esk153_1(X1)) ),
c_0_1510,
[final] ).
cnf(c_0_2633,plain,
( singleton(esk150_1(X1)) = esk152_1(X1)
| singleton(esk154_2(X1,X2)) = X2
| ~ in(X2,esk153_1(X1)) ),
c_0_1511,
[final] ).
cnf(c_0_2634,plain,
( subset(X1,X2)
| ~ in(esk55_2(X1,X2),X2) ),
c_0_1512,
[final] ).
cnf(c_0_2635,plain,
( singleton(esk154_2(X1,X2)) = X2
| esk152_1(X1) != esk151_1(X1)
| ~ in(X2,esk153_1(X1)) ),
c_0_1513,
[final] ).
cnf(c_0_2636,plain,
( ordinal(esk195_0)
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
c_0_1514,
[final] ).
cnf(c_0_2637,plain,
( ordinal(esk196_0)
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
c_0_1515,
[final] ).
cnf(c_0_2638,plain,
( in(X1,esk214_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk214_1(X2)) ),
c_0_1516,
[final] ).
cnf(c_0_2639,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_1517,
[final] ).
cnf(c_0_2640,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_1518,
[final] ).
cnf(c_0_2641,plain,
( in(esk198_2(X2,X1),X2)
| esk196_0 != esk195_0
| ~ in(X1,esk197_1(X2)) ),
c_0_1519,
[final] ).
cnf(c_0_2642,plain,
( in(X1,esk214_1(X2))
| are_equipotent(X1,esk214_1(X2))
| ~ subset(X1,esk214_1(X2)) ),
c_0_1520,
[final] ).
cnf(c_0_2643,plain,
( esk194_0 = esk195_0
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
c_0_1521,
[final] ).
cnf(c_0_2644,plain,
( esk194_0 = esk196_0
| in(esk198_2(X2,X1),X2)
| ~ in(X1,esk197_1(X2)) ),
c_0_1522,
[final] ).
cnf(c_0_2645,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
c_0_1523,
[final] ).
cnf(c_0_2646,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
c_0_1524,
[final] ).
cnf(c_0_2647,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1525,
[final] ).
cnf(c_0_2648,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1526,
[final] ).
cnf(c_0_2649,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
c_0_1527,
[final] ).
cnf(c_0_2650,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_1528,
[final] ).
cnf(c_0_2651,plain,
( function(X1)
| in(ordered_pair(esk19_1(X1),esk20_1(X1)),X1) ),
c_0_1529,
[final] ).
cnf(c_0_2652,plain,
( function(X1)
| in(ordered_pair(esk19_1(X1),esk21_1(X1)),X1) ),
c_0_1530,
[final] ).
cnf(c_0_2653,plain,
( X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ subset(X1,esk72_1(X1)) ),
c_0_1531,
[final] ).
cnf(c_0_2654,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_1532,
[final] ).
cnf(c_0_2655,plain,
( esk170_2(X1,X2) = X2
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1533,
[final] ).
cnf(c_0_2656,plain,
( esk171_2(X1,X2) = X2
| ~ ordinal(X1)
| esk168_1(X1) != esk167_1(X1)
| ~ in(X2,esk169_1(X1)) ),
c_0_1534,
[final] ).
cnf(c_0_2657,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| esk76_2(X1,X2) != esk77_2(X1,X2) ),
c_0_1535,
[final] ).
cnf(c_0_2658,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| esk63_2(X1,X2) != esk62_2(X1,X2) ),
c_0_1536,
[final] ).
cnf(c_0_2659,plain,
( in(esk213_2(X1,X2),X2)
| ~ in(X1,X2) ),
c_0_1537,
[final] ).
cnf(c_0_2660,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_1538,
[final] ).
cnf(c_0_2661,plain,
( is_transitive_in(X1,X2)
| in(esk90_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1539,
[final] ).
cnf(c_0_2662,plain,
( is_transitive_in(X1,X2)
| in(esk91_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1540,
[final] ).
cnf(c_0_2663,plain,
( is_transitive_in(X1,X2)
| in(esk92_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1541,
[final] ).
cnf(c_0_2664,plain,
( is_connected_in(X1,X2)
| in(esk76_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1542,
[final] ).
cnf(c_0_2665,plain,
( is_connected_in(X1,X2)
| in(esk77_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1543,
[final] ).
cnf(c_0_2666,plain,
( is_antisymmetric_in(X1,X2)
| in(esk62_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1544,
[final] ).
cnf(c_0_2667,plain,
( is_antisymmetric_in(X1,X2)
| in(esk63_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1545,
[final] ).
cnf(c_0_2668,plain,
( is_well_founded_in(X1,X2)
| subset(esk57_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1546,
[final] ).
cnf(c_0_2669,plain,
( is_reflexive_in(X1,X2)
| in(esk27_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_1547,
[final] ).
cnf(c_0_2670,plain,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_1548,
[final] ).
cnf(c_0_2671,plain,
( X1 = inclusion_relation(X2)
| in(esk33_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
c_0_1549,
[final] ).
cnf(c_0_2672,plain,
( X1 = inclusion_relation(X2)
| in(esk34_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
c_0_1550,
[final] ).
cnf(c_0_2673,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_1551,
[final] ).
cnf(c_0_2674,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_1552,
[final] ).
cnf(c_0_2675,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_1553,
[final] ).
cnf(c_0_2676,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_1554,
[final] ).
cnf(c_0_2677,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_1555,
[final] ).
cnf(c_0_2678,plain,
( X1 = singleton(X2)
| esk31_2(X2,X1) = X2
| in(esk31_2(X2,X1),X1) ),
c_0_1556,
[final] ).
cnf(c_0_2679,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
c_0_1557,
[final] ).
cnf(c_0_2680,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
c_0_1558,
[final] ).
cnf(c_0_2681,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_1559,
[final] ).
cnf(c_0_2682,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_1560,
[final] ).
cnf(c_0_2683,plain,
( one_to_one(X1)
| apply(X1,esk83_1(X1)) = apply(X1,esk82_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1561,
[final] ).
cnf(c_0_2684,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_1562,
[final] ).
cnf(c_0_2685,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_1563,
[final] ).
cnf(c_0_2686,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X6,X5)
| X4 != pair_second(X1) ),
c_0_1564,
[final] ).
cnf(c_0_2687,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X1 != ordered_pair(X5,X6)
| X4 != pair_first(X1) ),
c_0_1565,
[final] ).
cnf(c_0_2688,plain,
( ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2)
| X4 != X3 ),
c_0_1566,
[final] ).
cnf(c_0_2689,plain,
( finite(X1)
| ~ in(relation_dom(X2),omega)
| relation_rng(X2) != X1
| ~ function(X2)
| ~ relation(X2) ),
c_0_1567,
[final] ).
cnf(c_0_2690,plain,
( ordinal(esk195_0)
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1568,
[final] ).
cnf(c_0_2691,plain,
( ordinal(esk196_0)
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1569,
[final] ).
cnf(c_0_2692,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
c_0_1570,
[final] ).
cnf(c_0_2693,plain,
( in(X1,esk197_1(X2))
| esk196_0 != esk195_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1571,
[final] ).
cnf(c_0_2694,plain,
( X1 = omega
| in(empty_set,esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
c_0_1572,
[final] ).
cnf(c_0_2695,plain,
( esk194_0 = esk195_0
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1573,
[final] ).
cnf(c_0_2696,plain,
( esk194_0 = esk196_0
| in(X1,esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
c_0_1574,
[final] ).
cnf(c_0_2697,plain,
( subset(X1,X2)
| in(esk55_2(X1,X2),X1) ),
c_0_1575,
[final] ).
cnf(c_0_2698,plain,
( relation_dom(esk67_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
c_0_1576,
[final] ).
cnf(c_0_2699,plain,
( relation_rng(esk67_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
c_0_1577,
[final] ).
cnf(c_0_2700,plain,
( relation(esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
c_0_1578,
[final] ).
cnf(c_0_2701,plain,
( function(esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
c_0_1579,
[final] ).
cnf(c_0_2702,plain,
( one_to_one(esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
c_0_1580,
[final] ).
cnf(c_0_2703,plain,
( X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3)
| esk38_2(X1,X4) != X4 ),
c_0_1581,
[final] ).
cnf(c_0_2704,plain,
( X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3)
| esk22_2(X1,X4) != X4 ),
c_0_1582,
[final] ).
cnf(c_0_2705,plain,
( equipotent(X1,X2)
| relation_rng(X3) != X2
| relation_dom(X3) != X1
| ~ one_to_one(X3)
| ~ function(X3)
| ~ relation(X3) ),
c_0_1583,
[final] ).
cnf(c_0_2706,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
c_0_1584,
[final] ).
cnf(c_0_2707,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_1585,
[final] ).
cnf(c_0_2708,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_1586,
[final] ).
cnf(c_0_2709,plain,
( finite(relation_image(X1,X2))
| ~ finite(X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1587,
[final] ).
cnf(c_0_2710,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
c_0_1588,
[final] ).
cnf(c_0_2711,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
c_0_1589,
[final] ).
cnf(c_0_2712,plain,
( subset(X1,X2)
| X1 != omega
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| ~ ordinal(X2) ),
c_0_1590,
[final] ).
cnf(c_0_2713,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_1591,
[final] ).
cnf(c_0_2714,plain,
( ordinal(esk195_0)
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
c_0_1592,
[final] ).
cnf(c_0_2715,plain,
( ordinal(esk196_0)
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
c_0_1593,
[final] ).
cnf(c_0_2716,plain,
( empty_carrier(X1)
| element(esk125_1(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
c_0_1594,
[final] ).
cnf(c_0_2717,plain,
( esk198_2(X2,X1) = X1
| esk196_0 != esk195_0
| ~ in(X1,esk197_1(X2)) ),
c_0_1595,
[final] ).
cnf(c_0_2718,plain,
( esk194_0 = esk195_0
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
c_0_1596,
[final] ).
cnf(c_0_2719,plain,
( esk194_0 = esk196_0
| esk198_2(X2,X1) = X1
| ~ in(X1,esk197_1(X2)) ),
c_0_1597,
[final] ).
cnf(c_0_2720,plain,
~ empty(unordered_pair(X1,X2)),
c_0_1598,
[final] ).
cnf(c_0_2721,plain,
~ empty(ordered_pair(X1,X2)),
c_0_1599,
[final] ).
cnf(c_0_2722,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_1600,
[final] ).
cnf(c_0_2723,plain,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
c_0_1601,
[final] ).
cnf(c_0_2724,plain,
( X1 = omega
| ordinal(esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
c_0_1602,
[final] ).
cnf(c_0_2725,plain,
( X1 = omega
| being_limit_ordinal(esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
c_0_1603,
[final] ).
cnf(c_0_2726,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
c_0_1604,
[final] ).
cnf(c_0_2727,plain,
( epsilon_connected(X1)
| ~ in(esk51_1(X1),esk52_1(X1)) ),
c_0_1605,
[final] ).
cnf(c_0_2728,plain,
( epsilon_connected(X1)
| ~ in(esk52_1(X1),esk51_1(X1)) ),
c_0_1606,
[final] ).
cnf(c_0_2729,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
c_0_1607,
[final] ).
cnf(c_0_2730,plain,
( one_to_one(X1)
| in(esk82_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1608,
[final] ).
cnf(c_0_2731,plain,
( one_to_one(X1)
| in(esk83_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1609,
[final] ).
cnf(c_0_2732,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_1610,
[final] ).
cnf(c_0_2733,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_1611,
[final] ).
cnf(c_0_2734,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_1612,
[final] ).
cnf(c_0_2735,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_1613,
[final] ).
cnf(c_0_2736,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1614,
[final] ).
cnf(c_0_2737,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1615,
[final] ).
cnf(c_0_2738,plain,
( finite(set_union2(X1,X2))
| ~ finite(X2)
| ~ finite(X1) ),
c_0_1616,
[final] ).
cnf(c_0_2739,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1617,
[final] ).
cnf(c_0_2740,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1618,
[final] ).
cnf(c_0_2741,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1619,
[final] ).
cnf(c_0_2742,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1620,
[final] ).
cnf(c_0_2743,plain,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1621,
[final] ).
cnf(c_0_2744,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1622,
[final] ).
cnf(c_0_2745,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1623,
[final] ).
cnf(c_0_2746,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_1624,
[final] ).
cnf(c_0_2747,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_1625,
[final] ).
cnf(c_0_2748,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1626,
[final] ).
cnf(c_0_2749,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_1627,
[final] ).
cnf(c_0_2750,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1628,
[final] ).
cnf(c_0_2751,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1629,
[final] ).
cnf(c_0_2752,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1630,
[final] ).
cnf(c_0_2753,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1631,
[final] ).
cnf(c_0_2754,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1632,
[final] ).
cnf(c_0_2755,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1633,
[final] ).
cnf(c_0_2756,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk57_2(X1,X2) != empty_set ),
c_0_1634,
[final] ).
cnf(c_0_2757,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
c_0_1635,
[final] ).
cnf(c_0_2758,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
c_0_1636,
[final] ).
cnf(c_0_2759,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
c_0_1637,
[final] ).
cnf(c_0_2760,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
c_0_1638,
[final] ).
cnf(c_0_2761,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
c_0_1639,
[final] ).
cnf(c_0_2762,plain,
( finite(X1)
| ~ element(X1,powerset(X2))
| ~ finite(X2) ),
c_0_1640,
[final] ).
cnf(c_0_2763,plain,
( v1_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1641,
[final] ).
cnf(c_0_2764,plain,
( v2_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1642,
[final] ).
cnf(c_0_2765,plain,
( v3_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1643,
[final] ).
cnf(c_0_2766,plain,
( v4_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1644,
[final] ).
cnf(c_0_2767,plain,
( v5_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1645,
[final] ).
cnf(c_0_2768,plain,
( v1_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1646,
[final] ).
cnf(c_0_2769,plain,
( v2_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1647,
[final] ).
cnf(c_0_2770,plain,
( v3_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1648,
[final] ).
cnf(c_0_2771,plain,
( v4_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1649,
[final] ).
cnf(c_0_2772,plain,
( v1_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1650,
[final] ).
cnf(c_0_2773,plain,
( v2_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1651,
[final] ).
cnf(c_0_2774,plain,
( v3_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1652,
[final] ).
cnf(c_0_2775,plain,
( v1_membered(X2)
| ~ v2_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1653,
[final] ).
cnf(c_0_2776,plain,
( v2_membered(X2)
| ~ v2_membered(X1)
| ~ element(X2,powerset(X1)) ),
c_0_1654,
[final] ).
cnf(c_0_2777,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v1_membered(X2) ),
c_0_1655,
[final] ).
cnf(c_0_2778,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
c_0_1656,
[final] ).
cnf(c_0_2779,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
c_0_1657,
[final] ).
cnf(c_0_2780,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| element(esk84_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
c_0_1658,
[final] ).
cnf(c_0_2781,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| element(esk85_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
c_0_1659,
[final] ).
cnf(c_0_2782,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_1660,
[final] ).
cnf(c_0_2783,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_1661,
[final] ).
cnf(c_0_2784,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
c_0_1662,
[final] ).
cnf(c_0_2785,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_1663,
[final] ).
cnf(c_0_2786,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_1664,
[final] ).
cnf(c_0_2787,plain,
( ordinal(esk195_0)
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
c_0_1665,
[final] ).
cnf(c_0_2788,plain,
( ordinal(esk196_0)
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
c_0_1666,
[final] ).
cnf(c_0_2789,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_1667,
[final] ).
cnf(c_0_2790,plain,
( well_founded_relation(X1)
| subset(esk44_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1668,
[final] ).
cnf(c_0_2791,plain,
( in(relation_dom(esk18_1(X1)),omega)
| ~ finite(X1) ),
c_0_1669,
[final] ).
cnf(c_0_2792,plain,
( ordinal(X1)
| esk196_0 != esk195_0
| ~ in(X1,esk197_1(X2)) ),
c_0_1670,
[final] ).
cnf(c_0_2793,plain,
( esk194_0 = esk195_0
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
c_0_1671,
[final] ).
cnf(c_0_2794,plain,
( esk194_0 = esk196_0
| ordinal(X1)
| ~ in(X1,esk197_1(X2)) ),
c_0_1672,
[final] ).
cnf(c_0_2795,plain,
( finite(set_difference(X1,X2))
| ~ finite(X1) ),
c_0_1673,
[final] ).
cnf(c_0_2796,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
c_0_1674,
[final] ).
cnf(c_0_2797,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X2) ),
c_0_1675,
[final] ).
cnf(c_0_2798,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
c_0_1676,
[final] ).
cnf(c_0_2799,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
c_0_1677,
[final] ).
cnf(c_0_2800,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
c_0_1678,
[final] ).
cnf(c_0_2801,plain,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
c_0_1679,
[final] ).
cnf(c_0_2802,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
c_0_1680,
[final] ).
cnf(c_0_2803,plain,
( equipotent(X1,X2)
| ~ equipotent(X2,X1) ),
c_0_1681,
[final] ).
cnf(c_0_2804,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_1682,
[final] ).
cnf(c_0_2805,plain,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
c_0_1683,
[final] ).
cnf(c_0_2806,plain,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
c_0_1684,
[final] ).
cnf(c_0_2807,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_1685,
[final] ).
cnf(c_0_2808,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_1686,
[final] ).
cnf(c_0_2809,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_1687,
[final] ).
cnf(c_0_2810,plain,
( epsilon_transitive(X1)
| ~ subset(esk39_1(X1),X1) ),
c_0_1688,
[final] ).
cnf(c_0_2811,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
c_0_1689,
[final] ).
cnf(c_0_2812,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
c_0_1690,
[final] ).
cnf(c_0_2813,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
c_0_1691,
[final] ).
cnf(c_0_2814,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
c_0_1692,
[final] ).
cnf(c_0_2815,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_1693,
[final] ).
cnf(c_0_2816,plain,
( epsilon_transitive(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
c_0_1694,
[final] ).
cnf(c_0_2817,plain,
( epsilon_connected(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
c_0_1695,
[final] ).
cnf(c_0_2818,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
c_0_1696,
[final] ).
cnf(c_0_2819,plain,
( v1_xcmplx_0(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
c_0_1697,
[final] ).
cnf(c_0_2820,plain,
( natural(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
c_0_1698,
[final] ).
cnf(c_0_2821,plain,
( v1_xreal_0(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
c_0_1699,
[final] ).
cnf(c_0_2822,plain,
( v1_int_1(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
c_0_1700,
[final] ).
cnf(c_0_2823,plain,
( v1_rat_1(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
c_0_1701,
[final] ).
cnf(c_0_2824,plain,
( v1_xcmplx_0(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
c_0_1702,
[final] ).
cnf(c_0_2825,plain,
( v1_xreal_0(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
c_0_1703,
[final] ).
cnf(c_0_2826,plain,
( v1_int_1(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
c_0_1704,
[final] ).
cnf(c_0_2827,plain,
( v1_rat_1(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
c_0_1705,
[final] ).
cnf(c_0_2828,plain,
( v1_xcmplx_0(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
c_0_1706,
[final] ).
cnf(c_0_2829,plain,
( v1_xreal_0(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
c_0_1707,
[final] ).
cnf(c_0_2830,plain,
( v1_rat_1(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
c_0_1708,
[final] ).
cnf(c_0_2831,plain,
( v1_xcmplx_0(X2)
| ~ v2_membered(X1)
| ~ element(X2,X1) ),
c_0_1709,
[final] ).
cnf(c_0_2832,plain,
( v1_xreal_0(X2)
| ~ v2_membered(X1)
| ~ element(X2,X1) ),
c_0_1710,
[final] ).
cnf(c_0_2833,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v1_membered(X2) ),
c_0_1711,
[final] ).
cnf(c_0_2834,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_1712,
[final] ).
cnf(c_0_2835,plain,
( relation(X1)
| esk26_1(X1) != ordered_pair(X2,X3) ),
c_0_1713,
[final] ).
cnf(c_0_2836,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1714,
[final] ).
cnf(c_0_2837,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1715,
[final] ).
cnf(c_0_2838,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk83_1(X1) != esk82_1(X1) ),
c_0_1716,
[final] ).
cnf(c_0_2839,plain,
( empty(X1)
| element(esk119_1(X1),powerset(X1)) ),
c_0_1717,
[final] ).
cnf(c_0_2840,plain,
( empty(X1)
| element(esk110_1(X1),powerset(X1)) ),
c_0_1718,
[final] ).
cnf(c_0_2841,plain,
( ~ natural(X1)
| ~ ordinal(X1)
| ~ empty(succ(X1)) ),
c_0_1719,
[final] ).
cnf(c_0_2842,plain,
relation(esk115_2(X1,X2)),
c_0_1720,
[final] ).
cnf(c_0_2843,plain,
function(esk115_2(X1,X2)),
c_0_1721,
[final] ).
cnf(c_0_2844,plain,
relation(esk104_2(X1,X2)),
c_0_1722,
[final] ).
cnf(c_0_2845,plain,
function(esk104_2(X1,X2)),
c_0_1723,
[final] ).
cnf(c_0_2846,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_1724,
[final] ).
cnf(c_0_2847,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1725,
[final] ).
cnf(c_0_2848,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
c_0_1726,
[final] ).
cnf(c_0_2849,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_1727,
[final] ).
cnf(c_0_2850,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(esk125_1(X1)) ),
c_0_1728,
[final] ).
cnf(c_0_2851,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
c_0_1729,
[final] ).
cnf(c_0_2852,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
c_0_1730,
[final] ).
cnf(c_0_2853,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
c_0_1731,
[final] ).
cnf(c_0_2854,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_1732,
[final] ).
cnf(c_0_2855,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_1733,
[final] ).
cnf(c_0_2856,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_1734,
[final] ).
cnf(c_0_2857,plain,
element(esk117_1(X1),powerset(X1)),
c_0_1735,
[final] ).
cnf(c_0_2858,plain,
element(esk112_1(X1),powerset(X1)),
c_0_1736,
[final] ).
cnf(c_0_2859,plain,
element(cast_to_subset(X1),powerset(X1)),
c_0_1737,
[final] ).
cnf(c_0_2860,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_1738,
[final] ).
cnf(c_0_2861,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_1739,
[final] ).
cnf(c_0_2862,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_1740,
[final] ).
cnf(c_0_2863,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_1741,
[final] ).
cnf(c_0_2864,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_1742,
[final] ).
cnf(c_0_2865,plain,
( epsilon_connected(X1)
| in(esk51_1(X1),X1) ),
c_0_1743,
[final] ).
cnf(c_0_2866,plain,
( epsilon_connected(X1)
| in(esk52_1(X1),X1) ),
c_0_1744,
[final] ).
cnf(c_0_2867,plain,
( epsilon_transitive(X1)
| in(esk39_1(X1),X1) ),
c_0_1745,
[final] ).
cnf(c_0_2868,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_1746,
[final] ).
cnf(c_0_2869,plain,
( relation(X1)
| in(esk26_1(X1),X1) ),
c_0_1747,
[final] ).
cnf(c_0_2870,plain,
( epsilon_transitive(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
c_0_1748,
[final] ).
cnf(c_0_2871,plain,
( epsilon_connected(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
c_0_1749,
[final] ).
cnf(c_0_2872,plain,
( ordinal(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
c_0_1750,
[final] ).
cnf(c_0_2873,plain,
( natural(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
c_0_1751,
[final] ).
cnf(c_0_2874,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1752,
[final] ).
cnf(c_0_2875,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1753,
[final] ).
cnf(c_0_2876,plain,
( epsilon_transitive(X1)
| ~ element(X1,omega) ),
c_0_1754,
[final] ).
cnf(c_0_2877,plain,
( epsilon_connected(X1)
| ~ element(X1,omega) ),
c_0_1755,
[final] ).
cnf(c_0_2878,plain,
( ordinal(X1)
| ~ element(X1,omega) ),
c_0_1756,
[final] ).
cnf(c_0_2879,plain,
( natural(X1)
| ~ element(X1,omega) ),
c_0_1757,
[final] ).
cnf(c_0_2880,plain,
set_union2(X1,singleton(X1)) = succ(X1),
c_0_1758,
[final] ).
cnf(c_0_2881,plain,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
c_0_1759,
[final] ).
cnf(c_0_2882,plain,
~ proper_subset(X1,X1),
c_0_1760,
[final] ).
cnf(c_0_2883,plain,
( X1 = empty_set
| in(esk35_1(X1),X1) ),
c_0_1761,
[final] ).
cnf(c_0_2884,plain,
( empty(X1)
| ~ empty(esk119_1(X1)) ),
c_0_1762,
[final] ).
cnf(c_0_2885,plain,
( empty(X1)
| ~ empty(esk110_1(X1)) ),
c_0_1763,
[final] ).
cnf(c_0_2886,plain,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
c_0_1764,
[final] ).
cnf(c_0_2887,plain,
in(X1,esk214_1(X1)),
c_0_1765,
[final] ).
cnf(c_0_2888,plain,
element(esk99_1(X1),X1),
c_0_1766,
[final] ).
cnf(c_0_2889,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1767,
[final] ).
cnf(c_0_2890,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1768,
[final] ).
cnf(c_0_2891,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1769,
[final] ).
cnf(c_0_2892,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1770,
[final] ).
cnf(c_0_2893,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1771,
[final] ).
cnf(c_0_2894,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_1772,
[final] ).
cnf(c_0_2895,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk44_1(X1) != empty_set ),
c_0_1773,
[final] ).
cnf(c_0_2896,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_1774,
[final] ).
cnf(c_0_2897,plain,
( preboolean(X1)
| ~ diff_closed(X1)
| ~ cup_closed(X1) ),
c_0_1775,
[final] ).
cnf(c_0_2898,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1776,
[final] ).
cnf(c_0_2899,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1777,
[final] ).
cnf(c_0_2900,plain,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1778,
[final] ).
cnf(c_0_2901,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_1779,
[final] ).
cnf(c_0_2902,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
c_0_1780,
[final] ).
cnf(c_0_2903,plain,
( relation_rng(esk18_1(X1)) = X1
| ~ finite(X1) ),
c_0_1781,
[final] ).
cnf(c_0_2904,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_1782,
[final] ).
cnf(c_0_2905,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_1783,
[final] ).
cnf(c_0_2906,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
c_0_1784,
[final] ).
cnf(c_0_2907,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
c_0_1785,
[final] ).
cnf(c_0_2908,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
c_0_1786,
[final] ).
cnf(c_0_2909,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
c_0_1787,
[final] ).
cnf(c_0_2910,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
c_0_1788,
[final] ).
cnf(c_0_2911,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
c_0_1789,
[final] ).
cnf(c_0_2912,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
c_0_1790,
[final] ).
cnf(c_0_2913,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
c_0_1791,
[final] ).
cnf(c_0_2914,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
c_0_1792,
[final] ).
cnf(c_0_2915,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
c_0_1793,
[final] ).
cnf(c_0_2916,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
c_0_1794,
[final] ).
cnf(c_0_2917,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
c_0_1795,
[final] ).
cnf(c_0_2918,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
c_0_1796,
[final] ).
cnf(c_0_2919,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
c_0_1797,
[final] ).
cnf(c_0_2920,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
c_0_1798,
[final] ).
cnf(c_0_2921,plain,
( relation(esk18_1(X1))
| ~ finite(X1) ),
c_0_1799,
[final] ).
cnf(c_0_2922,plain,
( function(esk18_1(X1))
| ~ finite(X1) ),
c_0_1800,
[final] ).
cnf(c_0_2923,plain,
( epsilon_connected(X1)
| esk51_1(X1) != esk52_1(X1) ),
c_0_1801,
[final] ).
cnf(c_0_2924,plain,
( function(X1)
| esk21_1(X1) != esk20_1(X1) ),
c_0_1802,
[final] ).
cnf(c_0_2925,plain,
~ empty(singleton(X1)),
c_0_1803,
[final] ).
cnf(c_0_2926,plain,
~ empty(powerset(X1)),
c_0_1804,
[final] ).
cnf(c_0_2927,plain,
~ empty(succ(X1)),
c_0_1805,
[final] ).
cnf(c_0_2928,plain,
~ empty(powerset(X1)),
c_0_1806,
[final] ).
cnf(c_0_2929,plain,
~ empty(singleton(X1)),
c_0_1807,
[final] ).
cnf(c_0_2930,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_1808,
[final] ).
cnf(c_0_2931,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
c_0_1809,
[final] ).
cnf(c_0_2932,plain,
( in(empty_set,X1)
| X1 != omega ),
c_0_1810,
[final] ).
cnf(c_0_2933,plain,
( empty(X1)
| finite(esk119_1(X1)) ),
c_0_1811,
[final] ).
cnf(c_0_2934,plain,
set_intersection2(X1,X1) = X1,
c_0_1812,
[final] ).
cnf(c_0_2935,plain,
set_union2(X1,X1) = X1,
c_0_1813,
[final] ).
cnf(c_0_2936,plain,
equipotent(X1,X1),
c_0_1814,
[final] ).
cnf(c_0_2937,plain,
subset(X1,X1),
c_0_1815,
[final] ).
cnf(c_0_2938,plain,
set_difference(X1,empty_set) = X1,
c_0_1816,
[final] ).
cnf(c_0_2939,plain,
set_union2(X1,empty_set) = X1,
c_0_1817,
[final] ).
cnf(c_0_2940,plain,
set_difference(empty_set,X1) = empty_set,
c_0_1818,
[final] ).
cnf(c_0_2941,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_1819,
[final] ).
cnf(c_0_2942,plain,
( being_limit_ordinal(X1)
| union(X1) != X1 ),
c_0_1820,
[final] ).
cnf(c_0_2943,plain,
( union(X1) = X1
| ~ being_limit_ordinal(X1) ),
c_0_1821,
[final] ).
cnf(c_0_2944,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
c_0_1822,
[final] ).
cnf(c_0_2945,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
c_0_1823,
[final] ).
cnf(c_0_2946,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
c_0_1824,
[final] ).
cnf(c_0_2947,plain,
( one_sorted_str(X1)
| ~ join_semilatt_str(X1) ),
c_0_1825,
[final] ).
cnf(c_0_2948,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
c_0_1826,
[final] ).
cnf(c_0_2949,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_1827,
[final] ).
cnf(c_0_2950,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_1828,
[final] ).
cnf(c_0_2951,plain,
( v1_membered(X1)
| ~ v2_membered(X1) ),
c_0_1829,
[final] ).
cnf(c_0_2952,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
c_0_1830,
[final] ).
cnf(c_0_2953,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
c_0_1831,
[final] ).
cnf(c_0_2954,plain,
( ordinal(X1)
| ~ empty(X1) ),
c_0_1832,
[final] ).
cnf(c_0_2955,plain,
( v2_membered(X1)
| ~ v3_membered(X1) ),
c_0_1833,
[final] ).
cnf(c_0_2956,plain,
( v3_membered(X1)
| ~ v4_membered(X1) ),
c_0_1834,
[final] ).
cnf(c_0_2957,plain,
( relation(X1)
| ~ empty(X1) ),
c_0_1835,
[final] ).
cnf(c_0_2958,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_1836,
[final] ).
cnf(c_0_2959,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_1837,
[final] ).
cnf(c_0_2960,plain,
( v4_membered(X1)
| ~ v5_membered(X1) ),
c_0_1838,
[final] ).
cnf(c_0_2961,plain,
( function(X1)
| ~ empty(X1) ),
c_0_1839,
[final] ).
cnf(c_0_2962,plain,
( cup_closed(X1)
| ~ preboolean(X1) ),
c_0_1840,
[final] ).
cnf(c_0_2963,plain,
( diff_closed(X1)
| ~ preboolean(X1) ),
c_0_1841,
[final] ).
cnf(c_0_2964,plain,
( finite(X1)
| ~ empty(X1) ),
c_0_1842,
[final] ).
cnf(c_0_2965,plain,
( v1_membered(X1)
| ~ empty(X1) ),
c_0_1843,
[final] ).
cnf(c_0_2966,plain,
( v2_membered(X1)
| ~ empty(X1) ),
c_0_1844,
[final] ).
cnf(c_0_2967,plain,
( v3_membered(X1)
| ~ empty(X1) ),
c_0_1845,
[final] ).
cnf(c_0_2968,plain,
( v4_membered(X1)
| ~ empty(X1) ),
c_0_1846,
[final] ).
cnf(c_0_2969,plain,
( v5_membered(X1)
| ~ empty(X1) ),
c_0_1847,
[final] ).
cnf(c_0_2970,plain,
empty(esk117_1(X1)),
c_0_1848,
[final] ).
cnf(c_0_2971,plain,
empty(esk112_1(X1)),
c_0_1849,
[final] ).
cnf(c_0_2972,plain,
relation(esk112_1(X1)),
c_0_1850,
[final] ).
cnf(c_0_2973,plain,
function(esk112_1(X1)),
c_0_1851,
[final] ).
cnf(c_0_2974,plain,
one_to_one(esk112_1(X1)),
c_0_1852,
[final] ).
cnf(c_0_2975,plain,
epsilon_transitive(esk112_1(X1)),
c_0_1853,
[final] ).
cnf(c_0_2976,plain,
epsilon_connected(esk112_1(X1)),
c_0_1854,
[final] ).
cnf(c_0_2977,plain,
ordinal(esk112_1(X1)),
c_0_1855,
[final] ).
cnf(c_0_2978,plain,
natural(esk112_1(X1)),
c_0_1856,
[final] ).
cnf(c_0_2979,plain,
finite(esk112_1(X1)),
c_0_1857,
[final] ).
cnf(c_0_2980,plain,
relation(identity_relation(X1)),
c_0_1858,
[final] ).
cnf(c_0_2981,plain,
function(identity_relation(X1)),
c_0_1859,
[final] ).
cnf(c_0_2982,plain,
cup_closed(powerset(X1)),
c_0_1860,
[final] ).
cnf(c_0_2983,plain,
diff_closed(powerset(X1)),
c_0_1861,
[final] ).
cnf(c_0_2984,plain,
preboolean(powerset(X1)),
c_0_1862,
[final] ).
cnf(c_0_2985,plain,
finite(singleton(X1)),
c_0_1863,
[final] ).
cnf(c_0_2986,plain,
relation(identity_relation(X1)),
c_0_1864,
[final] ).
cnf(c_0_2987,plain,
relation(inclusion_relation(X1)),
c_0_1865,
[final] ).
cnf(c_0_2988,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
c_0_1866,
[final] ).
cnf(c_0_2989,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_1867,
[final] ).
cnf(c_0_2990,plain,
( being_limit_ordinal(X1)
| X1 != omega ),
c_0_1868,
[final] ).
cnf(c_0_2991,plain,
( ordinal(X1)
| X1 != omega ),
c_0_1869,
[final] ).
cnf(c_0_2992,plain,
cast_to_subset(X1) = X1,
c_0_1870,
[final] ).
cnf(c_0_2993,plain,
~ empty_carrier(esk123_0),
c_0_1871,
[final] ).
cnf(c_0_2994,plain,
~ empty(esk121_0),
c_0_1872,
[final] ).
cnf(c_0_2995,plain,
~ empty(esk118_0),
c_0_1873,
[final] ).
cnf(c_0_2996,plain,
~ empty(esk116_0),
c_0_1874,
[final] ).
cnf(c_0_2997,plain,
~ empty(esk105_0),
c_0_1875,
[final] ).
cnf(c_0_2998,plain,
~ empty(esk102_0),
c_0_1876,
[final] ).
cnf(c_0_2999,plain,
~ empty(esk101_0),
c_0_1877,
[final] ).
cnf(c_0_3000,plain,
~ empty(omega),
c_0_1878,
[final] ).
cnf(c_0_3001,plain,
relation(esk124_0),
c_0_1879,
[final] ).
cnf(c_0_3002,plain,
relation_empty_yielding(esk124_0),
c_0_1880,
[final] ).
cnf(c_0_3003,plain,
function(esk124_0),
c_0_1881,
[final] ).
cnf(c_0_3004,plain,
one_sorted_str(esk123_0),
c_0_1882,
[final] ).
cnf(c_0_3005,plain,
relation(esk122_0),
c_0_1883,
[final] ).
cnf(c_0_3006,plain,
relation_empty_yielding(esk122_0),
c_0_1884,
[final] ).
cnf(c_0_3007,plain,
epsilon_transitive(esk121_0),
c_0_1885,
[final] ).
cnf(c_0_3008,plain,
epsilon_connected(esk121_0),
c_0_1886,
[final] ).
cnf(c_0_3009,plain,
ordinal(esk121_0),
c_0_1887,
[final] ).
cnf(c_0_3010,plain,
relation(esk120_0),
c_0_1888,
[final] ).
cnf(c_0_3011,plain,
function(esk120_0),
c_0_1889,
[final] ).
cnf(c_0_3012,plain,
one_to_one(esk120_0),
c_0_1890,
[final] ).
cnf(c_0_3013,plain,
relation(esk116_0),
c_0_1891,
[final] ).
cnf(c_0_3014,plain,
relation(esk114_0),
c_0_1892,
[final] ).
cnf(c_0_3015,plain,
function(esk114_0),
c_0_1893,
[final] ).
cnf(c_0_3016,plain,
one_to_one(esk114_0),
c_0_1894,
[final] ).
cnf(c_0_3017,plain,
empty(esk114_0),
c_0_1895,
[final] ).
cnf(c_0_3018,plain,
epsilon_transitive(esk114_0),
c_0_1896,
[final] ).
cnf(c_0_3019,plain,
epsilon_connected(esk114_0),
c_0_1897,
[final] ).
cnf(c_0_3020,plain,
ordinal(esk114_0),
c_0_1898,
[final] ).
cnf(c_0_3021,plain,
relation(esk113_0),
c_0_1899,
[final] ).
cnf(c_0_3022,plain,
empty(esk113_0),
c_0_1900,
[final] ).
cnf(c_0_3023,plain,
function(esk113_0),
c_0_1901,
[final] ).
cnf(c_0_3024,plain,
empty(esk111_0),
c_0_1902,
[final] ).
cnf(c_0_3025,plain,
empty(esk109_0),
c_0_1903,
[final] ).
cnf(c_0_3026,plain,
relation(esk109_0),
c_0_1904,
[final] ).
cnf(c_0_3027,plain,
relation(esk108_0),
c_0_1905,
[final] ).
cnf(c_0_3028,plain,
function(esk108_0),
c_0_1906,
[final] ).
cnf(c_0_3029,plain,
one_to_one(esk108_0),
c_0_1907,
[final] ).
cnf(c_0_3030,plain,
empty(esk108_0),
c_0_1908,
[final] ).
cnf(c_0_3031,plain,
epsilon_transitive(esk107_0),
c_0_1909,
[final] ).
cnf(c_0_3032,plain,
epsilon_connected(esk107_0),
c_0_1910,
[final] ).
cnf(c_0_3033,plain,
ordinal(esk107_0),
c_0_1911,
[final] ).
cnf(c_0_3034,plain,
being_limit_ordinal(esk107_0),
c_0_1912,
[final] ).
cnf(c_0_3035,plain,
epsilon_transitive(esk106_0),
c_0_1913,
[final] ).
cnf(c_0_3036,plain,
epsilon_connected(esk106_0),
c_0_1914,
[final] ).
cnf(c_0_3037,plain,
ordinal(esk106_0),
c_0_1915,
[final] ).
cnf(c_0_3038,plain,
v1_membered(esk105_0),
c_0_1916,
[final] ).
cnf(c_0_3039,plain,
v2_membered(esk105_0),
c_0_1917,
[final] ).
cnf(c_0_3040,plain,
v3_membered(esk105_0),
c_0_1918,
[final] ).
cnf(c_0_3041,plain,
v4_membered(esk105_0),
c_0_1919,
[final] ).
cnf(c_0_3042,plain,
v5_membered(esk105_0),
c_0_1920,
[final] ).
cnf(c_0_3043,plain,
relation(esk103_0),
c_0_1921,
[final] ).
cnf(c_0_3044,plain,
function(esk103_0),
c_0_1922,
[final] ).
cnf(c_0_3045,plain,
finite(esk102_0),
c_0_1923,
[final] ).
cnf(c_0_3046,plain,
epsilon_transitive(esk101_0),
c_0_1924,
[final] ).
cnf(c_0_3047,plain,
epsilon_connected(esk101_0),
c_0_1925,
[final] ).
cnf(c_0_3048,plain,
ordinal(esk101_0),
c_0_1926,
[final] ).
cnf(c_0_3049,plain,
natural(esk101_0),
c_0_1927,
[final] ).
cnf(c_0_3050,plain,
empty(empty_set),
c_0_1928,
[final] ).
cnf(c_0_3051,plain,
v1_membered(empty_set),
c_0_1929,
[final] ).
cnf(c_0_3052,plain,
v2_membered(empty_set),
c_0_1930,
[final] ).
cnf(c_0_3053,plain,
v3_membered(empty_set),
c_0_1931,
[final] ).
cnf(c_0_3054,plain,
v4_membered(empty_set),
c_0_1932,
[final] ).
cnf(c_0_3055,plain,
v5_membered(empty_set),
c_0_1933,
[final] ).
cnf(c_0_3056,plain,
empty(empty_set),
c_0_1934,
[final] ).
cnf(c_0_3057,plain,
relation(empty_set),
c_0_1935,
[final] ).
cnf(c_0_3058,plain,
relation(empty_set),
c_0_1936,
[final] ).
cnf(c_0_3059,plain,
relation_empty_yielding(empty_set),
c_0_1937,
[final] ).
cnf(c_0_3060,plain,
function(empty_set),
c_0_1938,
[final] ).
cnf(c_0_3061,plain,
one_to_one(empty_set),
c_0_1939,
[final] ).
cnf(c_0_3062,plain,
empty(empty_set),
c_0_1940,
[final] ).
cnf(c_0_3063,plain,
epsilon_transitive(empty_set),
c_0_1941,
[final] ).
cnf(c_0_3064,plain,
epsilon_connected(empty_set),
c_0_1942,
[final] ).
cnf(c_0_3065,plain,
ordinal(empty_set),
c_0_1943,
[final] ).
cnf(c_0_3066,plain,
empty(empty_set),
c_0_1944,
[final] ).
cnf(c_0_3067,plain,
epsilon_transitive(omega),
c_0_1945,
[final] ).
cnf(c_0_3068,plain,
epsilon_connected(omega),
c_0_1946,
[final] ).
cnf(c_0_3069,plain,
ordinal(omega),
c_0_1947,
[final] ).
cnf(c_0_3070,plain,
empty(empty_set),
c_0_1948,
[final] ).
cnf(c_0_3071,plain,
relation(empty_set),
c_0_1949,
[final] ).
cnf(c_0_3072,plain,
relation_empty_yielding(empty_set),
c_0_1950,
[final] ).
cnf(c_0_3073,plain,
latt_str(esk97_0),
c_0_1951,
[final] ).
cnf(c_0_3074,plain,
join_semilatt_str(esk96_0),
c_0_1952,
[final] ).
cnf(c_0_3075,plain,
one_sorted_str(esk95_0),
c_0_1953,
[final] ).
cnf(c_0_3076,plain,
meet_semilatt_str(esk94_0),
c_0_1954,
[final] ).
cnf(c_0_3077,plain,
$true,
c_0_1955,
[final] ).
cnf(c_0_3078,plain,
$true,
c_0_1956,
[final] ).
cnf(c_0_3079,plain,
$true,
c_0_1957,
[final] ).
cnf(c_0_3080,plain,
$true,
c_0_1958,
[final] ).
cnf(c_0_3081,plain,
$true,
c_0_1959,
[final] ).
cnf(c_0_3082,plain,
$true,
c_0_1960,
[final] ).
cnf(c_0_3083,plain,
$true,
c_0_1961,
[final] ).
cnf(c_0_3084,plain,
$true,
c_0_1962,
[final] ).
cnf(c_0_3085,plain,
$true,
c_0_1963,
[final] ).
cnf(c_0_3086,plain,
$true,
c_0_1964,
[final] ).
cnf(c_0_3087,plain,
$true,
c_0_1965,
[final] ).
cnf(c_0_3088,plain,
$true,
c_0_1966,
[final] ).
cnf(c_0_3089,plain,
$true,
c_0_1967,
[final] ).
cnf(c_0_3090,plain,
$true,
c_0_1968,
[final] ).
cnf(c_0_3091,plain,
$true,
c_0_1969,
[final] ).
cnf(c_0_3092,plain,
$true,
c_0_1970,
[final] ).
cnf(c_0_3093,plain,
$true,
c_0_1971,
[final] ).
cnf(c_0_3094,plain,
$true,
c_0_1972,
[final] ).
cnf(c_0_3095,plain,
$true,
c_0_1973,
[final] ).
cnf(c_0_3096,plain,
$true,
c_0_1974,
[final] ).
cnf(c_0_3097,plain,
$true,
c_0_1975,
[final] ).
cnf(c_0_3098,plain,
$true,
c_0_1976,
[final] ).
cnf(c_0_3099,plain,
$true,
c_0_1977,
[final] ).
cnf(c_0_3100,plain,
$true,
c_0_1978,
[final] ).
cnf(c_0_3101,plain,
$true,
c_0_1979,
[final] ).
cnf(c_0_3102,plain,
$true,
c_0_1980,
[final] ).
cnf(c_0_3103,plain,
$true,
c_0_1981,
[final] ).
cnf(c_0_3104,plain,
$true,
c_0_1982,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1983_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_2,axiom,
( in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_5,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_6,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_7,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_8,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_9,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_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_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_11,axiom,
( ~ in(ordered_pair(X8,sk1_esk149_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_esk140_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk144_3(X2,X1,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_2,axiom,
( in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_5,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_6,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_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_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_7,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_8,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_9,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_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_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X8,sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_11,axiom,
( ~ in(ordered_pair(X8,sk1_esk149_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_esk143_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_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_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_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_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_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_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_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_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_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_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_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_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_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_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_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_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
( empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_1,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_2,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_8,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_9,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1990_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_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_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_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_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_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_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_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_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1992_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_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_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_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_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_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_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_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_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_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_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_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_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_4,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_5,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ordered_pair(X6,X7) != X3
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_6,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_7,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_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_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X7,X8)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_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_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X7,sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_10,axiom,
( ~ in(ordered_pair(X7,sk1_esk149_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_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1996_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_1996]) ).
cnf(c_0_1996_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_1996]) ).
cnf(c_0_1996_2,axiom,
( in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_1996]) ).
cnf(c_0_1996_3,axiom,
( in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_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_1996]) ).
cnf(c_0_1996_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_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_1996]) ).
cnf(c_0_1996_5,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_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_1996]) ).
cnf(c_0_1996_6,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_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_1996]) ).
cnf(c_0_1996_7,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_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_1996]) ).
cnf(c_0_1996_8,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_9,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_10,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_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_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_1997]) ).
cnf(c_0_1997_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_1997]) ).
cnf(c_0_1997_2,axiom,
( in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_1997]) ).
cnf(c_0_1997_3,axiom,
( in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_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_1997]) ).
cnf(c_0_1997_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_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_1997]) ).
cnf(c_0_1997_5,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_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_1997]) ).
cnf(c_0_1997_6,axiom,
( ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_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_1997]) ).
cnf(c_0_1997_7,axiom,
( X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_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_1997]) ).
cnf(c_0_1997_8,axiom,
( ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X7,X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_9,axiom,
( ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| X7 != X9
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_10,axiom,
( X7 != X9
| ~ in(X7,X2)
| ordered_pair(X7,X8) != X4
| X6 != X4
| ~ in(X6,cartesian_product2(X2,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_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_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X5,X4,X6,X7,X8,X9),X9)
| in(X4,sk1_esk144_3(X2,X1,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_1998]) ).
cnf(c_0_1998_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_1998]) ).
cnf(c_0_1998_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk149_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_1998]) ).
cnf(c_0_1998_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_1998]) ).
cnf(c_0_1998_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_1998]) ).
cnf(c_0_1998_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_1998]) ).
cnf(c_0_1998_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_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_1998]) ).
cnf(c_0_1998_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_1999]) ).
cnf(c_0_1999_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_1999]) ).
cnf(c_0_1999_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk149_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_1999]) ).
cnf(c_0_1999_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_1999]) ).
cnf(c_0_1999_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_1999]) ).
cnf(c_0_1999_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_1999]) ).
cnf(c_0_1999_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_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_1999]) ).
cnf(c_0_1999_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2000]) ).
cnf(c_0_2000_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2000]) ).
cnf(c_0_2000_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(sk1_esk149_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_2000]) ).
cnf(c_0_2000_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_2000]) ).
cnf(c_0_2000_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_2000]) ).
cnf(c_0_2000_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_2000]) ).
cnf(c_0_2000_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_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_2000]) ).
cnf(c_0_2000_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2001]) ).
cnf(c_0_2001_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2001]) ).
cnf(c_0_2001_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(sk1_esk149_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_2001]) ).
cnf(c_0_2001_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_2001]) ).
cnf(c_0_2001_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_2001]) ).
cnf(c_0_2001_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_2001]) ).
cnf(c_0_2001_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_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_2001]) ).
cnf(c_0_2001_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_0,axiom,
( empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_2002]) ).
cnf(c_0_2002_1,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_2002]) ).
cnf(c_0_2002_2,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_2002]) ).
cnf(c_0_2002_3,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_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_2002]) ).
cnf(c_0_2002_4,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_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_2002]) ).
cnf(c_0_2002_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_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_2002]) ).
cnf(c_0_2002_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_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_2002]) ).
cnf(c_0_2002_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_10,axiom,
( ~ in(X7,X8)
| X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2003]) ).
cnf(c_0_2003_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2003]) ).
cnf(c_0_2003_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk149_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_2003]) ).
cnf(c_0_2003_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_2003]) ).
cnf(c_0_2003_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_2003]) ).
cnf(c_0_2003_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_2003]) ).
cnf(c_0_2003_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_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_2003]) ).
cnf(c_0_2003_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2004]) ).
cnf(c_0_2004_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2004]) ).
cnf(c_0_2004_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk149_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_2004]) ).
cnf(c_0_2004_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_2004]) ).
cnf(c_0_2004_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_2004]) ).
cnf(c_0_2004_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_2004]) ).
cnf(c_0_2004_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_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_2004]) ).
cnf(c_0_2004_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2005]) ).
cnf(c_0_2005_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2005]) ).
cnf(c_0_2005_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk149_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_2005]) ).
cnf(c_0_2005_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_2005]) ).
cnf(c_0_2005_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_2005]) ).
cnf(c_0_2005_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_2005]) ).
cnf(c_0_2005_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_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_2005]) ).
cnf(c_0_2005_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2006]) ).
cnf(c_0_2006_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2006]) ).
cnf(c_0_2006_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(sk1_esk149_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_2006]) ).
cnf(c_0_2006_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_2006]) ).
cnf(c_0_2006_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_2006]) ).
cnf(c_0_2006_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_2006]) ).
cnf(c_0_2006_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_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_2006]) ).
cnf(c_0_2006_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2007_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2007]) ).
cnf(c_0_2007_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2007]) ).
cnf(c_0_2007_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk149_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_2007]) ).
cnf(c_0_2007_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_2007]) ).
cnf(c_0_2007_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_2007]) ).
cnf(c_0_2007_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_2007]) ).
cnf(c_0_2007_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_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_2007]) ).
cnf(c_0_2007_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2008]) ).
cnf(c_0_2008_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk144_3(X2,X1,X4))
| in(sk1_esk149_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_2008]) ).
cnf(c_0_2008_2,axiom,
( in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(sk1_esk149_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_2008]) ).
cnf(c_0_2008_3,axiom,
( in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_2008]) ).
cnf(c_0_2008_4,axiom,
( ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_2008]) ).
cnf(c_0_2008_5,axiom,
( ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_2008]) ).
cnf(c_0_2008_6,axiom,
( X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_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_2008]) ).
cnf(c_0_2008_7,axiom,
( ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X6,X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_8,axiom,
( ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| X6 != X8
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_9,axiom,
( X6 != X8
| ~ in(X6,X2)
| ordered_pair(X6,X7) != X3
| X5 != X3
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X1)
| in(sk1_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_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_esk149_8(X2,X1,X4,X3,X5,X6,X7,X8),X8)
| in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_2,axiom,
( empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_3,axiom,
( ~ element(X6,X2)
| empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_4,axiom,
( ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_5,axiom,
( ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_6,axiom,
( ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_7,axiom,
( ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X3,X4,X5,X6),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(X4,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_2,axiom,
( in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_4,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_5,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_6,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_7,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_8,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_9,axiom,
( ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1)
| ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| in(X4,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_2,axiom,
( in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_4,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_5,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_6,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_7,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_8,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_9,axiom,
( ~ in(ordered_pair(X4,sk1_esk134_5(X2,X1,X4,X5,X6)),X1)
| ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_2,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_3,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_4,axiom,
( ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_4,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_5,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_6,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,X5)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_7,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_8,axiom,
( ~ in(ordered_pair(X3,sk1_esk134_5(X2,X1,X3,X4,X5)),X1)
| ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| empty(X2)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| empty(X1)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_2,axiom,
( empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_3,axiom,
( ~ element(X6,X2)
| empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| ~ element(X5,X1)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_4,axiom,
( ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_5,axiom,
( ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_6,axiom,
( ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6)
| ~ function(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_7,axiom,
( ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X1,X2),X3)
| ~ relation_of2(X4,cartesian_product2(X1,X2),X3)
| ~ element(X5,X1)
| ~ element(X6,X2)
| empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) = meet(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) = meet(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) = meet(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) = meet(X1,X2,X3)
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_4,axiom,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) = meet(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) = join(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) = join(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) = join(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) = join(X1,X2,X3)
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_4,axiom,
( ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) = join(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( in(ordered_pair(X4,sk1_esk86_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_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk86_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_2024]) ).
cnf(c_0_2024_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk86_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_2024]) ).
cnf(c_0_2024_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk86_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_2024]) ).
cnf(c_0_2024_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk86_5(X1,X2,X3,X4,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk86_5(X1,X2,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_0,axiom,
( in(ordered_pair(sk1_esk86_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_2025]) ).
cnf(c_0_2025_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk86_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_2025]) ).
cnf(c_0_2025_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk86_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_2025]) ).
cnf(c_0_2025_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk86_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_2025]) ).
cnf(c_0_2025_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk86_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2025_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk86_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2026_0,axiom,
( ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2027_0,axiom,
( ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_1,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_4,axiom,
( sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2029_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_2,axiom,
( ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(apply(X1,sk1_esk192_4(X3,X2,X1,X4)),apply(X1,sk1_esk193_4(X3,X2,X1,X4))),X2)
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X2,sk1_esk169_1(X1))
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_1,axiom,
( in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,axiom,
( in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_3,axiom,
( ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_4,axiom,
( ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_8,axiom,
( ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_0,axiom,
( in(X2,sk1_esk169_1(X1))
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_1,axiom,
( in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_3,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_4,axiom,
( ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1))
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_8,axiom,
( ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk174_5(X1,X2,X3,X4,X5),sk1_esk173_4(X1,X2,X3,X4))
| in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2033_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X2,sk1_esk169_1(X1))
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_1,axiom,
( in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_2,axiom,
( subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_3,axiom,
( ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_4,axiom,
( ~ in(X3,succ(X1))
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_8,axiom,
( ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2034_0,axiom,
( in(X2,sk1_esk169_1(X1))
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_1,axiom,
( subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_2,axiom,
( ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_3,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_4,axiom,
( ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1))
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_8,axiom,
( ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| subset(X5,sk1_esk174_5(X1,X2,X3,X4,X5))
| in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2035_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_1,axiom,
( in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_2,axiom,
( ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_3,axiom,
( ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_4,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_5,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_6,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_7,axiom,
( ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_8,axiom,
( sk1_esk174_5(X1,X2,X3,X4,X5) != X5
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_8,axiom,
( ~ in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_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_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_9,axiom,
( ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_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_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_10,axiom,
( ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_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_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_11,axiom,
( ~ in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| ~ in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| ~ in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_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_2036]) ).
cnf(c_0_2037_0,axiom,
( in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_1,axiom,
( ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_2,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_3,axiom,
( ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_4,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X4)
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_5,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| X2 != X4
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_6,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_7,axiom,
( ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| sk1_esk174_5(X1,X2,X3,X4,X5) != X5 ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_8,axiom,
( sk1_esk174_5(X1,X2,X3,X4,X5) != X5
| ~ in(X5,sk1_esk173_4(X1,X2,X3,X4))
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2038_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk131_2(X2,X1))
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_2,axiom,
( in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_3,axiom,
( in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_5,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_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_2038]) ).
cnf(c_0_2038_6,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_7,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_8,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_9,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2039_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| in(X4,sk1_esk131_2(X2,X1))
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk131_2(X2,X1))
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_2,axiom,
( in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_3,axiom,
( in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X5,X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_5,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_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_2039]) ).
cnf(c_0_2039_6,axiom,
( ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_7,axiom,
( ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| X5 != X6
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_8,axiom,
( X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_9,axiom,
( ~ in(X4,X6)
| X5 != X6
| ~ in(X5,X2)
| ~ in(X5,X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X4,X5,X6),X6)
| in(X4,sk1_esk131_2(X2,X1))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2040_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2040]) ).
cnf(c_0_2040_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2040]) ).
cnf(c_0_2040_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(sk1_esk134_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_2040]) ).
cnf(c_0_2040_3,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_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_2040]) ).
cnf(c_0_2040_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2041_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2041]) ).
cnf(c_0_2041_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2041]) ).
cnf(c_0_2041_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(sk1_esk134_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_2041]) ).
cnf(c_0_2041_3,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_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_2041]) ).
cnf(c_0_2041_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2042_0,axiom,
( empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_1,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_2,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_3,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_4,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_5,axiom,
( ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2043_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2043]) ).
cnf(c_0_2043_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2043]) ).
cnf(c_0_2043_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk134_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_2043]) ).
cnf(c_0_2043_3,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_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_2043]) ).
cnf(c_0_2043_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2044_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2044]) ).
cnf(c_0_2044_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2044]) ).
cnf(c_0_2044_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk134_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_2044]) ).
cnf(c_0_2044_3,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_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_2044]) ).
cnf(c_0_2044_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2044_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2044_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2044_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2044_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2045_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2045]) ).
cnf(c_0_2045_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2045]) ).
cnf(c_0_2045_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(sk1_esk134_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_2045]) ).
cnf(c_0_2045_3,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_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_2045]) ).
cnf(c_0_2045_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2046_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2046]) ).
cnf(c_0_2046_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk131_2(X2,X1))
| in(sk1_esk134_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_2046]) ).
cnf(c_0_2046_2,axiom,
( in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(sk1_esk134_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_2046]) ).
cnf(c_0_2046_3,axiom,
( in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_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_2046]) ).
cnf(c_0_2046_4,axiom,
( ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_5,axiom,
( ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X4,X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_6,axiom,
( ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| X4 != X5
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_7,axiom,
( X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_8,axiom,
( ~ in(X3,X5)
| X4 != X5
| ~ in(X4,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| in(sk1_esk134_5(X2,X1,X3,X4,X5),X5)
| in(X3,sk1_esk131_2(X2,X1))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2047_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_1,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2048_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_1,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2049_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_6,axiom,
( ~ in(X6,sk1_esk148_4(X2,X1,X5,X4))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2050_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X6,sk1_esk148_4(X2,X1,X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_6,axiom,
( ~ in(X6,sk1_esk148_4(X2,X1,X5,X4))
| ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X5,X4),X6),X1)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2051_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2052_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2053_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2054_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2055_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_1,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2056_0,axiom,
( X4 = empty_set
| X5 = sk1_esk217_4(X3,X2,X1,X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_1,axiom,
( X5 = sk1_esk217_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_2,axiom,
( ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk217_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_3,axiom,
( ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk217_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_4,axiom,
( ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk217_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_5,axiom,
( ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk217_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_6,axiom,
( ~ in(X5,X4)
| ~ subset(sk1_esk217_4(X3,X2,X1,X4),X5)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk217_4(X3,X2,X1,X4)
| X4 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2057_0,axiom,
( X4 = empty_set
| X5 = sk1_esk219_4(X3,X2,X1,X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_1,axiom,
( X5 = sk1_esk219_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_2,axiom,
( ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk219_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_3,axiom,
( ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk219_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_4,axiom,
( ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk219_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_5,axiom,
( ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk219_4(X3,X2,X1,X4)
| X4 = empty_set
| ~ in(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_6,axiom,
( ~ in(X5,X4)
| ~ subset(sk1_esk219_4(X3,X2,X1,X4),X5)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| X5 = sk1_esk219_4(X3,X2,X1,X4)
| X4 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2058_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2059_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2060_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2061_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2062_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_2,axiom,
( in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X5,sk1_esk148_4(X2,X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_5,axiom,
( ~ in(X5,sk1_esk148_4(X2,X1,X4,X3))
| ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(ordered_pair(sk1_esk147_4(X2,X1,X4,X3),X5),X1)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2064_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_1,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_2,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2065_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_1,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_2,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2068_0,axiom,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_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_2068]) ).
cnf(c_0_2068_1,axiom,
( in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_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_2068]) ).
cnf(c_0_2068_2,axiom,
( in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2068]) ).
cnf(c_0_2068_3,axiom,
( ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2068]) ).
cnf(c_0_2068_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2068]) ).
cnf(c_0_2068_5,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2068]) ).
cnf(c_0_2068_6,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2068]) ).
cnf(c_0_2068_7,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(apply(X3,sk1_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2068]) ).
cnf(c_0_2068_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2068_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_esk80_3(X1,X2,X3)),apply(X3,sk1_esk81_3(X1,X2,X3))),X2)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2069_0,axiom,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_1,axiom,
( ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_4,axiom,
( ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_5,axiom,
( ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_6,axiom,
( ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(sk1_esk87_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk88_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2070_0,axiom,
( X4 = empty_set
| in(sk1_esk217_4(X3,X2,X1,X4),X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_1,axiom,
( in(sk1_esk217_4(X3,X2,X1,X4),X4)
| X4 = empty_set
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_2,axiom,
( ~ epred1_3(X1,X2,X3)
| in(sk1_esk217_4(X3,X2,X1,X4),X4)
| X4 = empty_set
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_3,axiom,
( ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| in(sk1_esk217_4(X3,X2,X1,X4),X4)
| X4 = empty_set
| ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_4,axiom,
( ~ element(X4,powerset(powerset(sk1_esk216_3(X3,X2,X1))))
| ~ in(sk1_esk216_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| in(sk1_esk217_4(X3,X2,X1,X4),X4)
| X4 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2071_0,axiom,
( X4 = empty_set
| in(sk1_esk219_4(X3,X2,X1,X4),X4)
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_1,axiom,
( in(sk1_esk219_4(X3,X2,X1,X4),X4)
| X4 = empty_set
| ~ epred1_3(X1,X2,X3)
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_2,axiom,
( ~ epred1_3(X1,X2,X3)
| in(sk1_esk219_4(X3,X2,X1,X4),X4)
| X4 = empty_set
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_3,axiom,
( ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| in(sk1_esk219_4(X3,X2,X1,X4),X4)
| X4 = empty_set
| ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_4,axiom,
( ~ element(X4,powerset(powerset(sk1_esk218_3(X3,X2,X1))))
| ~ in(sk1_esk218_3(X3,X2,X1),omega)
| ~ epred1_3(X1,X2,X3)
| in(sk1_esk219_4(X3,X2,X1,X4),X4)
| X4 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2072_0,axiom,
( ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_1,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2073_0,axiom,
( ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_1,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2074_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_1,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_2,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2075_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_1,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_2,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2076_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| in(X4,sk1_esk190_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_2076]) ).
cnf(c_0_2076_1,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_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_2076]) ).
cnf(c_0_2076_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_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_2076]) ).
cnf(c_0_2076_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_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_2076]) ).
cnf(c_0_2076_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_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_2076]) ).
cnf(c_0_2076_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_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_2076]) ).
cnf(c_0_2076_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_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_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_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_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_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk186_3(X3,X2,X1)),apply(X1,sk1_esk187_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| in(X4,sk1_esk190_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_2077]) ).
cnf(c_0_2077_1,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_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_2077]) ).
cnf(c_0_2077_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_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_2077]) ).
cnf(c_0_2077_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_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_2077]) ).
cnf(c_0_2077_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_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_2077]) ).
cnf(c_0_2077_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_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_2077]) ).
cnf(c_0_2077_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_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_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_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_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_esk190_3(X3,X2,X1))
| in(ordered_pair(apply(X1,sk1_esk188_3(X3,X2,X1)),apply(X1,sk1_esk189_3(X3,X2,X1))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2078_0,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_1,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_4,axiom,
( sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2079_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2080_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X5,X4),sk1_esk147_4(X2,X1,X5,X4)) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2081_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_2,axiom,
( in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_2,axiom,
( in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X5,X4),sk1_esk148_4(X2,X1,X5,X4))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_1,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_1,axiom,
( ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_2,axiom,
( ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| ordered_pair(sk1_esk192_4(X3,X2,X1,X4),sk1_esk193_4(X3,X2,X1,X4)) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2085_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_2085]) ).
cnf(c_0_2086_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2087_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2088_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2089_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2090_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2091_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2092_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2093_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2094_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_1,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_2,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2095_0,axiom,
( empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2095_1,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2095_2,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2095_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2095_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2096_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2097_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2098_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_2098]) ).
cnf(c_0_2099_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_2099]) ).
cnf(c_0_2099_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_2099]) ).
cnf(c_0_2099_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_2099]) ).
cnf(c_0_2100_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_2100]) ).
cnf(c_0_2100_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_2100]) ).
cnf(c_0_2100_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_2100]) ).
cnf(c_0_2101_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2102_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2103_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2104_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2105_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_2,axiom,
( ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_3,axiom,
( ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| ordered_pair(sk1_esk146_4(X2,X1,X4,X3),sk1_esk147_4(X2,X1,X4,X3)) = X3
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2107_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2109_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2109_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2110_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_2,axiom,
( in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_3,axiom,
( ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk147_4(X2,X1,X4,X3),sk1_esk148_4(X2,X1,X4,X3))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_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_2111]) ).
cnf(c_0_2111_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_2111]) ).
cnf(c_0_2111_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_2111]) ).
cnf(c_0_2111_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_2111]) ).
cnf(c_0_2112_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_2112]) ).
cnf(c_0_2112_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_2112]) ).
cnf(c_0_2112_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_2112]) ).
cnf(c_0_2112_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_2112]) ).
cnf(c_0_2113_0,axiom,
( ordered_pair(sk1_esk46_4(X2,X3,X1,X4),sk1_esk47_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk46_4(X2,X3,X1,X4),sk1_esk47_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk46_4(X2,X3,X1,X4),sk1_esk47_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2114_0,axiom,
( in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_1,axiom,
( in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_2,axiom,
( ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2115_0,axiom,
( in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_1,axiom,
( in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_2,axiom,
( ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_0,axiom,
( ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_1,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_2,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2117_0,axiom,
( ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_1,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_2,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2118_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk89_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_1,axiom,
( in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk89_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_2,axiom,
( in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk89_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk89_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk89_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk89_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2119_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk89_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_1,axiom,
( in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk89_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_2,axiom,
( in(ordered_pair(sk1_esk89_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk89_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk89_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk89_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk87_3(X1,X2,X3),sk1_esk88_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2121_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_2121]) ).
cnf(c_0_2121_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_2121]) ).
cnf(c_0_2121_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_2121]) ).
cnf(c_0_2121_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_2121]) ).
cnf(c_0_2121_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_2121]) ).
cnf(c_0_2122_0,axiom,
( in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_1,axiom,
( ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_3,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_4,axiom,
( sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2123_0,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_1,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_4,axiom,
( sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2123_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2123]) ).
cnf(c_0_2124_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_2,axiom,
( in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2124_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2124]) ).
cnf(c_0_2125_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_2,axiom,
( in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X5,X4),cartesian_product2(X2,X5))
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2126_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_1,axiom,
( in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_2,axiom,
( ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2126_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2126]) ).
cnf(c_0_2127_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_1,axiom,
( in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_2,axiom,
( ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2127_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk203_4(X3,X2,X1,X4),powerset(relation_dom(X1)))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2127]) ).
cnf(c_0_2128_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_2,axiom,
( in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2129_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_2,axiom,
( in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2129_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X5,X4),X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2130_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_1,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_2,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2130_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2130]) ).
cnf(c_0_2131_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_1,axiom,
( in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_2,axiom,
( ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2131_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk191_4(X3,X2,X1,X4),cartesian_product2(X3,X3))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2131]) ).
cnf(c_0_2132_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_2,axiom,
( sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2133_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_2,axiom,
( sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X5,X4) = sk1_esk148_4(X2,X1,X5,X4)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2134_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_2134]) ).
cnf(c_0_2135_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2136_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2137_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2138_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2139_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2141_0,axiom,
( empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_1,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_2,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2142_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2144_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2145_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2146_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2147_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2148_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2149_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2150_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2151_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2151_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2152_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_2,axiom,
( in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_3,axiom,
( ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2152_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk145_4(X2,X1,X4,X3),cartesian_product2(X2,X4))
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2153_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2153_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2154_0,axiom,
( in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_1,axiom,
( sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_2,axiom,
( ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2154_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2155_0,axiom,
( in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_1,axiom,
( sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_2,axiom,
( ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2156_0,axiom,
( empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_1,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_2,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2157_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2157_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2158_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2158_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2159_0,axiom,
( ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_1,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_2,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2159_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2160_0,axiom,
( ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_1,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_2,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2161_0,axiom,
( ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| in(X4,sk1_esk190_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_2161]) ).
cnf(c_0_2161_1,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_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_2161]) ).
cnf(c_0_2161_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_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_2161]) ).
cnf(c_0_2161_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_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_2161]) ).
cnf(c_0_2161_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_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_2161]) ).
cnf(c_0_2161_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_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_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_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_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_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_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk186_3(X3,X2,X1),sk1_esk187_3(X3,X2,X1)) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2162_0,axiom,
( ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| in(X4,sk1_esk190_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_2162]) ).
cnf(c_0_2162_1,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_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_2162]) ).
cnf(c_0_2162_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_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_2162]) ).
cnf(c_0_2162_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_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_2162]) ).
cnf(c_0_2162_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_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_2162]) ).
cnf(c_0_2162_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_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_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_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_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_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_esk190_3(X3,X2,X1))
| ordered_pair(sk1_esk188_3(X3,X2,X1),sk1_esk189_3(X3,X2,X1)) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2163_0,axiom,
( empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_1,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_2,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2164_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2165_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2166_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2167_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2168_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2169_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_2,axiom,
( in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_3,axiom,
( ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| in(sk1_esk146_4(X2,X1,X4,X3),X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2170_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2170_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2171_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2171_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2172_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2172_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2173_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_2,axiom,
( sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_3,axiom,
( ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk146_4(X2,X1,X4,X3) = sk1_esk148_4(X2,X1,X4,X3)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2174_0,axiom,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| in(sk1_esk80_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_2174]) ).
cnf(c_0_2174_1,axiom,
( in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| in(sk1_esk80_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_2174]) ).
cnf(c_0_2174_2,axiom,
( in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2174]) ).
cnf(c_0_2174_3,axiom,
( ~ relation(X1)
| in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2174]) ).
cnf(c_0_2174_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2174]) ).
cnf(c_0_2174_5,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2174]) ).
cnf(c_0_2174_6,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2174]) ).
cnf(c_0_2174_7,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2174]) ).
cnf(c_0_2174_8,axiom,
( relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_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_esk80_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2175_0,axiom,
( relation_isomorphism(X1,X2,X3)
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| in(sk1_esk81_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_2175]) ).
cnf(c_0_2175_1,axiom,
( in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| in(sk1_esk81_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_2175]) ).
cnf(c_0_2175_2,axiom,
( in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2175]) ).
cnf(c_0_2175_3,axiom,
( ~ relation(X1)
| in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2175]) ).
cnf(c_0_2175_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2175]) ).
cnf(c_0_2175_5,axiom,
( ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2175]) ).
cnf(c_0_2175_6,axiom,
( ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2175]) ).
cnf(c_0_2175_7,axiom,
( relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_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_2175]) ).
cnf(c_0_2175_8,axiom,
( relation_rng(X3) != relation_field(X2)
| relation_dom(X3) != relation_field(X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3)
| ~ one_to_one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2175_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_esk81_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(sk1_esk80_3(X1,X2,X3),sk1_esk81_3(X1,X2,X3)),X1)
| relation_isomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2176_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| ~ in(sk1_esk93_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| ~ in(sk1_esk93_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| ~ in(sk1_esk93_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_3,axiom,
( ~ in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(sk1_esk93_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_4,axiom,
( ~ in(sk1_esk93_3(X2,X1,X3),X3)
| ~ in(subset_complement(X2,sk1_esk93_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_2176]) ).
cnf(c_0_2177_0,axiom,
( sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_3,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_4,axiom,
( sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2178_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X2,sk1_esk169_1(X1))
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_1,axiom,
( in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_2,axiom,
( element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_3,axiom,
( ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_4,axiom,
( ~ in(X3,succ(X1))
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2179_0,axiom,
( X2 = fiber(X1,X3)
| sk1_esk32_3(X1,X3,X2) = X3
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ in(sk1_esk32_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_1,axiom,
( sk1_esk32_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ in(sk1_esk32_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_2,axiom,
( ~ relation(X1)
| sk1_esk32_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3)
| ~ in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ in(sk1_esk32_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_3,axiom,
( ~ in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ relation(X1)
| sk1_esk32_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3)
| ~ in(sk1_esk32_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2179_4,axiom,
( ~ in(sk1_esk32_3(X1,X3,X2),X2)
| ~ in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ relation(X1)
| sk1_esk32_3(X1,X3,X2) = X3
| X2 = fiber(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 = empty_set
| X4 = sk1_esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_1,axiom,
( X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X4 = sk1_esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_2,axiom,
( X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_3,axiom,
( ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_4,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_5,axiom,
( ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_6,axiom,
( ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_7,axiom,
( ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2180_8,axiom,
( ~ in(X4,X3)
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2183_0,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_1,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_4,axiom,
( sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2184_0,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_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_2184]) ).
cnf(c_0_2184_1,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X1)
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_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_2184]) ).
cnf(c_0_2184_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_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_2184]) ).
cnf(c_0_2184_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_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_2184]) ).
cnf(c_0_2184_4,axiom,
( sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_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_2184]) ).
cnf(c_0_2184_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_6,axiom,
( X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_7,axiom,
( X7 != X4
| X4 != ordered_pair(X5,X6)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| sk1_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2184_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_esk185_3(X3,X2,X1) != sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2185_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_2185]) ).
cnf(c_0_2186_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_2186]) ).
cnf(c_0_2186_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_2186]) ).
cnf(c_0_2186_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_2186]) ).
cnf(c_0_2186_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_2186]) ).
cnf(c_0_2186_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_2186]) ).
cnf(c_0_2187_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_1,axiom,
( sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_2,axiom,
( ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_2,axiom,
( ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| sk1_esk203_4(X3,X2,X1,X4) = X4
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( in(X2,sk1_esk169_1(X1))
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_2,axiom,
( ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_3,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_4,axiom,
( ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| element(sk1_esk173_4(X1,X2,X3,X4),powerset(powerset(X4)))
| in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2192_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_1,axiom,
( in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_2,axiom,
( sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_4,axiom,
( ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2192_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk140_2(X2,X1))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk139_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_1,axiom,
( in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_2,axiom,
( sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_4,axiom,
( ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk144_3(X2,X1,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2193_5,axiom,
( ~ in(X4,sk1_esk144_3(X2,X1,X5))
| ~ in(X3,sk1_esk143_2(X2,X1))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X5,X4) = X4
| in(ordered_pair(sk1_esk142_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2194_0,axiom,
( X3 = empty_set
| X4 = sk1_esk172_3(X1,X2,X3)
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_1,axiom,
( X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_2,axiom,
( ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_3,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_4,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_5,axiom,
( ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_6,axiom,
( ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_7,axiom,
( ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_8,axiom,
( ~ in(X4,X3)
| ~ subset(sk1_esk172_3(X1,X2,X3),X4)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| X4 = sk1_esk172_3(X1,X2,X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2195_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk58_3(X2,X3,X1),X3)
| ~ in(sk1_esk58_3(X2,X3,X1),X2)
| ~ in(sk1_esk58_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_1,axiom,
( ~ in(sk1_esk58_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk58_3(X2,X3,X1),X2)
| ~ in(sk1_esk58_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_2,axiom,
( ~ in(sk1_esk58_3(X2,X3,X1),X2)
| ~ in(sk1_esk58_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk58_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2195_3,axiom,
( ~ in(sk1_esk58_3(X2,X3,X1),X1)
| ~ in(sk1_esk58_3(X2,X3,X1),X2)
| ~ in(sk1_esk58_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2196_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_2196]) ).
cnf(c_0_2197_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_1,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_2,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2198_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_1,axiom,
( sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_2,axiom,
( ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ relation(X2)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ in(X4,sk1_esk190_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2198_5,axiom,
( ~ in(X4,sk1_esk190_3(X3,X2,X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| sk1_esk191_4(X3,X2,X1,X4) = X4
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| in(X4,sk1_esk190_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_2199]) ).
cnf(c_0_2199_1,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_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_2199]) ).
cnf(c_0_2199_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_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_2199]) ).
cnf(c_0_2199_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_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_2199]) ).
cnf(c_0_2199_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_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_2199]) ).
cnf(c_0_2199_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_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_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_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_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2199_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_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk184_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
( sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| in(X4,sk1_esk190_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_2200]) ).
cnf(c_0_2200_1,axiom,
( in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_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_2200]) ).
cnf(c_0_2200_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_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_2200]) ).
cnf(c_0_2200_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_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_2200]) ).
cnf(c_0_2200_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_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_2200]) ).
cnf(c_0_2200_5,axiom,
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| X4 != ordered_pair(X5,X6)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_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_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| X7 != X4
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_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_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1)
| ~ in(X7,cartesian_product2(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2200_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_esk190_3(X3,X2,X1))
| sk1_esk183_3(X3,X2,X1) = sk1_esk185_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2203_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_2203]) ).
cnf(c_0_2204_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_2204]) ).
cnf(c_0_2204_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_2204]) ).
cnf(c_0_2204_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_2204]) ).
cnf(c_0_2204_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_2204]) ).
cnf(c_0_2205_0,axiom,
( in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_5,axiom,
( ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_6,axiom,
( X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_7,axiom,
( ~ in(X5,powerset(relation_dom(X1)))
| X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2206_0,axiom,
( in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_1,axiom,
( in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_5,axiom,
( ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_6,axiom,
( X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2206_7,axiom,
( ~ in(X5,powerset(relation_dom(X1)))
| X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
( in(sk1_esk46_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk46_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2207_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk46_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
( in(sk1_esk47_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk47_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2208_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk47_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2209_0,axiom,
( in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_1,axiom,
( in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_2,axiom,
( ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk200_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
( in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_2,axiom,
( ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| in(relation_image(X1,sk1_esk201_3(X3,X2,X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_3,axiom,
( ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_4,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_5,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_6,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_7,axiom,
( sk1_esk173_4(X1,X2,X3,X4) != empty_set
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk138_2(X2,X1),sk1_esk139_2(X2,X1)) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( empty(X2)
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ordered_pair(sk1_esk141_2(X2,X1),sk1_esk142_2(X2,X1)) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk68_3(X2,X3,X1),X3)
| ~ in(sk1_esk68_3(X2,X3,X1),X2)
| ~ in(sk1_esk68_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( in(sk1_esk68_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk68_3(X2,X3,X1),X2)
| ~ in(sk1_esk68_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_2,axiom,
( ~ in(sk1_esk68_3(X2,X3,X1),X2)
| in(sk1_esk68_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk68_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_3,axiom,
( ~ in(sk1_esk68_3(X2,X3,X1),X1)
| ~ in(sk1_esk68_3(X2,X3,X1),X2)
| in(sk1_esk68_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2215_0,axiom,
( empty(X2)
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_1,axiom,
( in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk139_2(X2,X1),sk1_esk140_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_0,axiom,
( empty(X2)
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk142_2(X2,X1),sk1_esk143_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 = empty_set
| in(sk1_esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(sk1_esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_2,axiom,
( in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_3,axiom,
( ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_4,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_5,axiom,
( ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_6,axiom,
( ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2218_0,axiom,
( empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_1,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| empty(X2)
| ~ relation(X1)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_2,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| empty(X2)
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_3,axiom,
( sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2218_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| sk1_esk137_2(X2,X1) != sk1_esk136_2(X2,X1)
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2219_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| in(sk1_esk93_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_1,axiom,
( in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| in(sk1_esk93_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_2,axiom,
( in(sk1_esk93_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk93_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_2219]) ).
cnf(c_0_2219_3,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk93_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2219_4,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk93_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk93_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
( empty(X2)
| in(sk1_esk138_2(X2,X1),X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_1,axiom,
( in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2220_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk138_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2221_0,axiom,
( empty(X2)
| in(sk1_esk141_2(X2,X1),X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_1,axiom,
( in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| in(sk1_esk141_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk135_2(X2,X1) = sk1_esk136_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( empty(X2)
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk138_2(X2,X1) = sk1_esk140_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( empty(X2)
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk135_2(X2,X1) = sk1_esk137_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( empty(X2)
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_2,axiom,
( sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_3,axiom,
( ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk144_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_4,axiom,
( ~ in(X3,sk1_esk144_3(X2,X1,X4))
| ~ relation(X1)
| sk1_esk145_4(X2,X1,X4,X3) = X3
| sk1_esk141_2(X2,X1) = sk1_esk143_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
( in(X4,sk1_esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_3,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_4,axiom,
( sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_5,axiom,
( ~ in(relation_image(X1,X4),X2)
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_6,axiom,
( X5 != X4
| ~ in(relation_image(X1,X4),X2)
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_7,axiom,
( ~ in(X5,powerset(relation_dom(X1)))
| X5 != X4
| ~ in(relation_image(X1,X4),X2)
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_2,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_3,axiom,
( ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_4,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X4)
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_5,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| X2 != X4
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_6,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1))
| sk1_esk173_4(X1,X2,X3,X4) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_7,axiom,
( sk1_esk173_4(X1,X2,X3,X4) != empty_set
| X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_3,axiom,
( ~ in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_4,axiom,
( ~ in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( ~ relation(X1)
| X1 = X2
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_3,axiom,
( ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_4,axiom,
( ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_0,axiom,
( in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( ~ function(X1)
| in(relation_image(X1,X4),X2)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_3,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_4,axiom,
( sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk201_3(X3,X2,X1) != sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2231_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_2,axiom,
( in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_4,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2231_6,axiom,
( ~ in(X5,sk1_esk133_3(X2,X1,X4))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2232_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_2,axiom,
( in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_4,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X5,sk1_esk133_3(X2,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_6,axiom,
( ~ in(X5,sk1_esk133_3(X2,X1,X4))
| ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2233_0,axiom,
( X3 = empty_set
| in(sk1_esk172_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_1,axiom,
( in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_3,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ in(X2,sk1_esk169_1(X1))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_4,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_5,axiom,
( ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2233_6,axiom,
( ~ element(X3,powerset(powerset(sk1_esk171_2(X1,X2))))
| ~ in(sk1_esk171_2(X1,X2),omega)
| ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk172_3(X1,X2,X3),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2235_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk48_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk49_3(X2,X3,X1),sk1_esk50_3(X2,X3,X1)) = sk1_esk48_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( in(sk1_esk48_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk49_3(X2,X3,X1),sk1_esk50_3(X2,X3,X1)) = sk1_esk48_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_2,axiom,
( ordered_pair(sk1_esk49_3(X2,X3,X1),sk1_esk50_3(X2,X3,X1)) = sk1_esk48_3(X2,X3,X1)
| in(sk1_esk48_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_5,axiom,
( ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_6,axiom,
( X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_7,axiom,
( ~ in(X5,powerset(relation_dom(X1)))
| X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_2,axiom,
( ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ in(relation_image(X1,X4),X2)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_5,axiom,
( ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| X5 != X4
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_6,axiom,
( X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ in(X5,powerset(relation_dom(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_7,axiom,
( ~ in(X5,powerset(relation_dom(X1)))
| X5 != X4
| ~ in(relation_image(X1,X4),X2)
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(X4,sk1_esk202_3(X3,X2,X1))
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_2,axiom,
( ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk200_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_0,axiom,
( sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_1,axiom,
( in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_2,axiom,
( ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_4,axiom,
( ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1)
| ~ in(X4,sk1_esk202_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_5,axiom,
( ~ in(X4,sk1_esk202_3(X3,X2,X1))
| ~ element(X2,powerset(powerset(X3)))
| ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,X4),X2)
| sk1_esk199_3(X3,X2,X1) = sk1_esk201_3(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2241_0,axiom,
( X2 = fiber(X1,X3)
| in(sk1_esk32_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_1,axiom,
( in(sk1_esk32_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_2,axiom,
( in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| in(sk1_esk32_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2241_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk32_3(X1,X3,X2),X3),X1)
| in(sk1_esk32_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2242_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk45_3(X2,X3,X1),X1)
| ~ in(sk1_esk45_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_1,axiom,
( ~ in(sk1_esk45_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk45_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_2,axiom,
( ~ in(sk1_esk45_3(X2,X3,X1),X2)
| ~ in(sk1_esk45_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2243_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk45_3(X2,X3,X1),X1)
| ~ in(sk1_esk45_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( ~ in(sk1_esk45_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk45_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_2,axiom,
( ~ in(sk1_esk45_3(X2,X3,X1),X3)
| ~ in(sk1_esk45_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2245_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk45_3(X2,X3,X1),X3)
| in(sk1_esk45_3(X2,X3,X1),X2)
| in(sk1_esk45_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_1,axiom,
( in(sk1_esk45_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk45_3(X2,X3,X1),X2)
| in(sk1_esk45_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_2,axiom,
( in(sk1_esk45_3(X2,X3,X1),X2)
| in(sk1_esk45_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk45_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2245_3,axiom,
( in(sk1_esk45_3(X2,X3,X1),X1)
| in(sk1_esk45_3(X2,X3,X1),X2)
| in(sk1_esk45_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2246_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk48_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( sk1_esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk48_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_2,axiom,
( ~ in(X5,X3)
| sk1_esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk48_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk48_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_4,axiom,
( ~ in(sk1_esk48_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk48_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_2,axiom,
( in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_4,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_2,axiom,
( in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_4,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2250_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_2,axiom,
( in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_4,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2251_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2252_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_2,axiom,
( in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_4,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X4),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_2,axiom,
( in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_4,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X4),X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2254_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| in(X4,sk1_esk133_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_2,axiom,
( in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_3,axiom,
( ~ relation(X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_4,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| in(X4,sk1_esk133_3(X2,X1,X4))
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2
| ~ subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| ~ in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ relation(X1)
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2
| ~ subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| ~ in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_2,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| X1 = inclusion_relation(X2)
| ~ subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| ~ in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_3,axiom,
( ~ subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| relation_field(X1) != X2
| ~ relation(X1)
| X1 = inclusion_relation(X2)
| ~ in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_4,axiom,
( ~ in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1)
| ~ subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| relation_field(X1) != X2
| ~ relation(X1)
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_1,axiom,
( in(ordered_pair(X3,X4),X1)
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_2,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_3,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2259_0,axiom,
( set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_1,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2259_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
( set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_1,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2260_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2261_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_2261]) ).
cnf(c_0_2262_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_2,axiom,
( in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2265_0,axiom,
( set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_1,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2266_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_1,axiom,
( in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_2,axiom,
( sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_4,axiom,
( ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk129_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk127_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
( empty(X2)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_1,axiom,
( in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_2,axiom,
( sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_4,axiom,
( ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2)
| ~ in(X4,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_5,axiom,
( ~ in(X4,sk1_esk131_2(X2,X1))
| ~ in(X3,sk1_esk130_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X4) = sk1_esk133_3(X2,X1,X4)
| in(ordered_pair(sk1_esk128_2(X2,X1),X3),X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2268_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_2,axiom,
( in(ordered_pair(X3,X4),X1)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_2,axiom,
( in(ordered_pair(X3,X4),X1)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_3,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X4,sk1_esk133_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2269_5,axiom,
( ~ in(X4,sk1_esk133_3(X2,X1,X3))
| ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_2,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_3,axiom,
( sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_2,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_3,axiom,
( sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( in(sk1_esk178_2(X2,X1),X1)
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk178_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk178_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk178_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk178_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( in(sk1_esk179_2(X2,X1),X1)
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk179_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk179_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk179_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| in(sk1_esk179_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_0,axiom,
( in(sk1_esk178_2(X2,X1),X1)
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk178_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk178_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk178_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk178_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2275_0,axiom,
( in(sk1_esk179_2(X2,X1),X1)
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_1,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk179_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk179_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk179_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| in(sk1_esk179_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk68_3(X2,X3,X1),X1)
| ~ in(sk1_esk68_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_1,axiom,
( in(sk1_esk68_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk68_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_2,axiom,
( ~ in(sk1_esk68_3(X2,X3,X1),X3)
| in(sk1_esk68_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2278_0,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_1,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_2,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_3,axiom,
( sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
( empty_carrier(X1)
| meet_absorbing(X1)
| ~ latt_str(X1)
| join(X1,meet(X1,sk1_esk84_1(X1),sk1_esk85_1(X1)),sk1_esk85_1(X1)) != sk1_esk85_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ latt_str(X1)
| join(X1,meet(X1,sk1_esk84_1(X1),sk1_esk85_1(X1)),sk1_esk85_1(X1)) != sk1_esk85_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_2,axiom,
( ~ latt_str(X1)
| meet_absorbing(X1)
| empty_carrier(X1)
| join(X1,meet(X1,sk1_esk84_1(X1),sk1_esk85_1(X1)),sk1_esk85_1(X1)) != sk1_esk85_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_3,axiom,
( join(X1,meet(X1,sk1_esk84_1(X1),sk1_esk85_1(X1)),sk1_esk85_1(X1)) != sk1_esk85_1(X1)
| ~ latt_str(X1)
| meet_absorbing(X1)
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2282_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_2282]) ).
cnf(c_0_2283_0,axiom,
( in(sk1_esk178_2(X2,X1),X1)
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk178_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk178_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk178_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk178_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( in(sk1_esk179_2(X2,X1),X1)
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk179_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk179_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk179_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| in(sk1_esk179_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2285_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_1,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2285_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2286_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| set_difference(sk1_esk182_3(X2,X1,X3),singleton(X2)) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2287_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_1,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2287_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2288_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk181_3(X2,X1,X3),powerset(X2))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( in(sk1_esk158_1(X1),X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| in(sk1_esk158_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| in(sk1_esk158_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2290_0,axiom,
( in(sk1_esk160_1(X1),X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| in(sk1_esk160_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2290_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| in(sk1_esk160_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2291_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_1,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2291_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2292_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| in(sk1_esk182_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_1,axiom,
( in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(sk1_esk182_3(X2,X1,X3),X1)
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2293_0,axiom,
( X3 = empty_set
| disjoint(fiber(X1,sk1_esk56_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_1,axiom,
( disjoint(fiber(X1,sk1_esk56_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_2293]) ).
cnf(c_0_2293_2,axiom,
( ~ relation(X1)
| disjoint(fiber(X1,sk1_esk56_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_3,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk56_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_4,axiom,
( ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk56_3(X1,X2,X3)),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2294_0,axiom,
( X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_1,axiom,
( in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_2,axiom,
( in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk78_2(X1,X2),sk1_esk79_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk79_2(X1,X2),sk1_esk78_2(X1,X2)),X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2295_0,axiom,
( singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2296_0,axiom,
( singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( X1 = X2
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| X1 = X2
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_2,axiom,
( in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk40_2(X1,X2),sk1_esk41_2(X1,X2)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| sk1_esk155_1(X1) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2300_0,axiom,
( sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_1,axiom,
( ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk164_3(X1,X3,X2),sk1_esk165_3(X1,X3,X2)) = X2
| sk1_esk155_1(X1) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2301_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk42_3(X2,X3,X1),X1)
| sk1_esk42_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2301_1,axiom,
( ~ in(sk1_esk42_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk42_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2301_2,axiom,
( sk1_esk42_3(X2,X3,X1) != X2
| ~ in(sk1_esk42_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2301]) ).
cnf(c_0_2302_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk42_3(X2,X3,X1),X1)
| sk1_esk42_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ in(sk1_esk42_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk42_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_2,axiom,
( sk1_esk42_3(X2,X3,X1) != X3
| ~ in(sk1_esk42_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( in(ordered_pair(sk1_esk73_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk73_3(X1,X2,X3),X3),X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk73_3(X1,X2,X3),X3),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_3,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk73_3(X1,X2,X3),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( in(ordered_pair(X3,sk1_esk59_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,sk1_esk59_3(X1,X2,X3)),X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk59_3(X1,X2,X3)),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_3,axiom,
( ~ in(X3,X2)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk59_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2305_0,axiom,
( set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_1,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2306_0,axiom,
( set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_1,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_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_2307]) ).
cnf(c_0_2307_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_2307]) ).
cnf(c_0_2307_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_2307]) ).
cnf(c_0_2307_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_2307]) ).
cnf(c_0_2307_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_2307]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2309_0,axiom,
( set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_1,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk178_2(X2,X1),singleton(X2)) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2310_0,axiom,
( set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_1,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| set_difference(sk1_esk179_2(X2,X1),singleton(X2)) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_1,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_2,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_3,axiom,
( sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2313_0,axiom,
( in(sk1_esk178_2(X2,X1),X1)
| in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_1,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1)
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1)
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1)
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk178_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
( in(sk1_esk179_2(X2,X1),X1)
| in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_1,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1)
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1)
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1)
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| in(sk1_esk179_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2316_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_2316]) ).
cnf(c_0_2316_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_2316]) ).
cnf(c_0_2316_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_2316]) ).
cnf(c_0_2316_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_2316]) ).
cnf(c_0_2317_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_2317]) ).
cnf(c_0_2317_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_2317]) ).
cnf(c_0_2317_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_2317]) ).
cnf(c_0_2317_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_2317]) ).
cnf(c_0_2318_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2318_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2319_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2320_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_2,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2321_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2322_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2323_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_2,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2324_0,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_1,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| ~ ordinal(X2)
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_2,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_3,axiom,
( sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| sk1_esk177_2(X2,X1) != sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2325_0,axiom,
( ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2326_0,axiom,
( ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2327_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2328_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| in(X3,sk1_esk180_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_1,axiom,
( in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_4,axiom,
( X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ in(X4,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_5,axiom,
( ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| X5 != X3
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_6,axiom,
( X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ in(X5,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_7,axiom,
( ~ in(X5,powerset(X2))
| X5 != X3
| ~ in(X4,X1)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| in(X3,sk1_esk180_2(X2,X1))
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2329_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk68_3(X2,X3,X1),X1)
| in(sk1_esk68_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_1,axiom,
( in(sk1_esk68_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk68_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2329_2,axiom,
( in(sk1_esk68_3(X2,X3,X1),X2)
| in(sk1_esk68_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2330_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk58_3(X2,X3,X1),X1)
| in(sk1_esk58_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( in(sk1_esk58_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk58_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_2,axiom,
( in(sk1_esk58_3(X2,X3,X1),X2)
| in(sk1_esk58_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk58_3(X2,X3,X1),X1)
| in(sk1_esk58_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( in(sk1_esk58_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk58_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_2,axiom,
( in(sk1_esk58_3(X2,X3,X1),X3)
| in(sk1_esk58_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2332_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk48_3(X2,X3,X1),X1)
| in(sk1_esk49_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_1,axiom,
( in(sk1_esk48_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk49_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_2,axiom,
( in(sk1_esk49_3(X2,X3,X1),X2)
| in(sk1_esk48_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2333_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk48_3(X2,X3,X1),X1)
| in(sk1_esk50_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_1,axiom,
( in(sk1_esk48_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk50_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2333_2,axiom,
( in(sk1_esk50_3(X2,X3,X1),X3)
| in(sk1_esk48_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2334_0,axiom,
( in(sk1_esk178_2(X2,X1),X1)
| sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_1,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk178_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk178_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk178_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk178_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2335_0,axiom,
( in(sk1_esk179_2(X2,X1),X1)
| sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_1,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk179_2(X2,X1),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk179_2(X2,X1),X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk179_2(X2,X1),X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| in(sk1_esk179_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2336_0,axiom,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( ~ relation(X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2)
| ~ in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_3,axiom,
( ~ in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2337_0,axiom,
( empty(X2)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_1,axiom,
( in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_2,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk127_2(X2,X1),sk1_esk129_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2338_0,axiom,
( empty(X2)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_1,axiom,
( in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_2,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk128_2(X2,X1),sk1_esk130_2(X2,X1))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
( in(sk1_esk158_1(X1),X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| in(sk1_esk158_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| in(sk1_esk158_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
( in(sk1_esk160_1(X1),X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| in(sk1_esk160_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| in(sk1_esk160_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2341_0,axiom,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk90_2(X1,X2),sk1_esk92_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,X2)
| ~ in(ordered_pair(sk1_esk90_2(X1,X2),sk1_esk92_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_2,axiom,
( ~ in(ordered_pair(sk1_esk90_2(X1,X2),sk1_esk92_2(X1,X2)),X1)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2342_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_2,axiom,
( ~ in(ordered_pair(sk1_esk76_2(X1,X2),sk1_esk77_2(X1,X2)),X1)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_2,axiom,
( ~ in(ordered_pair(sk1_esk77_2(X1,X2),sk1_esk76_2(X1,X2)),X1)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2344_0,axiom,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk27_2(X1,X2),sk1_esk27_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,X2)
| ~ in(ordered_pair(sk1_esk27_2(X1,X2),sk1_esk27_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2344_2,axiom,
( ~ in(ordered_pair(sk1_esk27_2(X1,X2),sk1_esk27_2(X1,X2)),X1)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2345_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk42_3(X2,X3,X1) = X3
| sk1_esk42_3(X2,X3,X1) = X2
| in(sk1_esk42_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_1,axiom,
( sk1_esk42_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk42_3(X2,X3,X1) = X2
| in(sk1_esk42_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_2,axiom,
( sk1_esk42_3(X2,X3,X1) = X2
| sk1_esk42_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk42_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_3,axiom,
( in(sk1_esk42_3(X2,X3,X1),X1)
| sk1_esk42_3(X2,X3,X1) = X2
| sk1_esk42_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2346_0,axiom,
( empty_carrier(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| ~ latt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_1,axiom,
( join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_2,axiom,
( ~ latt_str(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_3,axiom,
( ~ element(X3,the_carrier(X1))
| ~ latt_str(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_4,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ latt_str(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ meet_absorbing(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_5,axiom,
( ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ latt_str(X1)
| join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2347_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| element(sk1_esk93_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_1,axiom,
( element(sk1_esk93_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_2347]) ).
cnf(c_0_2347_2,axiom,
( ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk93_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2347_3,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk93_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2348_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk176_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2349_0,axiom,
( sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| sk1_esk181_3(X2,X1,X3) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_1,axiom,
( sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_2,axiom,
( ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ ordinal(X2)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_3,axiom,
( ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1)
| ~ in(X3,sk1_esk180_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_4,axiom,
( ~ in(X3,sk1_esk180_2(X2,X1))
| ~ ordinal(X2)
| ~ element(X1,powerset(powerset(succ(X2))))
| sk1_esk181_3(X2,X1,X3) = X3
| sk1_esk175_2(X2,X1) = sk1_esk177_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2350_0,axiom,
( singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
( singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2352_0,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_2,axiom,
( sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( sk1_esk157_1(X1) != sk1_esk156_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2354_0,axiom,
( ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2355_0,axiom,
( ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2356_0,axiom,
( empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_1,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_2,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_3,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2357_0,axiom,
( empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_1,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_2,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_3,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2357_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2358_0,axiom,
( empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_1,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_2,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_3,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2359_0,axiom,
( in(sk1_esk207_2(X2,X1),X2)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| in(sk1_esk207_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| in(sk1_esk207_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2360_0,axiom,
( in(sk1_esk208_2(X2,X1),X2)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| in(sk1_esk208_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| in(sk1_esk208_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2361_0,axiom,
( sk1_esk155_1(X1) = sk1_esk156_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| sk1_esk155_1(X1) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
( sk1_esk155_1(X1) = sk1_esk157_1(X1)
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_1,axiom,
( singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk164_3(X1,X3,X2)) = sk1_esk165_3(X1,X3,X2)
| sk1_esk155_1(X1) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2363_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_2363]) ).
cnf(c_0_2363_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_2363]) ).
cnf(c_0_2363_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_2363]) ).
cnf(c_0_2363_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_2363]) ).
cnf(c_0_2363_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_2363]) ).
cnf(c_0_2363_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_2363]) ).
cnf(c_0_2364_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2365_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2366_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_2,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2367_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2369_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_2,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2370_0,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_1,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_2,axiom,
( sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2371_0,axiom,
( in(sk1_esk207_2(X2,X1),X2)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| in(sk1_esk207_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| in(sk1_esk207_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2372_0,axiom,
( in(sk1_esk208_2(X2,X1),X2)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| in(sk1_esk208_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| in(sk1_esk208_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2373_0,axiom,
( X1 = inclusion_relation(X2)
| subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_1,axiom,
( subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| X1 = inclusion_relation(X2)
| in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_2,axiom,
( in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1)
| subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1)
| subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2373_4,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| in(ordered_pair(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1)),X1)
| subset(sk1_esk33_2(X2,X1),sk1_esk34_2(X2,X1))
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2374_0,axiom,
( in(sk1_esk158_1(X1),X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2374_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk158_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2374_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk158_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2375_0,axiom,
( in(sk1_esk160_1(X1),X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2375_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk160_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2375_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| in(sk1_esk160_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2376_0,axiom,
( X2 = fiber(X1,X3)
| in(sk1_esk32_3(X1,X3,X2),X2)
| ~ relation(X1)
| sk1_esk32_3(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_1,axiom,
( in(sk1_esk32_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| ~ relation(X1)
| sk1_esk32_3(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_2,axiom,
( ~ relation(X1)
| in(sk1_esk32_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3)
| sk1_esk32_3(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_3,axiom,
( sk1_esk32_3(X1,X3,X2) != X3
| ~ relation(X1)
| in(sk1_esk32_3(X1,X3,X2),X2)
| X2 = fiber(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2377_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_2377]) ).
cnf(c_0_2377_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_2377]) ).
cnf(c_0_2377_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_2377]) ).
cnf(c_0_2377_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_2377]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2379_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_2379]) ).
cnf(c_0_2379_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_2379]) ).
cnf(c_0_2379_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_2379]) ).
cnf(c_0_2379_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_2379]) ).
cnf(c_0_2380_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_2380]) ).
cnf(c_0_2380_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_2380]) ).
cnf(c_0_2380_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_2380]) ).
cnf(c_0_2380_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_2380]) ).
cnf(c_0_2381_0,axiom,
( empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_1,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| empty(X2)
| ~ relation(X1)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_2,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| empty(X2)
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_3,axiom,
( sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| sk1_esk128_2(X2,X1) != sk1_esk127_2(X2,X1)
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2382_0,axiom,
( ordinal(sk1_esk207_2(X2,X1))
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk207_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk207_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2383_0,axiom,
( ordinal(sk1_esk208_2(X2,X1))
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk208_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ordinal(sk1_esk208_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2384_0,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_1,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_2,axiom,
( sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2385_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2385_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2386_0,axiom,
( sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2387_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2388_0,axiom,
( sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_1,axiom,
( in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk210_3(X2,X1,X3),succ(X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2389_0,axiom,
( singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2390_0,axiom,
( singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2390_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2390_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2391_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_2,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2392_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2393_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2394_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_2,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2395_0,axiom,
( empty(X2)
| in(sk1_esk126_2(X2,X1),X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_1,axiom,
( in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_2,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2395_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| in(sk1_esk126_2(X2,X1),X2)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2396_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2397_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(sk1_esk132_3(X2,X1,X3),X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_2,axiom,
( in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_3,axiom,
( ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(sk1_esk132_3(X2,X1,X3),X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2398_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2398_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| in(X3,sk1_esk133_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2398_2,axiom,
( in(X3,sk1_esk133_3(X2,X1,X3))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2398_3,axiom,
( ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2398_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| in(X3,sk1_esk133_3(X2,X1,X3))
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2399_0,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2399_1,axiom,
( sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2399_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2400_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_2400]) ).
cnf(c_0_2400_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_2400]) ).
cnf(c_0_2400_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_2400]) ).
cnf(c_0_2400_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_2400]) ).
cnf(c_0_2400_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_2400]) ).
cnf(c_0_2400_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_2400]) ).
cnf(c_0_2401_0,axiom,
( ordinal(sk1_esk207_2(X2,X1))
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| ordinal(sk1_esk207_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2401_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ordinal(sk1_esk207_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2402_0,axiom,
( in(sk1_esk207_2(X2,X1),X2)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| in(sk1_esk207_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| in(sk1_esk207_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2403_0,axiom,
( ordinal(sk1_esk208_2(X2,X1))
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| ordinal(sk1_esk208_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ordinal(sk1_esk208_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2404_0,axiom,
( in(sk1_esk208_2(X2,X1),X2)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| in(sk1_esk208_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| in(sk1_esk208_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2405_0,axiom,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sk1_esk74_2(X1,X2)),X1)
| ~ in(sk1_esk74_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_1,axiom,
( ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(ordered_pair(X3,sk1_esk74_2(X1,X2)),X1)
| ~ in(sk1_esk74_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_2,axiom,
( ~ in(ordered_pair(X3,sk1_esk74_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk74_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_3,axiom,
( ~ in(sk1_esk74_2(X1,X2),X2)
| ~ in(ordered_pair(X3,sk1_esk74_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2406_0,axiom,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk60_2(X1,X2),X3),X1)
| ~ in(sk1_esk60_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_1,axiom,
( ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(ordered_pair(sk1_esk60_2(X1,X2),X3),X1)
| ~ in(sk1_esk60_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_2,axiom,
( ~ in(ordered_pair(sk1_esk60_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(sk1_esk60_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_3,axiom,
( ~ in(sk1_esk60_2(X1,X2),X2)
| ~ in(ordered_pair(sk1_esk60_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2407_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2408_0,axiom,
( sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2409_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2409_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2409_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2409_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2410_0,axiom,
( sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_1,axiom,
( in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| in(sk1_esk211_3(X2,X1,X3),X2)
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2411_0,axiom,
( sk1_esk155_1(X1) = sk1_esk156_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2412_0,axiom,
( sk1_esk155_1(X1) = sk1_esk157_1(X1)
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2412_1,axiom,
( in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2412_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk163_3(X1,X3,X2),cartesian_product2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2413_0,axiom,
( empty_carrier(X1)
| below(X1,X2,X3)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_1,axiom,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_2,axiom,
( ~ join_semilatt_str(X1)
| below(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| below(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_4,axiom,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| below(X1,X2,X3)
| empty_carrier(X1)
| join(X1,X2,X3) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2413_5,axiom,
( join(X1,X2,X3) != X3
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| below(X1,X2,X3)
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2414_0,axiom,
( empty_carrier(X1)
| join(X1,X2,X3) = X3
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_1,axiom,
( join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_2,axiom,
( ~ join_semilatt_str(X1)
| join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_4,axiom,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ below(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2414_5,axiom,
( ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| join(X1,X2,X3) = X3
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2415_0,axiom,
( ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2416_0,axiom,
( ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2417_0,axiom,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk28_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_1,axiom,
( in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk28_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_2,axiom,
( X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set
| ~ in(X3,sk1_esk28_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_3,axiom,
( ~ in(X3,sk1_esk28_3(X1,X2,X3))
| X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2418_0,axiom,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2418_1,axiom,
( ~ relation_of2(X3,X1,X2)
| element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2419_0,axiom,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2419_1,axiom,
( ~ relation_of2(X3,X1,X2)
| element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2421_0,axiom,
( ordinal(sk1_esk207_2(X2,X1))
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2421_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| ordinal(sk1_esk207_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2421_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2421_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ordinal(sk1_esk207_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2422_0,axiom,
( ordinal(sk1_esk208_2(X2,X1))
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| ordinal(sk1_esk208_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ordinal(sk1_esk208_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2423_0,axiom,
( empty(X2)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_1,axiom,
( sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_2,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| sk1_esk129_2(X2,X1) = sk1_esk126_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2424_0,axiom,
( empty(X2)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_1,axiom,
( sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_2,axiom,
( sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ relation(X1)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_3,axiom,
( ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2)
| ~ in(X3,sk1_esk131_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_4,axiom,
( ~ in(X3,sk1_esk131_2(X2,X1))
| ~ relation(X1)
| sk1_esk132_3(X2,X1,X3) = sk1_esk133_3(X2,X1,X3)
| sk1_esk126_2(X2,X1) = sk1_esk130_2(X2,X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2425_0,axiom,
( element(meet_commut(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_1,axiom,
( empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_4,axiom,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2425_5,axiom,
( ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2426_0,axiom,
( element(join_commut(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_1,axiom,
( empty_carrier(X1)
| element(join_commut(X1,X2,X3),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join_commut(X1,X2,X3),the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join_commut(X1,X2,X3),the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_4,axiom,
( ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join_commut(X1,X2,X3),the_carrier(X1))
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_5,axiom,
( ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join_commut(X1,X2,X3),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2427_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2428_0,axiom,
( sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2428_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2429_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2430_0,axiom,
( sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_1,axiom,
( ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| ordinal(sk1_esk211_3(X2,X1,X3))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2431_0,axiom,
( in(sk1_esk158_1(X1),X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| in(sk1_esk158_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| in(sk1_esk158_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2432_0,axiom,
( in(sk1_esk160_1(X1),X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| in(sk1_esk160_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| in(sk1_esk160_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2433_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_2433]) ).
cnf(c_0_2434_0,axiom,
( element(meet(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_1,axiom,
( empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_4,axiom,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2435_0,axiom,
( element(join(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_1,axiom,
( empty_carrier(X1)
| element(join(X1,X2,X3),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join(X1,X2,X3),the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join(X1,X2,X3),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2435_4,axiom,
( ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| element(join(X1,X2,X3),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2436_0,axiom,
( singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2436_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2436_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2437_0,axiom,
( singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2437_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2437_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2438_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_2438]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2439_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_2439]) ).
cnf(c_0_2440_0,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2440_1,axiom,
( sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2440_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2441_0,axiom,
( ordinal(sk1_esk216_3(X3,X2,X1))
| ~ epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2441_1,axiom,
( ~ epred1_3(X1,X2,X3)
| ordinal(sk1_esk216_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2442_0,axiom,
( ordinal(sk1_esk218_3(X3,X2,X1))
| ~ epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_1,axiom,
( ~ epred1_3(X1,X2,X3)
| ordinal(sk1_esk218_3(X3,X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
( X2 = relation_rng(X1)
| in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| in(sk1_esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_1,axiom,
( in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| in(sk1_esk74_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_2,axiom,
( in(sk1_esk74_2(X1,X2),X2)
| in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_3,axiom,
( ~ relation(X1)
| in(sk1_esk74_2(X1,X2),X2)
| in(ordered_pair(sk1_esk75_2(X1,X2),sk1_esk74_2(X1,X2)),X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
( X2 = relation_dom(X1)
| in(ordered_pair(sk1_esk60_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| in(sk1_esk60_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_1,axiom,
( in(ordered_pair(sk1_esk60_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| in(sk1_esk60_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_2,axiom,
( in(sk1_esk60_2(X1,X2),X2)
| in(ordered_pair(sk1_esk60_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_3,axiom,
( ~ relation(X1)
| in(sk1_esk60_2(X1,X2),X2)
| in(ordered_pair(sk1_esk60_2(X1,X2),sk1_esk61_2(X1,X2)),X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2445_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_2445]) ).
cnf(c_0_2446_0,axiom,
( sk1_esk155_1(X1) = sk1_esk156_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| sk1_esk155_1(X1) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
( ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| in(X2,sk1_esk162_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_2447]) ).
cnf(c_0_2447_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_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_2447]) ).
cnf(c_0_2447_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_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_2447]) ).
cnf(c_0_2447_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2448_0,axiom,
( sk1_esk155_1(X1) = sk1_esk157_1(X1)
| in(sk1_esk164_3(X1,X3,X2),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2448_1,axiom,
( in(sk1_esk164_3(X1,X3,X2),X1)
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2448_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk164_3(X1,X3,X2),X1)
| sk1_esk155_1(X1) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2449_0,axiom,
( ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| in(X2,sk1_esk162_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_2449]) ).
cnf(c_0_2449_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_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_2449]) ).
cnf(c_0_2449_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_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_2449]) ).
cnf(c_0_2449_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2449_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2449_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2449_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2450_0,axiom,
( meet(X1,X2,X3) = meet_commut(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_1,axiom,
( empty_carrier(X1)
| meet(X1,X2,X3) = meet_commut(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet(X1,X2,X3) = meet_commut(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet(X1,X2,X3) = meet_commut(X1,X2,X3)
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_4,axiom,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet(X1,X2,X3) = meet_commut(X1,X2,X3)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_5,axiom,
( ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet(X1,X2,X3) = meet_commut(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2451_0,axiom,
( join(X1,X2,X3) = join_commut(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_1,axiom,
( empty_carrier(X1)
| join(X1,X2,X3) = join_commut(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join(X1,X2,X3) = join_commut(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join(X1,X2,X3) = join_commut(X1,X2,X3)
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_4,axiom,
( ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join(X1,X2,X3) = join_commut(X1,X2,X3)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_5,axiom,
( ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join(X1,X2,X3) = join_commut(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2452_0,axiom,
( meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_1,axiom,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_4,axiom,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ meet_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2452_5,axiom,
( ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2453_0,axiom,
( join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_1,axiom,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_2,axiom,
( ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_3,axiom,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_4,axiom,
( ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ join_commutative(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_5,axiom,
( ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2454_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_2454]) ).
cnf(c_0_2454_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_2454]) ).
cnf(c_0_2454_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_2454]) ).
cnf(c_0_2455_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),sk1_esk57_2(X1,X2))
| ~ in(X3,sk1_esk57_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ disjoint(fiber(X1,X3),sk1_esk57_2(X1,X2))
| ~ in(X3,sk1_esk57_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_2,axiom,
( ~ disjoint(fiber(X1,X3),sk1_esk57_2(X1,X2))
| ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ in(X3,sk1_esk57_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_3,axiom,
( ~ in(X3,sk1_esk57_2(X1,X2))
| ~ disjoint(fiber(X1,X3),sk1_esk57_2(X1,X2))
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2456_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_2456]) ).
cnf(c_0_2456_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_2456]) ).
cnf(c_0_2456_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_2456]) ).
cnf(c_0_2456_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_2456]) ).
cnf(c_0_2457_0,axiom,
( in(sk1_esk158_1(X1),X1)
| in(X2,sk1_esk162_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_2457]) ).
cnf(c_0_2457_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk158_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_2457]) ).
cnf(c_0_2457_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk158_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_2457]) ).
cnf(c_0_2457_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk158_1(X1),X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk158_1(X1),X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk158_1(X1),X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2457_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk158_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2458_0,axiom,
( in(sk1_esk160_1(X1),X1)
| in(X2,sk1_esk162_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_2458]) ).
cnf(c_0_2458_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk160_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_2458]) ).
cnf(c_0_2458_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk160_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_2458]) ).
cnf(c_0_2458_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk160_1(X1),X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk160_1(X1),X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk160_1(X1),X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| in(sk1_esk160_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2459_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_2459]) ).
cnf(c_0_2459_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_2459]) ).
cnf(c_0_2459_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_2459]) ).
cnf(c_0_2459_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_2459]) ).
cnf(c_0_2459_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_2459]) ).
cnf(c_0_2460_0,axiom,
( singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| in(X2,sk1_esk162_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_2460]) ).
cnf(c_0_2460_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_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_2460]) ).
cnf(c_0_2460_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_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_2460]) ).
cnf(c_0_2460_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2461_0,axiom,
( singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| in(X2,sk1_esk162_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_2461]) ).
cnf(c_0_2461_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_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_2461]) ).
cnf(c_0_2461_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_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_2461]) ).
cnf(c_0_2461_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2462_0,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_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_2462]) ).
cnf(c_0_2462_1,axiom,
( sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(X2,sk1_esk162_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_2462]) ).
cnf(c_0_2462_2,axiom,
( X4 != singleton(X5)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(X2,sk1_esk162_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_2462]) ).
cnf(c_0_2462_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(X2,sk1_esk162_2(X1,X3))
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(X2,sk1_esk162_2(X1,X3))
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(X2,sk1_esk162_2(X1,X3))
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2463_0,axiom,
( X3 = empty_set
| in(sk1_esk56_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2463_1,axiom,
( in(sk1_esk56_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_2463]) ).
cnf(c_0_2463_2,axiom,
( ~ relation(X1)
| in(sk1_esk56_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2463_3,axiom,
( ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| in(sk1_esk56_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2463_4,axiom,
( ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1)
| in(sk1_esk56_3(X1,X2,X3),X3)
| X3 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2464_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(sk1_esk29_2(X1,X2),X2)
| ~ in(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2464_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk29_2(X1,X2),X2)
| ~ in(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2464_2,axiom,
( ~ in(sk1_esk29_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2464_3,axiom,
( ~ in(sk1_esk29_2(X1,X2),sk1_esk30_2(X1,X2))
| ~ in(sk1_esk29_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2465_0,axiom,
( subset(X1,X2)
| in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_1,axiom,
( in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk53_2(X1,X2),sk1_esk54_2(X1,X2)),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2466_0,axiom,
( in(sk1_esk69_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_2466]) ).
cnf(c_0_2466_1,axiom,
( ~ function(X1)
| in(sk1_esk69_3(X1,X2,X3),relation_dom(X1))
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2466_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk69_3(X1,X2,X3),relation_dom(X1))
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2466_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk69_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2466_4,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| in(sk1_esk69_3(X1,X2,X3),relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2467_0,axiom,
( sk1_esk155_1(X1) = sk1_esk156_1(X1)
| in(X2,sk1_esk162_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_2467]) ).
cnf(c_0_2467_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_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_2467]) ).
cnf(c_0_2467_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_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_2467]) ).
cnf(c_0_2467_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2468_0,axiom,
( sk1_esk155_1(X1) = sk1_esk157_1(X1)
| in(X2,sk1_esk162_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_2468]) ).
cnf(c_0_2468_1,axiom,
( in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_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_2468]) ).
cnf(c_0_2468_2,axiom,
( X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_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_2468]) ).
cnf(c_0_2468_3,axiom,
( ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ordered_pair(X5,X4) != X2
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2468_4,axiom,
( ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| X6 != X2
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2468_5,axiom,
( X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ~ in(X6,cartesian_product2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2468_6,axiom,
( ~ in(X6,cartesian_product2(X1,X3))
| X6 != X2
| ordered_pair(X5,X4) != X2
| ~ in(X5,X1)
| X4 != singleton(X5)
| in(X2,sk1_esk162_2(X1,X3))
| sk1_esk155_1(X1) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2469_0,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_1,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_2,axiom,
( sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2470_0,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_1,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_2,axiom,
( sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2471_0,axiom,
( apply(X1,sk1_esk69_3(X1,X2,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_1,axiom,
( ~ function(X1)
| apply(X1,sk1_esk69_3(X1,X2,X3)) = X3
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk69_3(X1,X2,X3)) = X3
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_3,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk69_3(X1,X2,X3)) = X3
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_4,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk69_3(X1,X2,X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2472_0,axiom,
( in(sk1_esk207_2(X2,X1),X2)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| in(sk1_esk207_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| in(sk1_esk207_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2473_0,axiom,
( in(sk1_esk207_2(X2,X1),X2)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| in(sk1_esk207_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| in(sk1_esk207_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2474_0,axiom,
( in(sk1_esk208_2(X2,X1),X2)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| in(sk1_esk208_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| in(sk1_esk208_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2475_0,axiom,
( in(sk1_esk208_2(X2,X1),X2)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| in(sk1_esk208_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| in(sk1_esk208_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2476_0,axiom,
( is_transitive_in(X1,X2)
| in(ordered_pair(sk1_esk90_2(X1,X2),sk1_esk91_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_1,axiom,
( in(ordered_pair(sk1_esk90_2(X1,X2),sk1_esk91_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk90_2(X1,X2),sk1_esk91_2(X1,X2)),X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2477_0,axiom,
( is_transitive_in(X1,X2)
| in(ordered_pair(sk1_esk91_2(X1,X2),sk1_esk92_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_1,axiom,
( in(ordered_pair(sk1_esk91_2(X1,X2),sk1_esk92_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk91_2(X1,X2),sk1_esk92_2(X1,X2)),X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2478_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk63_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_1,axiom,
( in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk63_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk62_2(X1,X2),sk1_esk63_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2479_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(ordered_pair(sk1_esk63_2(X1,X2),sk1_esk62_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_1,axiom,
( in(ordered_pair(sk1_esk63_2(X1,X2),sk1_esk62_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk63_2(X1,X2),sk1_esk62_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2482_0,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_1,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_2,axiom,
( sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_3,axiom,
( ~ in(X4,X2)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| sk1_esk206_2(X2,X1) != sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2483_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X2,sk1_esk169_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_1,axiom,
( in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_2,axiom,
( in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_3,axiom,
( ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_4,axiom,
( ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2484_0,axiom,
( X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk70_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk70_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_1,axiom,
( ~ function(X1)
| X2 = relation_rng(X1)
| ~ relation(X1)
| sk1_esk70_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk70_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| sk1_esk70_2(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk70_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_3,axiom,
( sk1_esk70_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| ~ in(X3,relation_dom(X1))
| ~ in(sk1_esk70_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_4,axiom,
( ~ in(X3,relation_dom(X1))
| sk1_esk70_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk70_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_5,axiom,
( ~ in(sk1_esk70_2(X1,X2),X2)
| ~ in(X3,relation_dom(X1))
| sk1_esk70_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2485_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| in(sk1_esk170_2(X1,X2),succ(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_1,axiom,
( in(sk1_esk170_2(X1,X2),succ(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_2,axiom,
( ~ ordinal(X1)
| in(sk1_esk170_2(X1,X2),succ(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| in(sk1_esk170_2(X1,X2),succ(X1))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2486_0,axiom,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_1,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2487_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_2487]) ).
cnf(c_0_2488_0,axiom,
( in(sk1_esk207_2(X2,X1),X2)
| in(X3,sk1_esk209_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_2488]) ).
cnf(c_0_2488_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_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_2488]) ).
cnf(c_0_2488_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_2(X2,X1),X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_2(X2,X1),X2)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_2(X2,X1),X2)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_2(X2,X1),X2)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk207_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2489_0,axiom,
( in(sk1_esk208_2(X2,X1),X2)
| in(X3,sk1_esk209_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_2489]) ).
cnf(c_0_2489_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_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_2489]) ).
cnf(c_0_2489_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_2(X2,X1),X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_2(X2,X1),X2)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_2(X2,X1),X2)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_2(X2,X1),X2)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| in(sk1_esk208_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2490_0,axiom,
( ordinal(sk1_esk207_2(X2,X1))
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| ordinal(sk1_esk207_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ordinal(sk1_esk207_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2491_0,axiom,
( ordinal(sk1_esk207_2(X2,X1))
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| ordinal(sk1_esk207_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ordinal(sk1_esk207_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2492_0,axiom,
( ordinal(sk1_esk208_2(X2,X1))
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| ordinal(sk1_esk208_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ordinal(sk1_esk208_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2493_0,axiom,
( ordinal(sk1_esk208_2(X2,X1))
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| ordinal(sk1_esk208_2(X2,X1))
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ordinal(sk1_esk208_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2494_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk65_2(X2,X1),X3)
| ~ in(sk1_esk65_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2494_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk65_2(X2,X1),X3)
| ~ in(sk1_esk65_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2494_2,axiom,
( ~ in(sk1_esk65_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk65_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2494_3,axiom,
( ~ in(sk1_esk65_2(X2,X1),X1)
| ~ in(sk1_esk65_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2495_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2495_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2495_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2495_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2495]) ).
cnf(c_0_2496_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2496_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2496_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2496_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2496]) ).
cnf(c_0_2497_0,axiom,
( sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2497_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2497_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2497_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2498_0,axiom,
( sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2498_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2498_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2498_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2498]) ).
cnf(c_0_2499_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2500_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2500_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2500_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2500_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2501_0,axiom,
( sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| sk1_esk210_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_1,axiom,
( sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_2,axiom,
( ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk210_3(X2,X1,X3) = X3
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2502_0,axiom,
( sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| sk1_esk211_3(X2,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_1,axiom,
( sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_2,axiom,
( ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X3,sk1_esk209_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2502_3,axiom,
( ~ in(X3,sk1_esk209_2(X2,X1))
| ~ ordinal(X1)
| sk1_esk211_3(X2,X1,X3) = X3
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2503_0,axiom,
( in(X3,sk1_esk64_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2503_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk64_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2503_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk64_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2503]) ).
cnf(c_0_2504_0,axiom,
( in(sk1_esk64_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2504_1,axiom,
( X1 != union(X2)
| in(sk1_esk64_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2504_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk64_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2505_0,axiom,
( ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2505_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2505_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk158_1(X1),sk1_esk159_1(X1)) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2506_0,axiom,
( ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2506_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2506_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| ordered_pair(sk1_esk160_1(X1),sk1_esk161_1(X1)) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2507_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_2507]) ).
cnf(c_0_2507_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_2507]) ).
cnf(c_0_2507_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_2507]) ).
cnf(c_0_2507_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_2507]) ).
cnf(c_0_2507_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_2507]) ).
cnf(c_0_2507_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_2507]) ).
cnf(c_0_2508_0,axiom,
( ordinal(sk1_esk207_2(X2,X1))
| in(X3,sk1_esk209_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_2508]) ).
cnf(c_0_2508_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_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_2508]) ).
cnf(c_0_2508_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_2(X2,X1))
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_2(X2,X1))
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_2(X2,X1))
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_2(X2,X1))
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk207_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2509_0,axiom,
( ordinal(sk1_esk208_2(X2,X1))
| in(X3,sk1_esk209_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_2509]) ).
cnf(c_0_2509_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_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_2509]) ).
cnf(c_0_2509_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_2(X2,X1))
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_2(X2,X1))
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_2(X2,X1))
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_2(X2,X1))
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| ordinal(sk1_esk208_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2511_0,axiom,
( X1 = empty_set
| in(X3,X2)
| in(sk1_esk28_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_1,axiom,
( in(X3,X2)
| X1 = empty_set
| in(sk1_esk28_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_2,axiom,
( in(sk1_esk28_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_3,axiom,
( X2 != set_meet(X1)
| in(sk1_esk28_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2512_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| in(X3,sk1_esk209_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_2512]) ).
cnf(c_0_2512_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_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_2512]) ).
cnf(c_0_2512_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2513_0,axiom,
( sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| in(X3,sk1_esk209_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_2513]) ).
cnf(c_0_2513_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_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_2513]) ).
cnf(c_0_2513_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk207_2(X2,X1) = sk1_esk205_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2514_0,axiom,
( sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| in(X3,sk1_esk209_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_2514]) ).
cnf(c_0_2514_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_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_2514]) ).
cnf(c_0_2514_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk204_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2515_0,axiom,
( sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| in(X3,sk1_esk209_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_2515]) ).
cnf(c_0_2515_1,axiom,
( in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_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_2515]) ).
cnf(c_0_2515_2,axiom,
( ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X4,X2)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_3,axiom,
( ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| X3 != X4
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_4,axiom,
( X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ ordinal(X4)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_5,axiom,
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| X5 != X3
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_6,axiom,
( X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1)
| ~ in(X5,succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_7,axiom,
( ~ in(X5,succ(X1))
| X5 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X2)
| ~ ordinal(X1)
| in(X3,sk1_esk209_2(X2,X1))
| sk1_esk208_2(X2,X1) = sk1_esk206_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2516_0,axiom,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_1,axiom,
( ~ relation_of2(X3,X1,X2)
| relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2517_0,axiom,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2517_1,axiom,
( ~ relation_of2(X3,X1,X2)
| relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2518_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ordinal(sk1_esk171_2(X1,X2))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_1,axiom,
( ordinal(sk1_esk171_2(X1,X2))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_2,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk171_2(X1,X2))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| ordinal(sk1_esk171_2(X1,X2))
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2519_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_2519]) ).
cnf(c_0_2519_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_2519]) ).
cnf(c_0_2519_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_2519]) ).
cnf(c_0_2519_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_2519]) ).
cnf(c_0_2519_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_2519]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2521_0,axiom,
( sk1_esk216_3(X3,X2,X1) = X2
| ~ epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2521_1,axiom,
( ~ epred1_3(X1,X2,X3)
| sk1_esk216_3(X3,X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2522_0,axiom,
( sk1_esk218_3(X3,X2,X1) = X1
| ~ epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2522_1,axiom,
( ~ epred1_3(X1,X2,X3)
| sk1_esk218_3(X3,X2,X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2523_0,axiom,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2523_1,axiom,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2524_0,axiom,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2524_1,axiom,
( ~ relation_of2(X1,X2,X3)
| relation_of2_as_subset(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2526_0,axiom,
( X2 = empty_set
| disjoint(fiber(X1,sk1_esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2526_1,axiom,
( disjoint(fiber(X1,sk1_esk43_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_2526]) ).
cnf(c_0_2526_2,axiom,
( ~ relation(X1)
| disjoint(fiber(X1,sk1_esk43_2(X1,X2)),X2)
| X2 = empty_set
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2526_3,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk43_2(X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2526_4,axiom,
( ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1)
| disjoint(fiber(X1,sk1_esk43_2(X1,X2)),X2)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2527_0,axiom,
( in(sk1_esk158_1(X1),X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2527_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| in(sk1_esk158_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2527_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| in(sk1_esk158_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2528_0,axiom,
( in(sk1_esk160_1(X1),X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2528_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| in(sk1_esk160_1(X1),X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2528_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| in(sk1_esk160_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2532_0,axiom,
( singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2532_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| singleton(sk1_esk158_1(X1)) = sk1_esk159_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2532]) ).
cnf(c_0_2533_0,axiom,
( singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2533_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| singleton(sk1_esk160_1(X1)) = sk1_esk161_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2533]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2536_0,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2536_1,axiom,
( sk1_esk157_1(X1) != sk1_esk156_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2536_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk157_1(X1) != sk1_esk156_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2537_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk36_2(X2,X1),X2)
| ~ in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_1,axiom,
( ~ subset(sk1_esk36_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_2,axiom,
( ~ in(sk1_esk36_2(X2,X1),X1)
| ~ subset(sk1_esk36_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2540_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_2540]) ).
cnf(c_0_2541_0,axiom,
( X1 = X2
| ~ in(sk1_esk212_2(X1,X2),X2)
| ~ in(sk1_esk212_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2541_1,axiom,
( ~ in(sk1_esk212_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk212_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2541_2,axiom,
( ~ in(sk1_esk212_2(X1,X2),X1)
| ~ in(sk1_esk212_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2542_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| sk1_esk170_2(X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_1,axiom,
( sk1_esk170_2(X1,X2) = X2
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_2,axiom,
( ~ ordinal(X1)
| sk1_esk170_2(X1,X2) = X2
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk170_2(X1,X2) = X2
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2543_0,axiom,
( epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| sk1_esk171_2(X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_1,axiom,
( sk1_esk171_2(X1,X2) = X2
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ ordinal(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_2,axiom,
( ~ ordinal(X1)
| sk1_esk171_2(X1,X2) = X2
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1))
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk171_2(X1,X2) = X2
| epred1_3(sk1_esk168_1(X1),sk1_esk167_1(X1),sk1_esk166_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2544_0,axiom,
( sk1_esk155_1(X1) = sk1_esk156_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| sk1_esk155_1(X1) = sk1_esk156_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| sk1_esk155_1(X1) = sk1_esk156_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2545_0,axiom,
( sk1_esk155_1(X1) = sk1_esk157_1(X1)
| sk1_esk163_3(X1,X3,X2) = X2
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_1,axiom,
( sk1_esk163_3(X1,X3,X2) = X2
| sk1_esk155_1(X1) = sk1_esk157_1(X1)
| ~ in(X2,sk1_esk162_2(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_2,axiom,
( ~ in(X2,sk1_esk162_2(X1,X3))
| sk1_esk163_3(X1,X3,X2) = X2
| sk1_esk155_1(X1) = sk1_esk157_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2546_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_2546]) ).
cnf(c_0_2546_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_2546]) ).
cnf(c_0_2546_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_2546]) ).
cnf(c_0_2546_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_2546]) ).
cnf(c_0_2546_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_2546]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2547_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_2547]) ).
cnf(c_0_2548_0,axiom,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_1,axiom,
( ~ relation_of2(X1,X2,X3)
| subset(X1,cartesian_product2(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2550_0,axiom,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2550_1,axiom,
( ~ join_semilatt_str(X1)
| quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2551_0,axiom,
( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2551_1,axiom,
( ~ join_semilatt_str(X1)
| relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2552_0,axiom,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_1,axiom,
( ~ meet_semilatt_str(X1)
| quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2553_0,axiom,
( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_1,axiom,
( ~ meet_semilatt_str(X1)
| relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2554_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_2554]) ).
cnf(c_0_2554_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_2554]) ).
cnf(c_0_2554_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_2554]) ).
cnf(c_0_2554_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_2554]) ).
cnf(c_0_2554_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_2554]) ).
cnf(c_0_2554_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_2554]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2556_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_2556]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2557_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_2557]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2559_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_2559]) ).
cnf(c_0_2560_0,axiom,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_1,axiom,
( ~ subset(X1,cartesian_product2(X2,X3))
| relation_of2(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2561_0,axiom,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_1,axiom,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2562_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),sk1_esk44_1(X1))
| ~ in(X2,sk1_esk44_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ disjoint(fiber(X1,X2),sk1_esk44_1(X1))
| ~ in(X2,sk1_esk44_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_2,axiom,
( ~ disjoint(fiber(X1,X2),sk1_esk44_1(X1))
| ~ relation(X1)
| well_founded_relation(X1)
| ~ in(X2,sk1_esk44_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_3,axiom,
( ~ in(X2,sk1_esk44_1(X1))
| ~ disjoint(fiber(X1,X2),sk1_esk44_1(X1))
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2563_0,axiom,
( X5 = X4
| X5 = X3
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_1,axiom,
( X5 = X3
| X5 = X4
| X5 = X2
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_2,axiom,
( X5 = X2
| X5 = X3
| X5 = X4
| X1 != unordered_triple(X2,X3,X4)
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_3,axiom,
( X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4
| ~ in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_4,axiom,
( ~ in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2565_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_2565]) ).
cnf(c_0_2565_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_2565]) ).
cnf(c_0_2565_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_2565]) ).
cnf(c_0_2565_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_2565]) ).
cnf(c_0_2565_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_2565]) ).
cnf(c_0_2566_0,axiom,
( X2 = relation_rng(X1)
| in(sk1_esk70_2(X1,X2),X2)
| apply(X1,sk1_esk71_2(X1,X2)) = sk1_esk70_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2566_1,axiom,
( in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1)
| apply(X1,sk1_esk71_2(X1,X2)) = sk1_esk70_2(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2566_2,axiom,
( apply(X1,sk1_esk71_2(X1,X2)) = sk1_esk70_2(X1,X2)
| in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2566_3,axiom,
( ~ function(X1)
| apply(X1,sk1_esk71_2(X1,X2)) = sk1_esk70_2(X1,X2)
| in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2566_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk71_2(X1,X2)) = sk1_esk70_2(X1,X2)
| in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2567_0,axiom,
( X1 = union(X2)
| in(sk1_esk65_2(X2,X1),X1)
| in(sk1_esk65_2(X2,X1),sk1_esk66_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_1,axiom,
( in(sk1_esk65_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk65_2(X2,X1),sk1_esk66_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_2,axiom,
( in(sk1_esk65_2(X2,X1),sk1_esk66_2(X2,X1))
| in(sk1_esk65_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2568_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_2568]) ).
cnf(c_0_2569_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_2569]) ).
cnf(c_0_2569_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_2569]) ).
cnf(c_0_2569_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_2569]) ).
cnf(c_0_2569_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_2569]) ).
cnf(c_0_2569_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_2569]) ).
cnf(c_0_2570_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk30_2(X1,X2),X1)
| ~ in(sk1_esk29_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk30_2(X1,X2),X1)
| ~ in(sk1_esk29_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_2,axiom,
( in(sk1_esk30_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk29_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_3,axiom,
( ~ in(sk1_esk29_2(X1,X2),X2)
| in(sk1_esk30_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2571_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk29_2(X1,X2),X3)
| in(sk1_esk29_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk29_2(X1,X2),X3)
| in(sk1_esk29_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_2,axiom,
( in(sk1_esk29_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk29_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_3,axiom,
( in(sk1_esk29_2(X1,X2),X2)
| in(sk1_esk29_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_4,axiom,
( ~ in(X3,X1)
| in(sk1_esk29_2(X1,X2),X2)
| in(sk1_esk29_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2572_0,axiom,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2573_0,axiom,
( ~ in(X1,X2)
| ~ in(X3,sk1_esk213_2(X1,X2))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_1,axiom,
( ~ in(X3,sk1_esk213_2(X1,X2))
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_2,axiom,
( ~ in(X3,X2)
| ~ in(X3,sk1_esk213_2(X1,X2))
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2575_0,axiom,
( X2 = relation_rng(X1)
| in(sk1_esk70_2(X1,X2),X2)
| in(sk1_esk71_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_1,axiom,
( in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1)
| in(sk1_esk71_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_2,axiom,
( in(sk1_esk71_2(X1,X2),relation_dom(X1))
| in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_3,axiom,
( ~ function(X1)
| in(sk1_esk71_2(X1,X2),relation_dom(X1))
| in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2575_4,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk71_2(X1,X2),relation_dom(X1))
| in(sk1_esk70_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2576_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2576_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2576_2,axiom,
( X5 != X2
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2577_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_2,axiom,
( X5 != X3
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2578_0,axiom,
( in(X5,X1)
| X1 != unordered_triple(X2,X3,X4)
| X5 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_1,axiom,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_2,axiom,
( X5 != X4
| X1 != unordered_triple(X2,X3,X4)
| in(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2580_0,axiom,
( in(X2,sk1_esk169_1(X1))
| in(X4,omega)
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_1,axiom,
( in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_2,axiom,
( ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_3,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| ~ in(X3,succ(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_4,axiom,
( ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| X3 != X2
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_5,axiom,
( X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| ~ ordinal(X4)
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_6,axiom,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1))
| X2 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2580_7,axiom,
( X2 != X4
| ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(X4,omega)
| in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2581_0,axiom,
( in(sk1_esk170_2(X1,X2),succ(X1))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_1,axiom,
( ~ ordinal(X1)
| in(sk1_esk170_2(X1,X2),succ(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_2,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk170_2(X1,X2),succ(X1))
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| in(sk1_esk170_2(X1,X2),succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2582_0,axiom,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2583_0,axiom,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2583_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(union_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2584_0,axiom,
( ordered_pair(sk1_esk24_2(X2,X1),sk1_esk25_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2584_1,axiom,
( ~ in(X1,X2)
| ordered_pair(sk1_esk24_2(X2,X1),sk1_esk25_2(X2,X1)) = X1
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2584_2,axiom,
( ~ relation(X2)
| ~ in(X1,X2)
| ordered_pair(sk1_esk24_2(X2,X1),sk1_esk25_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2585_0,axiom,
( X4 = pair_second(X1)
| ordered_pair(sk1_esk37_2(X1,X4),sk1_esk38_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_1,axiom,
( ordered_pair(sk1_esk37_2(X1,X4),sk1_esk38_2(X1,X4)) = X1
| X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_2,axiom,
( X1 != ordered_pair(X2,X3)
| ordered_pair(sk1_esk37_2(X1,X4),sk1_esk38_2(X1,X4)) = X1
| X4 = pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2586_0,axiom,
( X4 = pair_first(X1)
| ordered_pair(sk1_esk22_2(X1,X4),sk1_esk23_2(X1,X4)) = X1
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_1,axiom,
( ordered_pair(sk1_esk22_2(X1,X4),sk1_esk23_2(X1,X4)) = X1
| X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_2,axiom,
( X1 != ordered_pair(X2,X3)
| ordered_pair(sk1_esk22_2(X1,X4),sk1_esk23_2(X1,X4)) = X1
| X4 = pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2587_0,axiom,
( in(X3,sk1_esk215_2(X2,X1))
| ~ in(X1,sk1_esk214_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_1,axiom,
( ~ in(X1,sk1_esk214_1(X2))
| in(X3,sk1_esk215_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk214_1(X2))
| in(X3,sk1_esk215_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2588_0,axiom,
( in(sk1_esk150_1(X1),X1)
| in(X2,sk1_esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_1,axiom,
( in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2589_0,axiom,
( in(sk1_esk150_1(X1),X1)
| in(X2,sk1_esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_1,axiom,
( in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2590_0,axiom,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_2,axiom,
( X2 != fiber(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_3,axiom,
( ~ in(X4,X2)
| X2 != fiber(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2591_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_3,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2592_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_2592]) ).
cnf(c_0_2592_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_2592]) ).
cnf(c_0_2592_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_2592]) ).
cnf(c_0_2592_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_2592]) ).
cnf(c_0_2592_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_2592]) ).
cnf(c_0_2592_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_2592]) ).
cnf(c_0_2593_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2594_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2595_0,axiom,
( in(sk1_esk150_1(X1),X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2595_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2595_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2596_0,axiom,
( in(sk1_esk150_1(X1),X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2596_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2596_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2597_0,axiom,
( in(sk1_esk150_1(X1),X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2597_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2597_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2598_0,axiom,
( in(sk1_esk150_1(X1),X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2598_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2598_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2600_0,axiom,
( X1 = singleton(X2)
| sk1_esk31_2(X2,X1) != X2
| ~ in(sk1_esk31_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2600_1,axiom,
( sk1_esk31_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk31_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2600_2,axiom,
( ~ in(sk1_esk31_2(X2,X1),X1)
| sk1_esk31_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2601_0,axiom,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2601_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2602_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| in(X2,sk1_esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_1,axiom,
( in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2603_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| in(X2,sk1_esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_1,axiom,
( in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_2,axiom,
( X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2604_0,axiom,
( X2 = empty_set
| in(sk1_esk43_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_1,axiom,
( in(sk1_esk43_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_2604]) ).
cnf(c_0_2604_2,axiom,
( ~ relation(X1)
| in(sk1_esk43_2(X1,X2),X2)
| X2 = empty_set
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_3,axiom,
( ~ well_founded_relation(X1)
| ~ relation(X1)
| in(sk1_esk43_2(X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_4,axiom,
( ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1)
| in(sk1_esk43_2(X1,X2),X2)
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2605_0,axiom,
( X3 = X2
| ~ epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2605_1,axiom,
( ~ epred1_3(X1,X2,X3)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2606_0,axiom,
( X3 = X1
| ~ epred1_3(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_1,axiom,
( ~ epred1_3(X1,X2,X3)
| X3 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2607_0,axiom,
( in(X2,sk1_esk153_1(X1))
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_1,axiom,
( sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(X2,sk1_esk153_1(X1))
| X2 != singleton(X3)
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_2,axiom,
( X2 != singleton(X3)
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(X2,sk1_esk153_1(X1))
| ~ in(X3,X1)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_3,axiom,
( ~ in(X3,X1)
| X2 != singleton(X3)
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(X2,sk1_esk153_1(X1))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_4,axiom,
( ~ in(X3,X1)
| ~ in(X3,X1)
| X2 != singleton(X3)
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2608_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2608_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2608_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2609_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2609_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2609_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2610_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2610_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2610_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2611_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2611_1,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2611_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| in(sk1_esk154_2(X1,X2),X1)
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2612_0,axiom,
( X1 = union(X2)
| in(sk1_esk65_2(X2,X1),X1)
| in(sk1_esk66_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_1,axiom,
( in(sk1_esk65_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk66_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_2,axiom,
( in(sk1_esk66_2(X2,X1),X2)
| in(sk1_esk65_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2613_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk36_2(X2,X1),X2)
| in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2613_1,axiom,
( subset(sk1_esk36_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2613_2,axiom,
( in(sk1_esk36_2(X2,X1),X1)
| subset(sk1_esk36_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2614_0,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2614_1,axiom,
( sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2614_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(sk1_esk154_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2615_0,axiom,
( in(sk1_esk154_2(X1,X2),X1)
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_1,axiom,
( sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(sk1_esk154_2(X1,X2),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| in(sk1_esk154_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2616_0,axiom,
( in(sk1_esk150_1(X1),X1)
| singleton(sk1_esk154_2(X1,X2)) = X2
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_1,axiom,
( singleton(sk1_esk154_2(X1,X2)) = X2
| in(sk1_esk150_1(X1),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk154_2(X1,X2)) = X2
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2617_0,axiom,
( in(sk1_esk150_1(X1),X1)
| singleton(sk1_esk154_2(X1,X2)) = X2
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_1,axiom,
( singleton(sk1_esk154_2(X1,X2)) = X2
| in(sk1_esk150_1(X1),X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk154_2(X1,X2)) = X2
| in(sk1_esk150_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2618_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2619_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_2619]) ).
cnf(c_0_2619_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_2619]) ).
cnf(c_0_2619_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_2619]) ).
cnf(c_0_2619_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_2619]) ).
cnf(c_0_2619_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_2619]) ).
cnf(c_0_2619_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_2619]) ).
cnf(c_0_2620_0,axiom,
( ordinal(sk1_esk171_2(X1,X2))
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_1,axiom,
( ~ ordinal(X1)
| ordinal(sk1_esk171_2(X1,X2))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_2,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| ordinal(sk1_esk171_2(X1,X2))
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2620_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| ordinal(sk1_esk171_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2621_0,axiom,
( X1 = X2
| in(sk1_esk212_2(X1,X2),X2)
| in(sk1_esk212_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2621_1,axiom,
( in(sk1_esk212_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk212_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2621_2,axiom,
( in(sk1_esk212_2(X1,X2),X1)
| in(sk1_esk212_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2624_0,axiom,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_1,axiom,
( ~ relation(X1)
| X3 = X4
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2630_0,axiom,
( in(sk1_esk215_2(X2,X1),sk1_esk214_1(X2))
| ~ in(X1,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_1,axiom,
( ~ in(X1,sk1_esk214_1(X2))
| in(sk1_esk215_2(X2,X1),sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2631_0,axiom,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_1,axiom,
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2632_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| singleton(sk1_esk154_2(X1,X2)) = X2
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_1,axiom,
( singleton(sk1_esk154_2(X1,X2)) = X2
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk154_2(X1,X2)) = X2
| singleton(sk1_esk150_1(X1)) = sk1_esk151_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2633_0,axiom,
( singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| singleton(sk1_esk154_2(X1,X2)) = X2
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_1,axiom,
( singleton(sk1_esk154_2(X1,X2)) = X2
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2633_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| singleton(sk1_esk154_2(X1,X2)) = X2
| singleton(sk1_esk150_1(X1)) = sk1_esk152_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2634_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk55_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_1,axiom,
( ~ in(sk1_esk55_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2635_0,axiom,
( singleton(sk1_esk154_2(X1,X2)) = X2
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_1,axiom,
( sk1_esk152_1(X1) != sk1_esk151_1(X1)
| singleton(sk1_esk154_2(X1,X2)) = X2
| ~ in(X2,sk1_esk153_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_2,axiom,
( ~ in(X2,sk1_esk153_1(X1))
| sk1_esk152_1(X1) != sk1_esk151_1(X1)
| singleton(sk1_esk154_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2636_0,axiom,
( ordinal(sk1_esk195_0)
| in(sk1_esk198_2(X2,X1),X2)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_1,axiom,
( in(sk1_esk198_2(X2,X1),X2)
| ordinal(sk1_esk195_0)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| in(sk1_esk198_2(X2,X1),X2)
| ordinal(sk1_esk195_0) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2637_0,axiom,
( ordinal(sk1_esk196_0)
| in(sk1_esk198_2(X2,X1),X2)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_1,axiom,
( in(sk1_esk198_2(X2,X1),X2)
| ordinal(sk1_esk196_0)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| in(sk1_esk198_2(X2,X1),X2)
| ordinal(sk1_esk196_0) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2638_0,axiom,
( in(X1,sk1_esk214_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk214_1(X2))
| ~ in(X3,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_2,axiom,
( ~ in(X3,sk1_esk214_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2639_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2640_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2641_0,axiom,
( in(sk1_esk198_2(X2,X1),X2)
| sk1_esk196_0 != sk1_esk195_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2641_1,axiom,
( sk1_esk196_0 != sk1_esk195_0
| in(sk1_esk198_2(X2,X1),X2)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2641_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk196_0 != sk1_esk195_0
| in(sk1_esk198_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2642_0,axiom,
( in(X1,sk1_esk214_1(X2))
| are_equipotent(X1,sk1_esk214_1(X2))
| ~ subset(X1,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_1,axiom,
( are_equipotent(X1,sk1_esk214_1(X2))
| in(X1,sk1_esk214_1(X2))
| ~ subset(X1,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_2,axiom,
( ~ subset(X1,sk1_esk214_1(X2))
| are_equipotent(X1,sk1_esk214_1(X2))
| in(X1,sk1_esk214_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2643_0,axiom,
( sk1_esk194_0 = sk1_esk195_0
| in(sk1_esk198_2(X2,X1),X2)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2643_1,axiom,
( in(sk1_esk198_2(X2,X1),X2)
| sk1_esk194_0 = sk1_esk195_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2643_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| in(sk1_esk198_2(X2,X1),X2)
| sk1_esk194_0 = sk1_esk195_0 ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2644_0,axiom,
( sk1_esk194_0 = sk1_esk196_0
| in(sk1_esk198_2(X2,X1),X2)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2644_1,axiom,
( in(sk1_esk198_2(X2,X1),X2)
| sk1_esk194_0 = sk1_esk196_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2644_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| in(sk1_esk198_2(X2,X1),X2)
| sk1_esk194_0 = sk1_esk196_0 ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2645_0,axiom,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2645_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2647_0,axiom,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2647_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| meet_of_subsets(X1,X2) = set_meet(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2648_0,axiom,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2648_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| union_of_subsets(X1,X2) = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2649_0,axiom,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_1,axiom,
( ~ element(X3,powerset(X2))
| element(X1,X2)
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_2,axiom,
( ~ in(X1,X3)
| ~ element(X3,powerset(X2))
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2650_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2650_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2650_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2651_0,axiom,
( function(X1)
| in(ordered_pair(sk1_esk19_1(X1),sk1_esk20_1(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2651_1,axiom,
( in(ordered_pair(sk1_esk19_1(X1),sk1_esk20_1(X1)),X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2652_0,axiom,
( function(X1)
| in(ordered_pair(sk1_esk19_1(X1),sk1_esk21_1(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2652_1,axiom,
( in(ordered_pair(sk1_esk19_1(X1),sk1_esk21_1(X1)),X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2653_0,axiom,
( X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ subset(X1,sk1_esk72_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_1,axiom,
( ~ in(empty_set,X1)
| X1 = omega
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ subset(X1,sk1_esk72_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_2,axiom,
( ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| X1 = omega
| ~ ordinal(X1)
| ~ subset(X1,sk1_esk72_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_3,axiom,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| X1 = omega
| ~ subset(X1,sk1_esk72_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2653_4,axiom,
( ~ subset(X1,sk1_esk72_1(X1))
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| X1 = omega ),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2654_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2654_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2655_0,axiom,
( sk1_esk170_2(X1,X2) = X2
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_1,axiom,
( ~ ordinal(X1)
| sk1_esk170_2(X1,X2) = X2
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_2,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| sk1_esk170_2(X1,X2) = X2
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2655_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| sk1_esk170_2(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2656_0,axiom,
( sk1_esk171_2(X1,X2) = X2
| ~ ordinal(X1)
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_1,axiom,
( ~ ordinal(X1)
| sk1_esk171_2(X1,X2) = X2
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_2,axiom,
( sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| sk1_esk171_2(X1,X2) = X2
| ~ in(X2,sk1_esk169_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2656_3,axiom,
( ~ in(X2,sk1_esk169_1(X1))
| sk1_esk168_1(X1) != sk1_esk167_1(X1)
| ~ ordinal(X1)
| sk1_esk171_2(X1,X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2657_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| sk1_esk76_2(X1,X2) != sk1_esk77_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| sk1_esk76_2(X1,X2) != sk1_esk77_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2657_2,axiom,
( sk1_esk76_2(X1,X2) != sk1_esk77_2(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2658_0,axiom,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| sk1_esk63_2(X1,X2) != sk1_esk62_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2658_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,X2)
| sk1_esk63_2(X1,X2) != sk1_esk62_2(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2658_2,axiom,
( sk1_esk63_2(X1,X2) != sk1_esk62_2(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2659_0,axiom,
( in(sk1_esk213_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2659_1,axiom,
( ~ in(X1,X2)
| in(sk1_esk213_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2660_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2660]) ).
cnf(c_0_2660_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2660]) ).
cnf(c_0_2660_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2660]) ).
cnf(c_0_2661_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk90_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2661_1,axiom,
( in(sk1_esk90_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2661_2,axiom,
( ~ relation(X1)
| in(sk1_esk90_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2662_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk91_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2662_1,axiom,
( in(sk1_esk91_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2662_2,axiom,
( ~ relation(X1)
| in(sk1_esk91_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2663_0,axiom,
( is_transitive_in(X1,X2)
| in(sk1_esk92_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2663_1,axiom,
( in(sk1_esk92_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2663_2,axiom,
( ~ relation(X1)
| in(sk1_esk92_2(X1,X2),X2)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2664_0,axiom,
( is_connected_in(X1,X2)
| in(sk1_esk76_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2664_1,axiom,
( in(sk1_esk76_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2664_2,axiom,
( ~ relation(X1)
| in(sk1_esk76_2(X1,X2),X2)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
cnf(c_0_2665_0,axiom,
( is_connected_in(X1,X2)
| in(sk1_esk77_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2665_1,axiom,
( in(sk1_esk77_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2665_2,axiom,
( ~ relation(X1)
| in(sk1_esk77_2(X1,X2),X2)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2666_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(sk1_esk62_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2666_1,axiom,
( in(sk1_esk62_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2666_2,axiom,
( ~ relation(X1)
| in(sk1_esk62_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2666]) ).
cnf(c_0_2667_0,axiom,
( is_antisymmetric_in(X1,X2)
| in(sk1_esk63_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_1,axiom,
( in(sk1_esk63_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2667_2,axiom,
( ~ relation(X1)
| in(sk1_esk63_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2667]) ).
cnf(c_0_2668_0,axiom,
( is_well_founded_in(X1,X2)
| subset(sk1_esk57_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_1,axiom,
( subset(sk1_esk57_2(X1,X2),X2)
| is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2668_2,axiom,
( ~ relation(X1)
| subset(sk1_esk57_2(X1,X2),X2)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2668]) ).
cnf(c_0_2669_0,axiom,
( is_reflexive_in(X1,X2)
| in(sk1_esk27_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_1,axiom,
( in(sk1_esk27_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_2,axiom,
( ~ relation(X1)
| in(sk1_esk27_2(X1,X2),X2)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2670_0,axiom,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_1,axiom,
( ~ relation(X1)
| set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2671_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_2671]) ).
cnf(c_0_2671_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_2671]) ).
cnf(c_0_2671_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_2671]) ).
cnf(c_0_2671_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_2671]) ).
cnf(c_0_2672_0,axiom,
( X1 = inclusion_relation(X2)
| in(sk1_esk34_2(X2,X1),X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_1,axiom,
( in(sk1_esk34_2(X2,X1),X2)
| X1 = inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_2,axiom,
( ~ relation(X1)
| in(sk1_esk34_2(X2,X1),X2)
| X1 = inclusion_relation(X2)
| relation_field(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_3,axiom,
( relation_field(X1) != X2
| ~ relation(X1)
| in(sk1_esk34_2(X2,X1),X2)
| X1 = inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2673_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2673_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2673]) ).
cnf(c_0_2674_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2674_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2674]) ).
cnf(c_0_2675_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2675_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2676_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2676_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2677_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2677_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2677_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2678_0,axiom,
( X1 = singleton(X2)
| sk1_esk31_2(X2,X1) = X2
| in(sk1_esk31_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2678_1,axiom,
( sk1_esk31_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk31_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2678_2,axiom,
( in(sk1_esk31_2(X2,X1),X1)
| sk1_esk31_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2679_0,axiom,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2679_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2679]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2682_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2682_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2682_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2682]) ).
cnf(c_0_2683_0,axiom,
( one_to_one(X1)
| apply(X1,sk1_esk83_1(X1)) = apply(X1,sk1_esk82_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_1,axiom,
( apply(X1,sk1_esk83_1(X1)) = apply(X1,sk1_esk82_1(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_2,axiom,
( ~ function(X1)
| apply(X1,sk1_esk83_1(X1)) = apply(X1,sk1_esk82_1(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2683_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk83_1(X1)) = apply(X1,sk1_esk82_1(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2683]) ).
cnf(c_0_2684_0,axiom,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_1,axiom,
( ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2684_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2685_0,axiom,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_1,axiom,
( ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2686_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_2686]) ).
cnf(c_0_2686_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_2686]) ).
cnf(c_0_2686_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_2686]) ).
cnf(c_0_2686_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_2686]) ).
cnf(c_0_2687_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_2687]) ).
cnf(c_0_2687_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_2687]) ).
cnf(c_0_2687_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_2687]) ).
cnf(c_0_2687_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_2687]) ).
cnf(c_0_2688_0,axiom,
( ~ relation(X1)
| X2 != fiber(X1,X3)
| ~ in(X4,X2)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_1,axiom,
( X2 != fiber(X1,X3)
| ~ relation(X1)
| ~ in(X4,X2)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_2,axiom,
( ~ in(X4,X2)
| X2 != fiber(X1,X3)
| ~ relation(X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_3,axiom,
( X4 != X3
| ~ in(X4,X2)
| X2 != fiber(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2689_0,axiom,
( finite(X1)
| ~ in(relation_dom(X2),omega)
| relation_rng(X2) != X1
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_1,axiom,
( ~ in(relation_dom(X2),omega)
| finite(X1)
| relation_rng(X2) != X1
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_2,axiom,
( relation_rng(X2) != X1
| ~ in(relation_dom(X2),omega)
| finite(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_3,axiom,
( ~ function(X2)
| relation_rng(X2) != X1
| ~ in(relation_dom(X2),omega)
| finite(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| relation_rng(X2) != X1
| ~ in(relation_dom(X2),omega)
| finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2690_0,axiom,
( ordinal(sk1_esk195_0)
| in(X1,sk1_esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_1,axiom,
( in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk195_0)
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk195_0)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk195_0)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk195_0) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2691_0,axiom,
( ordinal(sk1_esk196_0)
| in(X1,sk1_esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_1,axiom,
( in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk196_0)
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk196_0)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk196_0)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2691_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| ordinal(sk1_esk196_0) ),
inference(literals_permutation,[status(thm)],[c_0_2691]) ).
cnf(c_0_2692_0,axiom,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2692_1,axiom,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2692_2,axiom,
( ~ empty(cartesian_product2(X1,X2))
| empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2692]) ).
cnf(c_0_2693_0,axiom,
( in(X1,sk1_esk197_1(X2))
| sk1_esk196_0 != sk1_esk195_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_1,axiom,
( sk1_esk196_0 != sk1_esk195_0
| in(X1,sk1_esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_2,axiom,
( ~ ordinal(X1)
| sk1_esk196_0 != sk1_esk195_0
| in(X1,sk1_esk197_1(X2))
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| sk1_esk196_0 != sk1_esk195_0
| in(X1,sk1_esk197_1(X2))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| sk1_esk196_0 != sk1_esk195_0
| in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2694_0,axiom,
( X1 = omega
| in(empty_set,sk1_esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_1,axiom,
( in(empty_set,sk1_esk72_1(X1))
| X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_2,axiom,
( ~ in(empty_set,X1)
| in(empty_set,sk1_esk72_1(X1))
| X1 = omega
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_3,axiom,
( ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| in(empty_set,sk1_esk72_1(X1))
| X1 = omega
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_4,axiom,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| in(empty_set,sk1_esk72_1(X1))
| X1 = omega ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2695_0,axiom,
( sk1_esk194_0 = sk1_esk195_0
| in(X1,sk1_esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_1,axiom,
( in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk195_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk195_0
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk195_0
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2695_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk195_0 ),
inference(literals_permutation,[status(thm)],[c_0_2695]) ).
cnf(c_0_2696_0,axiom,
( sk1_esk194_0 = sk1_esk196_0
| in(X1,sk1_esk197_1(X2))
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2696_1,axiom,
( in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk196_0
| ~ ordinal(X1)
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2696_2,axiom,
( ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk196_0
| X3 != X1
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2696_3,axiom,
( X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk196_0
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2696_4,axiom,
( ~ in(X3,X2)
| X3 != X1
| ~ ordinal(X1)
| in(X1,sk1_esk197_1(X2))
| sk1_esk194_0 = sk1_esk196_0 ),
inference(literals_permutation,[status(thm)],[c_0_2696]) ).
cnf(c_0_2697_0,axiom,
( subset(X1,X2)
| in(sk1_esk55_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2697_1,axiom,
( in(sk1_esk55_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2697]) ).
cnf(c_0_2698_0,axiom,
( relation_dom(sk1_esk67_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2698_1,axiom,
( ~ equipotent(X1,X2)
| relation_dom(sk1_esk67_2(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2698]) ).
cnf(c_0_2699_0,axiom,
( relation_rng(sk1_esk67_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2699_1,axiom,
( ~ equipotent(X1,X2)
| relation_rng(sk1_esk67_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2700_0,axiom,
( relation(sk1_esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2700_1,axiom,
( ~ equipotent(X1,X2)
| relation(sk1_esk67_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2700]) ).
cnf(c_0_2701_0,axiom,
( function(sk1_esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2701_1,axiom,
( ~ equipotent(X1,X2)
| function(sk1_esk67_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2701]) ).
cnf(c_0_2702_0,axiom,
( one_to_one(sk1_esk67_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2702]) ).
cnf(c_0_2702_1,axiom,
( ~ equipotent(X1,X2)
| one_to_one(sk1_esk67_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2702]) ).
cnf(c_0_2703_0,axiom,
( X4 = pair_second(X1)
| X1 != ordered_pair(X2,X3)
| sk1_esk38_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2703_1,axiom,
( X1 != ordered_pair(X2,X3)
| X4 = pair_second(X1)
| sk1_esk38_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2703_2,axiom,
( sk1_esk38_2(X1,X4) != X4
| X1 != ordered_pair(X2,X3)
| X4 = pair_second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2704_0,axiom,
( X4 = pair_first(X1)
| X1 != ordered_pair(X2,X3)
| sk1_esk22_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2704_1,axiom,
( X1 != ordered_pair(X2,X3)
| X4 = pair_first(X1)
| sk1_esk22_2(X1,X4) != X4 ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2704_2,axiom,
( sk1_esk22_2(X1,X4) != X4
| X1 != ordered_pair(X2,X3)
| X4 = pair_first(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2704]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2706_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_2706]) ).
cnf(c_0_2707_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2707]) ).
cnf(c_0_2707_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2707]) ).
cnf(c_0_2708_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2708]) ).
cnf(c_0_2708_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2708]) ).
cnf(c_0_2709_0,axiom,
( finite(relation_image(X1,X2))
| ~ finite(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2709_1,axiom,
( ~ finite(X2)
| finite(relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2709_2,axiom,
( ~ function(X1)
| ~ finite(X2)
| finite(relation_image(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2709_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ finite(X2)
| finite(relation_image(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2710_0,axiom,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2710_1,axiom,
( ~ ordinal(X1)
| subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2710_2,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| subset(X2,X1)
| ~ ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2710_3,axiom,
( ~ ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2711_0,axiom,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2711_1,axiom,
( ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2711_2,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2711_3,axiom,
( ~ subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2712_0,axiom,
( subset(X1,X2)
| X1 != omega
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2712_1,axiom,
( X1 != omega
| subset(X1,X2)
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2712_2,axiom,
( ~ being_limit_ordinal(X2)
| X1 != omega
| subset(X1,X2)
| ~ in(empty_set,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2712_3,axiom,
( ~ in(empty_set,X2)
| ~ being_limit_ordinal(X2)
| X1 != omega
| subset(X1,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2712_4,axiom,
( ~ ordinal(X2)
| ~ in(empty_set,X2)
| ~ being_limit_ordinal(X2)
| X1 != omega
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2712]) ).
cnf(c_0_2713_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2713_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2713_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2713_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2713]) ).
cnf(c_0_2714_0,axiom,
( ordinal(sk1_esk195_0)
| sk1_esk198_2(X2,X1) = X1
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2714_1,axiom,
( sk1_esk198_2(X2,X1) = X1
| ordinal(sk1_esk195_0)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2714_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk198_2(X2,X1) = X1
| ordinal(sk1_esk195_0) ),
inference(literals_permutation,[status(thm)],[c_0_2714]) ).
cnf(c_0_2715_0,axiom,
( ordinal(sk1_esk196_0)
| sk1_esk198_2(X2,X1) = X1
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2715_1,axiom,
( sk1_esk198_2(X2,X1) = X1
| ordinal(sk1_esk196_0)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2715_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk198_2(X2,X1) = X1
| ordinal(sk1_esk196_0) ),
inference(literals_permutation,[status(thm)],[c_0_2715]) ).
cnf(c_0_2716_0,axiom,
( empty_carrier(X1)
| element(sk1_esk125_1(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2716_1,axiom,
( element(sk1_esk125_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2716_2,axiom,
( ~ one_sorted_str(X1)
| element(sk1_esk125_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2716]) ).
cnf(c_0_2717_0,axiom,
( sk1_esk198_2(X2,X1) = X1
| sk1_esk196_0 != sk1_esk195_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2717]) ).
cnf(c_0_2717_1,axiom,
( sk1_esk196_0 != sk1_esk195_0
| sk1_esk198_2(X2,X1) = X1
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2717]) ).
cnf(c_0_2717_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk196_0 != sk1_esk195_0
| sk1_esk198_2(X2,X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2717]) ).
cnf(c_0_2718_0,axiom,
( sk1_esk194_0 = sk1_esk195_0
| sk1_esk198_2(X2,X1) = X1
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2718_1,axiom,
( sk1_esk198_2(X2,X1) = X1
| sk1_esk194_0 = sk1_esk195_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2718_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk198_2(X2,X1) = X1
| sk1_esk194_0 = sk1_esk195_0 ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2719_0,axiom,
( sk1_esk194_0 = sk1_esk196_0
| sk1_esk198_2(X2,X1) = X1
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2719_1,axiom,
( sk1_esk198_2(X2,X1) = X1
| sk1_esk194_0 = sk1_esk196_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2719_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk198_2(X2,X1) = X1
| sk1_esk194_0 = sk1_esk196_0 ),
inference(literals_permutation,[status(thm)],[c_0_2719]) ).
cnf(c_0_2722_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2722_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2722_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2723_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_2723]) ).
cnf(c_0_2724_0,axiom,
( X1 = omega
| ordinal(sk1_esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_1,axiom,
( ordinal(sk1_esk72_1(X1))
| X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_2,axiom,
( ~ in(empty_set,X1)
| ordinal(sk1_esk72_1(X1))
| X1 = omega
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_3,axiom,
( ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| ordinal(sk1_esk72_1(X1))
| X1 = omega
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2724_4,axiom,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| ordinal(sk1_esk72_1(X1))
| X1 = omega ),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2725_0,axiom,
( X1 = omega
| being_limit_ordinal(sk1_esk72_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2725_1,axiom,
( being_limit_ordinal(sk1_esk72_1(X1))
| X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2725_2,axiom,
( ~ in(empty_set,X1)
| being_limit_ordinal(sk1_esk72_1(X1))
| X1 = omega
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2725_3,axiom,
( ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| being_limit_ordinal(sk1_esk72_1(X1))
| X1 = omega
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2725_4,axiom,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| being_limit_ordinal(sk1_esk72_1(X1))
| X1 = omega ),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2726_0,axiom,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2726]) ).
cnf(c_0_2726_1,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2726]) ).
cnf(c_0_2727_0,axiom,
( epsilon_connected(X1)
| ~ in(sk1_esk51_1(X1),sk1_esk52_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2727_1,axiom,
( ~ in(sk1_esk51_1(X1),sk1_esk52_1(X1))
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2727]) ).
cnf(c_0_2728_0,axiom,
( epsilon_connected(X1)
| ~ in(sk1_esk52_1(X1),sk1_esk51_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2728_1,axiom,
( ~ in(sk1_esk52_1(X1),sk1_esk51_1(X1))
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2728]) ).
cnf(c_0_2729_0,axiom,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2729_1,axiom,
( ~ one_sorted_str(X1)
| element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2729]) ).
cnf(c_0_2730_0,axiom,
( one_to_one(X1)
| in(sk1_esk82_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_1,axiom,
( in(sk1_esk82_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_2,axiom,
( ~ function(X1)
| in(sk1_esk82_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2730_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk82_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2731_0,axiom,
( one_to_one(X1)
| in(sk1_esk83_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_1,axiom,
( in(sk1_esk83_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_2,axiom,
( ~ function(X1)
| in(sk1_esk83_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2731_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk83_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2731]) ).
cnf(c_0_2732_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2732_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2732_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2732]) ).
cnf(c_0_2733_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2733]) ).
cnf(c_0_2733_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2733]) ).
cnf(c_0_2733_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2733]) ).
cnf(c_0_2734_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
cnf(c_0_2734_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2734]) ).
cnf(c_0_2735_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2735]) ).
cnf(c_0_2735_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2735]) ).
cnf(c_0_2736_0,axiom,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2736]) ).
cnf(c_0_2736_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2736]) ).
cnf(c_0_2736_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2736]) ).
cnf(c_0_2737_0,axiom,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2737]) ).
cnf(c_0_2737_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2737]) ).
cnf(c_0_2737_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2737]) ).
cnf(c_0_2738_0,axiom,
( finite(set_union2(X1,X2))
| ~ finite(X2)
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2738]) ).
cnf(c_0_2738_1,axiom,
( ~ finite(X2)
| finite(set_union2(X1,X2))
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2738]) ).
cnf(c_0_2738_2,axiom,
( ~ finite(X1)
| ~ finite(X2)
| finite(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2738]) ).
cnf(c_0_2739_0,axiom,
( relation(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2739]) ).
cnf(c_0_2739_1,axiom,
( ~ function(X1)
| relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2739]) ).
cnf(c_0_2739_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_rng_restriction(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2739]) ).
cnf(c_0_2740_0,axiom,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2740]) ).
cnf(c_0_2740_1,axiom,
( ~ function(X1)
| function(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2740]) ).
cnf(c_0_2740_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_rng_restriction(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2740]) ).
cnf(c_0_2741_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2741]) ).
cnf(c_0_2741_1,axiom,
( ~ function(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2741]) ).
cnf(c_0_2741_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2741]) ).
cnf(c_0_2742_0,axiom,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2742_1,axiom,
( ~ function(X1)
| function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2742_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2742]) ).
cnf(c_0_2743_0,axiom,
( relation(set_difference(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2743_1,axiom,
( ~ relation(X2)
| relation(set_difference(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2743_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_difference(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2744_0,axiom,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2744]) ).
cnf(c_0_2744_1,axiom,
( ~ relation(X2)
| relation(set_union2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2744]) ).
cnf(c_0_2744_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2744]) ).
cnf(c_0_2745_0,axiom,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2745]) ).
cnf(c_0_2745_1,axiom,
( ~ relation(X2)
| relation(set_intersection2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2745]) ).
cnf(c_0_2745_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2745]) ).
cnf(c_0_2746_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2746]) ).
cnf(c_0_2746_1,axiom,
( ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2746]) ).
cnf(c_0_2746_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2746]) ).
cnf(c_0_2747_0,axiom,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2747]) ).
cnf(c_0_2747_1,axiom,
( ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2747]) ).
cnf(c_0_2747_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2747]) ).
cnf(c_0_2748_0,axiom,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2748]) ).
cnf(c_0_2748_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2748]) ).
cnf(c_0_2748_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2748]) ).
cnf(c_0_2749_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2749]) ).
cnf(c_0_2749_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2749]) ).
cnf(c_0_2749_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2749]) ).
cnf(c_0_2750_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2750]) ).
cnf(c_0_2750_1,axiom,
( ~ relation(X2)
| relation(relation_composition(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2750]) ).
cnf(c_0_2750_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2750]) ).
cnf(c_0_2751_0,axiom,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2751]) ).
cnf(c_0_2751_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2751]) ).
cnf(c_0_2751_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2751]) ).
cnf(c_0_2752_0,axiom,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2752_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2752_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2752]) ).
cnf(c_0_2753_0,axiom,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2754_0,axiom,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2754_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2754_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2755_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2755_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| ~ well_orders(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2755_2,axiom,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2756_0,axiom,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| sk1_esk57_2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2756_1,axiom,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| sk1_esk57_2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2756_2,axiom,
( sk1_esk57_2(X1,X2) != empty_set
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2757_0,axiom,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2757_1,axiom,
( ~ in(X1,X2)
| subset(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2757_2,axiom,
( ~ epsilon_transitive(X2)
| ~ in(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2757]) ).
cnf(c_0_2758_0,axiom,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2758]) ).
cnf(c_0_2758_1,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2758]) ).
cnf(c_0_2758_2,axiom,
( ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2758]) ).
cnf(c_0_2759_0,axiom,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2759]) ).
cnf(c_0_2759_1,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2759]) ).
cnf(c_0_2759_2,axiom,
( ~ is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2759]) ).
cnf(c_0_2760_0,axiom,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2760]) ).
cnf(c_0_2760_1,axiom,
( ~ relation(X1)
| connected(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2760]) ).
cnf(c_0_2760_2,axiom,
( ~ is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2760]) ).
cnf(c_0_2761_0,axiom,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2761]) ).
cnf(c_0_2761_1,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2761]) ).
cnf(c_0_2761_2,axiom,
( ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2761]) ).
cnf(c_0_2762_0,axiom,
( finite(X1)
| ~ element(X1,powerset(X2))
| ~ finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2762]) ).
cnf(c_0_2762_1,axiom,
( ~ element(X1,powerset(X2))
| finite(X1)
| ~ finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2762]) ).
cnf(c_0_2762_2,axiom,
( ~ finite(X2)
| ~ element(X1,powerset(X2))
| finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2762]) ).
cnf(c_0_2763_0,axiom,
( v1_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2763]) ).
cnf(c_0_2763_1,axiom,
( ~ v5_membered(X1)
| v1_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2763]) ).
cnf(c_0_2763_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v5_membered(X1)
| v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2763]) ).
cnf(c_0_2764_0,axiom,
( v2_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2764]) ).
cnf(c_0_2764_1,axiom,
( ~ v5_membered(X1)
| v2_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2764]) ).
cnf(c_0_2764_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v5_membered(X1)
| v2_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2764]) ).
cnf(c_0_2765_0,axiom,
( v3_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2765]) ).
cnf(c_0_2765_1,axiom,
( ~ v5_membered(X1)
| v3_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2765]) ).
cnf(c_0_2765_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v5_membered(X1)
| v3_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2765]) ).
cnf(c_0_2766_0,axiom,
( v4_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2766]) ).
cnf(c_0_2766_1,axiom,
( ~ v5_membered(X1)
| v4_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2766]) ).
cnf(c_0_2766_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v5_membered(X1)
| v4_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2766]) ).
cnf(c_0_2767_0,axiom,
( v5_membered(X2)
| ~ v5_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2767]) ).
cnf(c_0_2767_1,axiom,
( ~ v5_membered(X1)
| v5_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2767]) ).
cnf(c_0_2767_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v5_membered(X1)
| v5_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2767]) ).
cnf(c_0_2768_0,axiom,
( v1_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2768_1,axiom,
( ~ v4_membered(X1)
| v1_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2768_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v4_membered(X1)
| v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2769_0,axiom,
( v2_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_1,axiom,
( ~ v4_membered(X1)
| v2_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v4_membered(X1)
| v2_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2770_0,axiom,
( v3_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2770]) ).
cnf(c_0_2770_1,axiom,
( ~ v4_membered(X1)
| v3_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2770]) ).
cnf(c_0_2770_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v4_membered(X1)
| v3_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2770]) ).
cnf(c_0_2771_0,axiom,
( v4_membered(X2)
| ~ v4_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2771]) ).
cnf(c_0_2771_1,axiom,
( ~ v4_membered(X1)
| v4_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2771]) ).
cnf(c_0_2771_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v4_membered(X1)
| v4_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2771]) ).
cnf(c_0_2772_0,axiom,
( v1_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2772]) ).
cnf(c_0_2772_1,axiom,
( ~ v3_membered(X1)
| v1_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2772]) ).
cnf(c_0_2772_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v3_membered(X1)
| v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2772]) ).
cnf(c_0_2773_0,axiom,
( v2_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2773]) ).
cnf(c_0_2773_1,axiom,
( ~ v3_membered(X1)
| v2_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2773]) ).
cnf(c_0_2773_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v3_membered(X1)
| v2_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2773]) ).
cnf(c_0_2774_0,axiom,
( v3_membered(X2)
| ~ v3_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2774]) ).
cnf(c_0_2774_1,axiom,
( ~ v3_membered(X1)
| v3_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2774]) ).
cnf(c_0_2774_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v3_membered(X1)
| v3_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2774]) ).
cnf(c_0_2775_0,axiom,
( v1_membered(X2)
| ~ v2_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2775]) ).
cnf(c_0_2775_1,axiom,
( ~ v2_membered(X1)
| v1_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2775]) ).
cnf(c_0_2775_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v2_membered(X1)
| v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2775]) ).
cnf(c_0_2776_0,axiom,
( v2_membered(X2)
| ~ v2_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2776]) ).
cnf(c_0_2776_1,axiom,
( ~ v2_membered(X1)
| v2_membered(X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2776]) ).
cnf(c_0_2776_2,axiom,
( ~ element(X2,powerset(X1))
| ~ v2_membered(X1)
| v2_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2776]) ).
cnf(c_0_2777_0,axiom,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2777]) ).
cnf(c_0_2777_1,axiom,
( ~ element(X1,powerset(X2))
| v1_membered(X1)
| ~ v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2777]) ).
cnf(c_0_2777_2,axiom,
( ~ v1_membered(X2)
| ~ element(X1,powerset(X2))
| v1_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2777]) ).
cnf(c_0_2778_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2778]) ).
cnf(c_0_2778_1,axiom,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2778]) ).
cnf(c_0_2779_0,axiom,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2779]) ).
cnf(c_0_2779_1,axiom,
( ordinal_subset(X2,X1)
| ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2779]) ).
cnf(c_0_2779_2,axiom,
( ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ordinal_subset(X1,X2)
| ~ ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2779]) ).
cnf(c_0_2779_3,axiom,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ordinal_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2779]) ).
cnf(c_0_2780_0,axiom,
( empty_carrier(X1)
| meet_absorbing(X1)
| element(sk1_esk84_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2780_1,axiom,
( meet_absorbing(X1)
| empty_carrier(X1)
| element(sk1_esk84_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2780_2,axiom,
( element(sk1_esk84_1(X1),the_carrier(X1))
| meet_absorbing(X1)
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2780_3,axiom,
( ~ latt_str(X1)
| element(sk1_esk84_1(X1),the_carrier(X1))
| meet_absorbing(X1)
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2780]) ).
cnf(c_0_2781_0,axiom,
( empty_carrier(X1)
| meet_absorbing(X1)
| element(sk1_esk85_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2781_1,axiom,
( meet_absorbing(X1)
| empty_carrier(X1)
| element(sk1_esk85_1(X1),the_carrier(X1))
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2781_2,axiom,
( element(sk1_esk85_1(X1),the_carrier(X1))
| meet_absorbing(X1)
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2781_3,axiom,
( ~ latt_str(X1)
| element(sk1_esk85_1(X1),the_carrier(X1))
| meet_absorbing(X1)
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2781]) ).
cnf(c_0_2782_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2782]) ).
cnf(c_0_2782_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2782]) ).
cnf(c_0_2782_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2782]) ).
cnf(c_0_2783_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2783]) ).
cnf(c_0_2783_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2783]) ).
cnf(c_0_2783_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2783]) ).
cnf(c_0_2784_0,axiom,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2784]) ).
cnf(c_0_2784_1,axiom,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2784]) ).
cnf(c_0_2784_2,axiom,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2784]) ).
cnf(c_0_2785_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2785]) ).
cnf(c_0_2785_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2785]) ).
cnf(c_0_2785_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2785]) ).
cnf(c_0_2786_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2786_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2786_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2787_0,axiom,
( ordinal(sk1_esk195_0)
| ordinal(X1)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2787]) ).
cnf(c_0_2787_1,axiom,
( ordinal(X1)
| ordinal(sk1_esk195_0)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2787]) ).
cnf(c_0_2787_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| ordinal(X1)
| ordinal(sk1_esk195_0) ),
inference(literals_permutation,[status(thm)],[c_0_2787]) ).
cnf(c_0_2788_0,axiom,
( ordinal(sk1_esk196_0)
| ordinal(X1)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2788]) ).
cnf(c_0_2788_1,axiom,
( ordinal(X1)
| ordinal(sk1_esk196_0)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2788]) ).
cnf(c_0_2788_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| ordinal(X1)
| ordinal(sk1_esk196_0) ),
inference(literals_permutation,[status(thm)],[c_0_2788]) ).
cnf(c_0_2789_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2789]) ).
cnf(c_0_2789_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2789]) ).
cnf(c_0_2789_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2789]) ).
cnf(c_0_2790_0,axiom,
( well_founded_relation(X1)
| subset(sk1_esk44_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2790]) ).
cnf(c_0_2790_1,axiom,
( subset(sk1_esk44_1(X1),relation_field(X1))
| well_founded_relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2790]) ).
cnf(c_0_2790_2,axiom,
( ~ relation(X1)
| subset(sk1_esk44_1(X1),relation_field(X1))
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2790]) ).
cnf(c_0_2791_0,axiom,
( in(relation_dom(sk1_esk18_1(X1)),omega)
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2791]) ).
cnf(c_0_2791_1,axiom,
( ~ finite(X1)
| in(relation_dom(sk1_esk18_1(X1)),omega) ),
inference(literals_permutation,[status(thm)],[c_0_2791]) ).
cnf(c_0_2792_0,axiom,
( ordinal(X1)
| sk1_esk196_0 != sk1_esk195_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2792_1,axiom,
( sk1_esk196_0 != sk1_esk195_0
| ordinal(X1)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2792_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| sk1_esk196_0 != sk1_esk195_0
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2793_0,axiom,
( sk1_esk194_0 = sk1_esk195_0
| ordinal(X1)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2793_1,axiom,
( ordinal(X1)
| sk1_esk194_0 = sk1_esk195_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2793_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| ordinal(X1)
| sk1_esk194_0 = sk1_esk195_0 ),
inference(literals_permutation,[status(thm)],[c_0_2793]) ).
cnf(c_0_2794_0,axiom,
( sk1_esk194_0 = sk1_esk196_0
| ordinal(X1)
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2794_1,axiom,
( ordinal(X1)
| sk1_esk194_0 = sk1_esk196_0
| ~ in(X1,sk1_esk197_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2794_2,axiom,
( ~ in(X1,sk1_esk197_1(X2))
| ordinal(X1)
| sk1_esk194_0 = sk1_esk196_0 ),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2795_0,axiom,
( finite(set_difference(X1,X2))
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2795]) ).
cnf(c_0_2795_1,axiom,
( ~ finite(X1)
| finite(set_difference(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2795]) ).
cnf(c_0_2796_0,axiom,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2796]) ).
cnf(c_0_2796_1,axiom,
( ~ finite(X1)
| finite(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2796]) ).
cnf(c_0_2797_0,axiom,
( finite(set_intersection2(X1,X2))
| ~ finite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2797]) ).
cnf(c_0_2797_1,axiom,
( ~ finite(X2)
| finite(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2797]) ).
cnf(c_0_2798_0,axiom,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2798]) ).
cnf(c_0_2798_1,axiom,
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2798]) ).
cnf(c_0_2799_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2799]) ).
cnf(c_0_2799_1,axiom,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2799]) ).
cnf(c_0_2800_0,axiom,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2800]) ).
cnf(c_0_2800_1,axiom,
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2800]) ).
cnf(c_0_2801_0,axiom,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2801]) ).
cnf(c_0_2801_1,axiom,
( ~ relation(X1)
| set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2801]) ).
cnf(c_0_2802_0,axiom,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2802]) ).
cnf(c_0_2802_1,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2802]) ).
cnf(c_0_2803_0,axiom,
( equipotent(X1,X2)
| ~ equipotent(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2803]) ).
cnf(c_0_2803_1,axiom,
( ~ equipotent(X2,X1)
| equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2803]) ).
cnf(c_0_2804_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2804]) ).
cnf(c_0_2804_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2804]) ).
cnf(c_0_2805_0,axiom,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2805]) ).
cnf(c_0_2805_1,axiom,
( ~ equipotent(X1,X2)
| are_equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2805]) ).
cnf(c_0_2806_0,axiom,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2806]) ).
cnf(c_0_2806_1,axiom,
( ~ are_equipotent(X1,X2)
| equipotent(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2806]) ).
cnf(c_0_2807_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2807]) ).
cnf(c_0_2807_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2807]) ).
cnf(c_0_2808_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2808]) ).
cnf(c_0_2808_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2808]) ).
cnf(c_0_2809_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2809]) ).
cnf(c_0_2809_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2809]) ).
cnf(c_0_2810_0,axiom,
( epsilon_transitive(X1)
| ~ subset(sk1_esk39_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2810]) ).
cnf(c_0_2810_1,axiom,
( ~ subset(sk1_esk39_1(X1),X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2810]) ).
cnf(c_0_2811_0,axiom,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2811]) ).
cnf(c_0_2811_1,axiom,
( ~ relation(X1)
| is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2811]) ).
cnf(c_0_2811_2,axiom,
( ~ reflexive(X1)
| ~ relation(X1)
| is_reflexive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2811]) ).
cnf(c_0_2812_0,axiom,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2812]) ).
cnf(c_0_2812_1,axiom,
( ~ relation(X1)
| is_transitive_in(X1,relation_field(X1))
| ~ transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2812]) ).
cnf(c_0_2812_2,axiom,
( ~ transitive(X1)
| ~ relation(X1)
| is_transitive_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2812]) ).
cnf(c_0_2813_0,axiom,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2813]) ).
cnf(c_0_2813_1,axiom,
( ~ relation(X1)
| is_connected_in(X1,relation_field(X1))
| ~ connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2813]) ).
cnf(c_0_2813_2,axiom,
( ~ connected(X1)
| ~ relation(X1)
| is_connected_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2813]) ).
cnf(c_0_2814_0,axiom,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2814]) ).
cnf(c_0_2814_1,axiom,
( ~ relation(X1)
| is_antisymmetric_in(X1,relation_field(X1))
| ~ antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2814]) ).
cnf(c_0_2814_2,axiom,
( ~ antisymmetric(X1)
| ~ relation(X1)
| is_antisymmetric_in(X1,relation_field(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2814]) ).
cnf(c_0_2815_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2815]) ).
cnf(c_0_2815_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2815]) ).
cnf(c_0_2815_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2815]) ).
cnf(c_0_2816_0,axiom,
( epsilon_transitive(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2816]) ).
cnf(c_0_2816_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2816]) ).
cnf(c_0_2816_2,axiom,
( ~ element(X2,X1)
| ~ ordinal(X1)
| epsilon_transitive(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2816]) ).
cnf(c_0_2817_0,axiom,
( epsilon_connected(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2817]) ).
cnf(c_0_2817_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2817]) ).
cnf(c_0_2817_2,axiom,
( ~ element(X2,X1)
| ~ ordinal(X1)
| epsilon_connected(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2817]) ).
cnf(c_0_2818_0,axiom,
( ordinal(X2)
| ~ ordinal(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2818]) ).
cnf(c_0_2818_1,axiom,
( ~ ordinal(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2818]) ).
cnf(c_0_2818_2,axiom,
( ~ element(X2,X1)
| ~ ordinal(X1)
| ordinal(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2818]) ).
cnf(c_0_2819_0,axiom,
( v1_xcmplx_0(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2819]) ).
cnf(c_0_2819_1,axiom,
( ~ v5_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2819]) ).
cnf(c_0_2819_2,axiom,
( ~ element(X2,X1)
| ~ v5_membered(X1)
| v1_xcmplx_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2819]) ).
cnf(c_0_2820_0,axiom,
( natural(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2820]) ).
cnf(c_0_2820_1,axiom,
( ~ v5_membered(X1)
| natural(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2820]) ).
cnf(c_0_2820_2,axiom,
( ~ element(X2,X1)
| ~ v5_membered(X1)
| natural(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2820]) ).
cnf(c_0_2821_0,axiom,
( v1_xreal_0(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2821]) ).
cnf(c_0_2821_1,axiom,
( ~ v5_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2821]) ).
cnf(c_0_2821_2,axiom,
( ~ element(X2,X1)
| ~ v5_membered(X1)
| v1_xreal_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2821]) ).
cnf(c_0_2822_0,axiom,
( v1_int_1(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2822]) ).
cnf(c_0_2822_1,axiom,
( ~ v5_membered(X1)
| v1_int_1(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2822]) ).
cnf(c_0_2822_2,axiom,
( ~ element(X2,X1)
| ~ v5_membered(X1)
| v1_int_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2822]) ).
cnf(c_0_2823_0,axiom,
( v1_rat_1(X2)
| ~ v5_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2823]) ).
cnf(c_0_2823_1,axiom,
( ~ v5_membered(X1)
| v1_rat_1(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2823]) ).
cnf(c_0_2823_2,axiom,
( ~ element(X2,X1)
| ~ v5_membered(X1)
| v1_rat_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2823]) ).
cnf(c_0_2824_0,axiom,
( v1_xcmplx_0(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2824]) ).
cnf(c_0_2824_1,axiom,
( ~ v4_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2824]) ).
cnf(c_0_2824_2,axiom,
( ~ element(X2,X1)
| ~ v4_membered(X1)
| v1_xcmplx_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2824]) ).
cnf(c_0_2825_0,axiom,
( v1_xreal_0(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2825]) ).
cnf(c_0_2825_1,axiom,
( ~ v4_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2825]) ).
cnf(c_0_2825_2,axiom,
( ~ element(X2,X1)
| ~ v4_membered(X1)
| v1_xreal_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2825]) ).
cnf(c_0_2826_0,axiom,
( v1_int_1(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2826]) ).
cnf(c_0_2826_1,axiom,
( ~ v4_membered(X1)
| v1_int_1(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2826]) ).
cnf(c_0_2826_2,axiom,
( ~ element(X2,X1)
| ~ v4_membered(X1)
| v1_int_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2826]) ).
cnf(c_0_2827_0,axiom,
( v1_rat_1(X2)
| ~ v4_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2827]) ).
cnf(c_0_2827_1,axiom,
( ~ v4_membered(X1)
| v1_rat_1(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2827]) ).
cnf(c_0_2827_2,axiom,
( ~ element(X2,X1)
| ~ v4_membered(X1)
| v1_rat_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2827]) ).
cnf(c_0_2828_0,axiom,
( v1_xcmplx_0(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2828]) ).
cnf(c_0_2828_1,axiom,
( ~ v3_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2828]) ).
cnf(c_0_2828_2,axiom,
( ~ element(X2,X1)
| ~ v3_membered(X1)
| v1_xcmplx_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2828]) ).
cnf(c_0_2829_0,axiom,
( v1_xreal_0(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2829]) ).
cnf(c_0_2829_1,axiom,
( ~ v3_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2829]) ).
cnf(c_0_2829_2,axiom,
( ~ element(X2,X1)
| ~ v3_membered(X1)
| v1_xreal_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2829]) ).
cnf(c_0_2830_0,axiom,
( v1_rat_1(X2)
| ~ v3_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2830]) ).
cnf(c_0_2830_1,axiom,
( ~ v3_membered(X1)
| v1_rat_1(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2830]) ).
cnf(c_0_2830_2,axiom,
( ~ element(X2,X1)
| ~ v3_membered(X1)
| v1_rat_1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2830]) ).
cnf(c_0_2831_0,axiom,
( v1_xcmplx_0(X2)
| ~ v2_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2831]) ).
cnf(c_0_2831_1,axiom,
( ~ v2_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2831]) ).
cnf(c_0_2831_2,axiom,
( ~ element(X2,X1)
| ~ v2_membered(X1)
| v1_xcmplx_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2831]) ).
cnf(c_0_2832_0,axiom,
( v1_xreal_0(X2)
| ~ v2_membered(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2832]) ).
cnf(c_0_2832_1,axiom,
( ~ v2_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2832]) ).
cnf(c_0_2832_2,axiom,
( ~ element(X2,X1)
| ~ v2_membered(X1)
| v1_xreal_0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2832]) ).
cnf(c_0_2833_0,axiom,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2833]) ).
cnf(c_0_2833_1,axiom,
( ~ element(X1,X2)
| v1_xcmplx_0(X1)
| ~ v1_membered(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2833]) ).
cnf(c_0_2833_2,axiom,
( ~ v1_membered(X2)
| ~ element(X1,X2)
| v1_xcmplx_0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2833]) ).
cnf(c_0_2834_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2834]) ).
cnf(c_0_2834_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2834]) ).
cnf(c_0_2834_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2834]) ).
cnf(c_0_2835_0,axiom,
( relation(X1)
| sk1_esk26_1(X1) != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2835]) ).
cnf(c_0_2835_1,axiom,
( sk1_esk26_1(X1) != ordered_pair(X2,X3)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2835]) ).
cnf(c_0_2836_0,axiom,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2836]) ).
cnf(c_0_2836_1,axiom,
( ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2836]) ).
cnf(c_0_2836_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2836]) ).
cnf(c_0_2836_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2836]) ).
cnf(c_0_2837_0,axiom,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2837]) ).
cnf(c_0_2837_1,axiom,
( ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2837]) ).
cnf(c_0_2837_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2837]) ).
cnf(c_0_2837_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2837]) ).
cnf(c_0_2838_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk83_1(X1) != sk1_esk82_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2838_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ relation(X1)
| sk1_esk83_1(X1) != sk1_esk82_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2838_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| one_to_one(X1)
| sk1_esk83_1(X1) != sk1_esk82_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2838_3,axiom,
( sk1_esk83_1(X1) != sk1_esk82_1(X1)
| ~ relation(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2838]) ).
cnf(c_0_2839_0,axiom,
( empty(X1)
| element(sk1_esk119_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2839]) ).
cnf(c_0_2839_1,axiom,
( element(sk1_esk119_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2839]) ).
cnf(c_0_2840_0,axiom,
( empty(X1)
| element(sk1_esk110_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2840]) ).
cnf(c_0_2840_1,axiom,
( element(sk1_esk110_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2840]) ).
cnf(c_0_2841_0,axiom,
( ~ natural(X1)
| ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2841_1,axiom,
( ~ ordinal(X1)
| ~ natural(X1)
| ~ empty(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2841_2,axiom,
( ~ empty(succ(X1))
| ~ ordinal(X1)
| ~ natural(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2846_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2846]) ).
cnf(c_0_2846_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2846]) ).
cnf(c_0_2847_0,axiom,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2847]) ).
cnf(c_0_2847_1,axiom,
( ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2847]) ).
cnf(c_0_2847_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2847]) ).
cnf(c_0_2847_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2847]) ).
cnf(c_0_2848_0,axiom,
( ordinal_subset(X1,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2848]) ).
cnf(c_0_2848_1,axiom,
( ~ ordinal(X2)
| ordinal_subset(X1,X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2848]) ).
cnf(c_0_2848_2,axiom,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2848]) ).
cnf(c_0_2849_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2849]) ).
cnf(c_0_2849_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2849]) ).
cnf(c_0_2849_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2849]) ).
cnf(c_0_2850_0,axiom,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(sk1_esk125_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2850_1,axiom,
( ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ empty(sk1_esk125_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2850_2,axiom,
( ~ empty(sk1_esk125_1(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2851_0,axiom,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2851]) ).
cnf(c_0_2851_1,axiom,
( ~ empty(relation_rng(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2851]) ).
cnf(c_0_2851_2,axiom,
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2851]) ).
cnf(c_0_2852_0,axiom,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2852_1,axiom,
( ~ empty(relation_dom(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2852_2,axiom,
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2853_0,axiom,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2853]) ).
cnf(c_0_2853_1,axiom,
( ~ empty(the_carrier(X1))
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2853]) ).
cnf(c_0_2853_2,axiom,
( ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1))
| empty_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2853]) ).
cnf(c_0_2860_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2860]) ).
cnf(c_0_2860_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2860]) ).
cnf(c_0_2860_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2860]) ).
cnf(c_0_2861_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2861]) ).
cnf(c_0_2861_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2861]) ).
cnf(c_0_2862_0,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2862_1,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2862_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2862_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2863_0,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2863_1,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2863_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2863_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2864_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2864_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2864_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2864_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2865_0,axiom,
( epsilon_connected(X1)
| in(sk1_esk51_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2865_1,axiom,
( in(sk1_esk51_1(X1),X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2866_0,axiom,
( epsilon_connected(X1)
| in(sk1_esk52_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2866]) ).
cnf(c_0_2866_1,axiom,
( in(sk1_esk52_1(X1),X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2866]) ).
cnf(c_0_2867_0,axiom,
( epsilon_transitive(X1)
| in(sk1_esk39_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2867]) ).
cnf(c_0_2867_1,axiom,
( in(sk1_esk39_1(X1),X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2867]) ).
cnf(c_0_2868_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2869_0,axiom,
( relation(X1)
| in(sk1_esk26_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_1,axiom,
( in(sk1_esk26_1(X1),X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2870_0,axiom,
( epsilon_transitive(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_1,axiom,
( ~ natural(X1)
| epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_2,axiom,
( ~ ordinal(X1)
| ~ natural(X1)
| epsilon_transitive(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2871_0,axiom,
( epsilon_connected(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_1,axiom,
( ~ natural(X1)
| epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_2,axiom,
( ~ ordinal(X1)
| ~ natural(X1)
| epsilon_connected(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2872_0,axiom,
( ordinal(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_1,axiom,
( ~ natural(X1)
| ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_2,axiom,
( ~ ordinal(X1)
| ~ natural(X1)
| ordinal(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2873_0,axiom,
( natural(succ(X1))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_1,axiom,
( ~ natural(X1)
| natural(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_2,axiom,
( ~ ordinal(X1)
| ~ natural(X1)
| natural(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2874_0,axiom,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_1,axiom,
( ~ function(X1)
| relation(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2875_0,axiom,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_1,axiom,
( ~ function(X1)
| function(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2876_0,axiom,
( epsilon_transitive(X1)
| ~ element(X1,omega) ),
inference(literals_permutation,[status(thm)],[c_0_2876]) ).
cnf(c_0_2876_1,axiom,
( ~ element(X1,omega)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2876]) ).
cnf(c_0_2877_0,axiom,
( epsilon_connected(X1)
| ~ element(X1,omega) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2877_1,axiom,
( ~ element(X1,omega)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2878_0,axiom,
( ordinal(X1)
| ~ element(X1,omega) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2878_1,axiom,
( ~ element(X1,omega)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2879_0,axiom,
( natural(X1)
| ~ element(X1,omega) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2879_1,axiom,
( ~ element(X1,omega)
| natural(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2881_0,axiom,
( ~ ordinal(X1)
| ~ empty(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_1,axiom,
( ~ empty(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2883_0,axiom,
( X1 = empty_set
| in(sk1_esk35_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2883_1,axiom,
( in(sk1_esk35_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2884_0,axiom,
( empty(X1)
| ~ empty(sk1_esk119_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_1,axiom,
( ~ empty(sk1_esk119_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2885_0,axiom,
( empty(X1)
| ~ empty(sk1_esk110_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_1,axiom,
( ~ empty(sk1_esk110_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2886_0,axiom,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_1,axiom,
( ~ relation(X1)
| relation_field(X1) = X2
| X1 != inclusion_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_2,axiom,
( X1 != inclusion_relation(X2)
| ~ relation(X1)
| relation_field(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2889_0,axiom,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2889_1,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2889_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| reflexive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2890_0,axiom,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2890_1,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2890_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2891_0,axiom,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2891_1,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2891_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| antisymmetric(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2892_0,axiom,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2892_1,axiom,
( ~ relation(X1)
| connected(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2892_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2893_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2893_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ well_ordering(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2893_2,axiom,
( ~ well_ordering(X1)
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2894_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_1,axiom,
( ~ epsilon_connected(X1)
| ordinal(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_2,axiom,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2895_0,axiom,
( well_founded_relation(X1)
| ~ relation(X1)
| sk1_esk44_1(X1) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2895_1,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| sk1_esk44_1(X1) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2895_2,axiom,
( sk1_esk44_1(X1) != empty_set
| ~ relation(X1)
| well_founded_relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2896_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2896_1,axiom,
( ~ epsilon_connected(X1)
| ordinal(X1)
| ~ epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2896_2,axiom,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2897_0,axiom,
( preboolean(X1)
| ~ diff_closed(X1)
| ~ cup_closed(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2897_1,axiom,
( ~ diff_closed(X1)
| preboolean(X1)
| ~ cup_closed(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2897_2,axiom,
( ~ cup_closed(X1)
| ~ diff_closed(X1)
| preboolean(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2898_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2898_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2898_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2899_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2899_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2899_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2900_0,axiom,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2900_1,axiom,
( ~ ordinal(X1)
| ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2900_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2901_0,axiom,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2901]) ).
cnf(c_0_2901_1,axiom,
( ~ ordinal(X1)
| natural(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2901]) ).
cnf(c_0_2901_2,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| natural(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2901]) ).
cnf(c_0_2902_0,axiom,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2902]) ).
cnf(c_0_2902_1,axiom,
( ~ relation(X1)
| relation_inverse(relation_inverse(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2902]) ).
cnf(c_0_2903_0,axiom,
( relation_rng(sk1_esk18_1(X1)) = X1
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2903_1,axiom,
( ~ finite(X1)
| relation_rng(sk1_esk18_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2904_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2904]) ).
cnf(c_0_2904_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2904]) ).
cnf(c_0_2905_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2905_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2906_0,axiom,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2906_1,axiom,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2907_0,axiom,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2907_1,axiom,
( ~ empty(X1)
| relation(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2908_0,axiom,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2908_1,axiom,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2909_0,axiom,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_1,axiom,
( ~ empty(X1)
| relation(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2910_0,axiom,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2910_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2911_0,axiom,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2912_0,axiom,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2912_1,axiom,
( ~ ordinal(X1)
| ordinal(union(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2913_0,axiom,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2913_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2914_0,axiom,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2914_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2915_0,axiom,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2915_1,axiom,
( ~ ordinal(X1)
| ordinal(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2916_0,axiom,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2916_1,axiom,
( ~ empty(X1)
| empty(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2917_0,axiom,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_1,axiom,
( ~ empty(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2918_0,axiom,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2918_1,axiom,
( ~ join_semilatt_str(X1)
| function(the_L_join(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2919_0,axiom,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2919]) ).
cnf(c_0_2919_1,axiom,
( ~ meet_semilatt_str(X1)
| function(the_L_meet(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2919]) ).
cnf(c_0_2920_0,axiom,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2920_1,axiom,
( ~ relation(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2921_0,axiom,
( relation(sk1_esk18_1(X1))
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2921]) ).
cnf(c_0_2921_1,axiom,
( ~ finite(X1)
| relation(sk1_esk18_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2921]) ).
cnf(c_0_2922_0,axiom,
( function(sk1_esk18_1(X1))
| ~ finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2922_1,axiom,
( ~ finite(X1)
| function(sk1_esk18_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2923_0,axiom,
( epsilon_connected(X1)
| sk1_esk51_1(X1) != sk1_esk52_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2923_1,axiom,
( sk1_esk51_1(X1) != sk1_esk52_1(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2924_0,axiom,
( function(X1)
| sk1_esk21_1(X1) != sk1_esk20_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2924_1,axiom,
( sk1_esk21_1(X1) != sk1_esk20_1(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2930_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2930_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2930_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2931_0,axiom,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2931]) ).
cnf(c_0_2931_1,axiom,
( ~ one_sorted_str(X1)
| cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2931]) ).
cnf(c_0_2932_0,axiom,
( in(empty_set,X1)
| X1 != omega ),
inference(literals_permutation,[status(thm)],[c_0_2932]) ).
cnf(c_0_2932_1,axiom,
( X1 != omega
| in(empty_set,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2932]) ).
cnf(c_0_2933_0,axiom,
( empty(X1)
| finite(sk1_esk119_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2933]) ).
cnf(c_0_2933_1,axiom,
( finite(sk1_esk119_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2933]) ).
cnf(c_0_2942_0,axiom,
( being_limit_ordinal(X1)
| union(X1) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_1,axiom,
( union(X1) != X1
| being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2943_0,axiom,
( union(X1) = X1
| ~ being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_1,axiom,
( ~ being_limit_ordinal(X1)
| union(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2944_0,axiom,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_1,axiom,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_2,axiom,
( X2 != set_meet(X1)
| X1 != empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2945_0,axiom,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2945_1,axiom,
( ~ latt_str(X1)
| meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2946_0,axiom,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2946_1,axiom,
( ~ latt_str(X1)
| join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2947_0,axiom,
( one_sorted_str(X1)
| ~ join_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_1,axiom,
( ~ join_semilatt_str(X1)
| one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2948_0,axiom,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_1,axiom,
( ~ meet_semilatt_str(X1)
| one_sorted_str(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2949_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2950_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2950_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2951_0,axiom,
( v1_membered(X1)
| ~ v2_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2951]) ).
cnf(c_0_2951_1,axiom,
( ~ v2_membered(X1)
| v1_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2951]) ).
cnf(c_0_2952_0,axiom,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2952_1,axiom,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2953_0,axiom,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2953_1,axiom,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2954_0,axiom,
( ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2954_1,axiom,
( ~ empty(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2955_0,axiom,
( v2_membered(X1)
| ~ v3_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2955_1,axiom,
( ~ v3_membered(X1)
| v2_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2956_0,axiom,
( v3_membered(X1)
| ~ v4_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2956]) ).
cnf(c_0_2956_1,axiom,
( ~ v4_membered(X1)
| v3_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2956]) ).
cnf(c_0_2957_0,axiom,
( relation(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2957]) ).
cnf(c_0_2957_1,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2957]) ).
cnf(c_0_2958_0,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2958]) ).
cnf(c_0_2958_1,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2958]) ).
cnf(c_0_2959_0,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2959]) ).
cnf(c_0_2959_1,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2959]) ).
cnf(c_0_2960_0,axiom,
( v4_membered(X1)
| ~ v5_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2960_1,axiom,
( ~ v5_membered(X1)
| v4_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2961_0,axiom,
( function(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2961_1,axiom,
( ~ empty(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2962_0,axiom,
( cup_closed(X1)
| ~ preboolean(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2962_1,axiom,
( ~ preboolean(X1)
| cup_closed(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2963_0,axiom,
( diff_closed(X1)
| ~ preboolean(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2963]) ).
cnf(c_0_2963_1,axiom,
( ~ preboolean(X1)
| diff_closed(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2963]) ).
cnf(c_0_2964_0,axiom,
( finite(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2964]) ).
cnf(c_0_2964_1,axiom,
( ~ empty(X1)
| finite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2964]) ).
cnf(c_0_2965_0,axiom,
( v1_membered(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2965_1,axiom,
( ~ empty(X1)
| v1_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2966_0,axiom,
( v2_membered(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2966_1,axiom,
( ~ empty(X1)
| v2_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2967_0,axiom,
( v3_membered(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2967]) ).
cnf(c_0_2967_1,axiom,
( ~ empty(X1)
| v3_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2967]) ).
cnf(c_0_2968_0,axiom,
( v4_membered(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2968]) ).
cnf(c_0_2968_1,axiom,
( ~ empty(X1)
| v4_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2968]) ).
cnf(c_0_2969_0,axiom,
( v5_membered(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2969]) ).
cnf(c_0_2969_1,axiom,
( ~ empty(X1)
| v5_membered(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2969]) ).
cnf(c_0_2988_0,axiom,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2988_1,axiom,
( X1 != empty_set
| X2 = set_meet(X1)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2988_2,axiom,
( X2 != empty_set
| X1 != empty_set
| X2 = set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2989_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2989]) ).
cnf(c_0_2989_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_2989]) ).
cnf(c_0_2990_0,axiom,
( being_limit_ordinal(X1)
| X1 != omega ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_1,axiom,
( X1 != omega
| being_limit_ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2991_0,axiom,
( ordinal(X1)
| X1 != omega ),
inference(literals_permutation,[status(thm)],[c_0_2991]) ).
cnf(c_0_2991_1,axiom,
( X1 != omega
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2991]) ).
cnf(c_0_2720_0,axiom,
~ empty(unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2720]) ).
cnf(c_0_2721_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2721]) ).
cnf(c_0_2882_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2925_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_2925]) ).
cnf(c_0_2926_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2926]) ).
cnf(c_0_2927_0,axiom,
~ empty(succ(X1)),
inference(literals_permutation,[status(thm)],[c_0_2927]) ).
cnf(c_0_2928_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2928]) ).
cnf(c_0_2929_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_2929]) ).
cnf(c_0_2993_0,axiom,
~ empty_carrier(sk1_esk123_0),
inference(literals_permutation,[status(thm)],[c_0_2993]) ).
cnf(c_0_2994_0,axiom,
~ empty(sk1_esk121_0),
inference(literals_permutation,[status(thm)],[c_0_2994]) ).
cnf(c_0_2995_0,axiom,
~ empty(sk1_esk118_0),
inference(literals_permutation,[status(thm)],[c_0_2995]) ).
cnf(c_0_2996_0,axiom,
~ empty(sk1_esk116_0),
inference(literals_permutation,[status(thm)],[c_0_2996]) ).
cnf(c_0_2997_0,axiom,
~ empty(sk1_esk105_0),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_2998_0,axiom,
~ empty(sk1_esk102_0),
inference(literals_permutation,[status(thm)],[c_0_2998]) ).
cnf(c_0_2999_0,axiom,
~ empty(sk1_esk101_0),
inference(literals_permutation,[status(thm)],[c_0_2999]) ).
cnf(c_0_3000_0,axiom,
~ empty(omega),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_2625_0,axiom,
relation_of2(sk1_esk115_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2626_0,axiom,
relation_of2(sk1_esk104_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2627_0,axiom,
quasi_total(sk1_esk104_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2628_0,axiom,
relation_of2_as_subset(sk1_esk100_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2629_0,axiom,
relation_of2(sk1_esk98_2(X1,X2),X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2681_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2681]) ).
cnf(c_0_2842_0,axiom,
relation(sk1_esk115_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2842]) ).
cnf(c_0_2843_0,axiom,
function(sk1_esk115_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2843]) ).
cnf(c_0_2844_0,axiom,
relation(sk1_esk104_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2844]) ).
cnf(c_0_2845_0,axiom,
function(sk1_esk104_2(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2845]) ).
cnf(c_0_2854_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2854]) ).
cnf(c_0_2855_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2855]) ).
cnf(c_0_2856_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2856]) ).
cnf(c_0_2857_0,axiom,
element(sk1_esk117_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2857]) ).
cnf(c_0_2858_0,axiom,
element(sk1_esk112_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2858]) ).
cnf(c_0_2859_0,axiom,
element(cast_to_subset(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2859]) ).
cnf(c_0_2880_0,axiom,
set_union2(X1,singleton(X1)) = succ(X1),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2887_0,axiom,
in(X1,sk1_esk214_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2887]) ).
cnf(c_0_2888_0,axiom,
element(sk1_esk99_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_2888]) ).
cnf(c_0_2934_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2934]) ).
cnf(c_0_2935_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2935]) ).
cnf(c_0_2936_0,axiom,
equipotent(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2936]) ).
cnf(c_0_2937_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2937]) ).
cnf(c_0_2938_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_2938]) ).
cnf(c_0_2939_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2940_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2941_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2970_0,axiom,
empty(sk1_esk117_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2971_0,axiom,
empty(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2971]) ).
cnf(c_0_2972_0,axiom,
relation(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_2973_0,axiom,
function(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2973]) ).
cnf(c_0_2974_0,axiom,
one_to_one(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2975_0,axiom,
epsilon_transitive(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2976_0,axiom,
epsilon_connected(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2977_0,axiom,
ordinal(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2977]) ).
cnf(c_0_2978_0,axiom,
natural(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2978]) ).
cnf(c_0_2979_0,axiom,
finite(sk1_esk112_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_2979]) ).
cnf(c_0_2980_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2980]) ).
cnf(c_0_2981_0,axiom,
function(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2982_0,axiom,
cup_closed(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2983_0,axiom,
diff_closed(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2984_0,axiom,
preboolean(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_2984]) ).
cnf(c_0_2985_0,axiom,
finite(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_2985]) ).
cnf(c_0_2986_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2987_0,axiom,
relation(inclusion_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2992_0,axiom,
cast_to_subset(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_2992]) ).
cnf(c_0_3001_0,axiom,
relation(sk1_esk124_0),
inference(literals_permutation,[status(thm)],[c_0_3001]) ).
cnf(c_0_3002_0,axiom,
relation_empty_yielding(sk1_esk124_0),
inference(literals_permutation,[status(thm)],[c_0_3002]) ).
cnf(c_0_3003_0,axiom,
function(sk1_esk124_0),
inference(literals_permutation,[status(thm)],[c_0_3003]) ).
cnf(c_0_3004_0,axiom,
one_sorted_str(sk1_esk123_0),
inference(literals_permutation,[status(thm)],[c_0_3004]) ).
cnf(c_0_3005_0,axiom,
relation(sk1_esk122_0),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3006_0,axiom,
relation_empty_yielding(sk1_esk122_0),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3007_0,axiom,
epsilon_transitive(sk1_esk121_0),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3008_0,axiom,
epsilon_connected(sk1_esk121_0),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3009_0,axiom,
ordinal(sk1_esk121_0),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3010_0,axiom,
relation(sk1_esk120_0),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3011_0,axiom,
function(sk1_esk120_0),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3012_0,axiom,
one_to_one(sk1_esk120_0),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3013_0,axiom,
relation(sk1_esk116_0),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3014_0,axiom,
relation(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3015_0,axiom,
function(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3016_0,axiom,
one_to_one(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3017_0,axiom,
empty(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3018_0,axiom,
epsilon_transitive(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3018]) ).
cnf(c_0_3019_0,axiom,
epsilon_connected(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3020_0,axiom,
ordinal(sk1_esk114_0),
inference(literals_permutation,[status(thm)],[c_0_3020]) ).
cnf(c_0_3021_0,axiom,
relation(sk1_esk113_0),
inference(literals_permutation,[status(thm)],[c_0_3021]) ).
cnf(c_0_3022_0,axiom,
empty(sk1_esk113_0),
inference(literals_permutation,[status(thm)],[c_0_3022]) ).
cnf(c_0_3023_0,axiom,
function(sk1_esk113_0),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3024_0,axiom,
empty(sk1_esk111_0),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3025_0,axiom,
empty(sk1_esk109_0),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3026_0,axiom,
relation(sk1_esk109_0),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3027_0,axiom,
relation(sk1_esk108_0),
inference(literals_permutation,[status(thm)],[c_0_3027]) ).
cnf(c_0_3028_0,axiom,
function(sk1_esk108_0),
inference(literals_permutation,[status(thm)],[c_0_3028]) ).
cnf(c_0_3029_0,axiom,
one_to_one(sk1_esk108_0),
inference(literals_permutation,[status(thm)],[c_0_3029]) ).
cnf(c_0_3030_0,axiom,
empty(sk1_esk108_0),
inference(literals_permutation,[status(thm)],[c_0_3030]) ).
cnf(c_0_3031_0,axiom,
epsilon_transitive(sk1_esk107_0),
inference(literals_permutation,[status(thm)],[c_0_3031]) ).
cnf(c_0_3032_0,axiom,
epsilon_connected(sk1_esk107_0),
inference(literals_permutation,[status(thm)],[c_0_3032]) ).
cnf(c_0_3033_0,axiom,
ordinal(sk1_esk107_0),
inference(literals_permutation,[status(thm)],[c_0_3033]) ).
cnf(c_0_3034_0,axiom,
being_limit_ordinal(sk1_esk107_0),
inference(literals_permutation,[status(thm)],[c_0_3034]) ).
cnf(c_0_3035_0,axiom,
epsilon_transitive(sk1_esk106_0),
inference(literals_permutation,[status(thm)],[c_0_3035]) ).
cnf(c_0_3036_0,axiom,
epsilon_connected(sk1_esk106_0),
inference(literals_permutation,[status(thm)],[c_0_3036]) ).
cnf(c_0_3037_0,axiom,
ordinal(sk1_esk106_0),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3038_0,axiom,
v1_membered(sk1_esk105_0),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3039_0,axiom,
v2_membered(sk1_esk105_0),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3040_0,axiom,
v3_membered(sk1_esk105_0),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3041_0,axiom,
v4_membered(sk1_esk105_0),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3042_0,axiom,
v5_membered(sk1_esk105_0),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3043_0,axiom,
relation(sk1_esk103_0),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3044_0,axiom,
function(sk1_esk103_0),
inference(literals_permutation,[status(thm)],[c_0_3044]) ).
cnf(c_0_3045_0,axiom,
finite(sk1_esk102_0),
inference(literals_permutation,[status(thm)],[c_0_3045]) ).
cnf(c_0_3046_0,axiom,
epsilon_transitive(sk1_esk101_0),
inference(literals_permutation,[status(thm)],[c_0_3046]) ).
cnf(c_0_3047_0,axiom,
epsilon_connected(sk1_esk101_0),
inference(literals_permutation,[status(thm)],[c_0_3047]) ).
cnf(c_0_3048_0,axiom,
ordinal(sk1_esk101_0),
inference(literals_permutation,[status(thm)],[c_0_3048]) ).
cnf(c_0_3049_0,axiom,
natural(sk1_esk101_0),
inference(literals_permutation,[status(thm)],[c_0_3049]) ).
cnf(c_0_3050_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3050]) ).
cnf(c_0_3051_0,axiom,
v1_membered(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3051]) ).
cnf(c_0_3052_0,axiom,
v2_membered(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3052]) ).
cnf(c_0_3053_0,axiom,
v3_membered(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3053]) ).
cnf(c_0_3054_0,axiom,
v4_membered(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3054]) ).
cnf(c_0_3055_0,axiom,
v5_membered(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3055]) ).
cnf(c_0_3056_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3056]) ).
cnf(c_0_3057_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3057]) ).
cnf(c_0_3058_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3059_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3060_0,axiom,
function(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3060]) ).
cnf(c_0_3061_0,axiom,
one_to_one(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3062_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3062]) ).
cnf(c_0_3063_0,axiom,
epsilon_transitive(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3063]) ).
cnf(c_0_3064_0,axiom,
epsilon_connected(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3064]) ).
cnf(c_0_3065_0,axiom,
ordinal(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3065]) ).
cnf(c_0_3066_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3066]) ).
cnf(c_0_3067_0,axiom,
epsilon_transitive(omega),
inference(literals_permutation,[status(thm)],[c_0_3067]) ).
cnf(c_0_3068_0,axiom,
epsilon_connected(omega),
inference(literals_permutation,[status(thm)],[c_0_3068]) ).
cnf(c_0_3069_0,axiom,
ordinal(omega),
inference(literals_permutation,[status(thm)],[c_0_3069]) ).
cnf(c_0_3070_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3070]) ).
cnf(c_0_3071_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3071]) ).
cnf(c_0_3072_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_3072]) ).
cnf(c_0_3073_0,axiom,
latt_str(sk1_esk97_0),
inference(literals_permutation,[status(thm)],[c_0_3073]) ).
cnf(c_0_3074_0,axiom,
join_semilatt_str(sk1_esk96_0),
inference(literals_permutation,[status(thm)],[c_0_3074]) ).
cnf(c_0_3075_0,axiom,
one_sorted_str(sk1_esk95_0),
inference(literals_permutation,[status(thm)],[c_0_3075]) ).
cnf(c_0_3076_0,axiom,
meet_semilatt_str(sk1_esk94_0),
inference(literals_permutation,[status(thm)],[c_0_3076]) ).
cnf(c_0_3077_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3077]) ).
cnf(c_0_3078_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3078]) ).
cnf(c_0_3079_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3079]) ).
cnf(c_0_3080_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3080]) ).
cnf(c_0_3081_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3081]) ).
cnf(c_0_3082_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3082]) ).
cnf(c_0_3083_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3083]) ).
cnf(c_0_3084_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3084]) ).
cnf(c_0_3085_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3085]) ).
cnf(c_0_3086_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3086]) ).
cnf(c_0_3087_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3087]) ).
cnf(c_0_3088_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3088]) ).
cnf(c_0_3089_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3089]) ).
cnf(c_0_3090_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3090]) ).
cnf(c_0_3091_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3091]) ).
cnf(c_0_3092_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3092]) ).
cnf(c_0_3093_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3093]) ).
cnf(c_0_3094_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3094]) ).
cnf(c_0_3095_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3095]) ).
cnf(c_0_3096_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3096]) ).
cnf(c_0_3097_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3097]) ).
cnf(c_0_3098_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3098]) ).
cnf(c_0_3099_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3099]) ).
cnf(c_0_3100_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3100]) ).
cnf(c_0_3101_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3101]) ).
cnf(c_0_3102_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3102]) ).
cnf(c_0_3103_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3103]) ).
cnf(c_0_3104_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_3104]) ).
% 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] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) ) ) ) ) ),
file('<stdin>',s1_xboole_0__e18_27__finset_1__1) ).
fof(c_0_7_008,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_8_009,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_9_010,lemma,
( ! [X1] :
( ordinal(X1)
=> ( ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> ( in(X2,omega)
=> ! [X3] :
( element(X3,powerset(powerset(X2)))
=> ~ ( X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& ! [X5] :
( ( in(X5,X3)
& subset(X4,X5) )
=> X5 = X4 ) ) ) ) ) ) )
=> ( in(X1,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X1)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) ) )
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,omega)
=> ! [X9] :
( element(X9,powerset(powerset(X1)))
=> ~ ( X9 != empty_set
& ! [X10] :
~ ( in(X10,X9)
& ! [X11] :
( ( in(X11,X9)
& subset(X10,X11) )
=> X11 = X10 ) ) ) ) ) ) ),
file('<stdin>',s2_ordinal1__e18_27__finset_1__1) ).
fof(c_0_10_011,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_11_012,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_12_013,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_13_014,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_14_015,lemma,
! [X1,X2,X3] :
( ( element(X2,powerset(powerset(X1)))
& relation(X3)
& function(X3) )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,powerset(relation_dom(X3)))
& in(relation_image(X3,X5),X2) ) ) ),
file('<stdin>',s1_xboole_0__e6_27__finset_1) ).
fof(c_0_15_016,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_16_017,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_17_018,lemma,
! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(X1))
& ? [X5] :
( in(X5,X2)
& X4 = set_difference(X5,singleton(X1)) ) ) ) ),
file('<stdin>',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(c_0_18_019,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_19_020,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('<stdin>',t26_lattices) ).
fof(c_0_20_021,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
file('<stdin>',t23_lattices) ).
fof(c_0_21_022,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_22_023,lemma,
( ( ( in(empty_set,omega)
=> ! [X1] :
( element(X1,powerset(powerset(empty_set)))
=> ~ ( X1 != empty_set
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
( ( in(X3,X1)
& subset(X2,X3) )
=> X3 = X2 ) ) ) ) )
& ! [X4] :
( ordinal(X4)
=> ( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) )
=> ( in(succ(X4),omega)
=> ! [X8] :
( element(X8,powerset(powerset(succ(X4))))
=> ~ ( X8 != empty_set
& ! [X9] :
~ ( in(X9,X8)
& ! [X10] :
( ( in(X10,X8)
& subset(X9,X10) )
=> X10 = X9 ) ) ) ) ) ) )
& ! [X4] :
( ordinal(X4)
=> ( ( being_limit_ordinal(X4)
& ! [X11] :
( ordinal(X11)
=> ( in(X11,X4)
=> ( in(X11,omega)
=> ! [X12] :
( element(X12,powerset(powerset(X11)))
=> ~ ( X12 != empty_set
& ! [X13] :
~ ( in(X13,X12)
& ! [X14] :
( ( in(X14,X12)
& subset(X13,X14) )
=> X14 = X13 ) ) ) ) ) ) ) )
=> ( X4 = empty_set
| ( in(X4,omega)
=> ! [X15] :
( element(X15,powerset(powerset(X4)))
=> ~ ( X15 != empty_set
& ! [X16] :
~ ( in(X16,X15)
& ! [X17] :
( ( in(X17,X15)
& subset(X16,X17) )
=> X17 = X16 ) ) ) ) ) ) ) ) )
=> ! [X4] :
( ordinal(X4)
=> ( in(X4,omega)
=> ! [X18] :
( element(X18,powerset(powerset(X4)))
=> ~ ( X18 != empty_set
& ! [X19] :
~ ( in(X19,X18)
& ! [X20] :
( ( in(X20,X18)
& subset(X19,X20) )
=> X20 = X19 ) ) ) ) ) ) ),
file('<stdin>',s1_ordinal2__e18_27__finset_1) ).
fof(c_0_23_024,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_24_025,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_25_026,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_26_027,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_27_028,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_28_029,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_29_030,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_30_031,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_31_032,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_32_033,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_33_034,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_34_035,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_35_036,lemma,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
( ( in(X4,X2)
& subset(X3,X4) )
=> X4 = X3 ) ) ) ) ),
file('<stdin>',t18_finset_1) ).
fof(c_0_36_037,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_37_038,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_38_039,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_39_040,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_40_041,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_41_042,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_42_043,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_43_044,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_44_045,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_45_046,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_46_047,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_47_048,lemma,
! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
file('<stdin>',t21_wellord1) ).
fof(c_0_48_049,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_49_050,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_50_051,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_51_052,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_52_053,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_53_054,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_54_055,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_55_056,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_56_057,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_57_058,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_58_059,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_59_060,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_60_061,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_61_062,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_62_063,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_63_064,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_64_065,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_65_066,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_66_067,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_67_068,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_68_069,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_69_070,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_70_071,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_71_072,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_72_073,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_73_074,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_74_075,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_75_076,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_76_077,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_77_078,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_78_079,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_79_080,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_80_081,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_81_082,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_82_083,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('<stdin>',t99_relat_1) ).
fof(c_0_83_084,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_84_085,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('<stdin>',t118_relat_1) ).
fof(c_0_85_086,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
file('<stdin>',l29_wellord1) ).
fof(c_0_86_087,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('<stdin>',l71_subset_1) ).
fof(c_0_87_088,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_88_089,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('<stdin>',t116_relat_1) ).
fof(c_0_89_090,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_90_091,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_91_092,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_92_093,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('<stdin>',t56_relat_1) ).
fof(c_0_93_094,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_94_095,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('<stdin>',t21_relat_1) ).
fof(c_0_95_096,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_96_097,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_97_098,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
file('<stdin>',t3_ordinal1) ).
fof(c_0_98_099,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_99_100,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_100_101,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_101_102,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_102_103,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_103_104,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_104_105,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_105_106,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('<stdin>',t33_ordinal1) ).
fof(c_0_106_107,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_107_108,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_108_109,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_109_110,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_110_111,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_111_112,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_112_113,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_113_114,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_114_115,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_115_116,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_116_117,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('<stdin>',t31_ordinal1) ).
fof(c_0_117_118,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('<stdin>',t167_relat_1) ).
fof(c_0_118_119,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('<stdin>',t144_relat_1) ).
fof(c_0_119_120,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( finite(X1)
=> finite(relation_image(X2,X1)) ) ),
file('<stdin>',t17_finset_1) ).
fof(c_0_120_121,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('<stdin>',t21_ordinal1) ).
fof(c_0_121_122,lemma,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
file('<stdin>',s1_xboole_0__e6_22__wellord2) ).
fof(c_0_122_123,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_123_124,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('<stdin>',t88_relat_1) ).
fof(c_0_124_125,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('<stdin>',t117_relat_1) ).
fof(c_0_125_126,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_126_127,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_127_128,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_128_129,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_129_130,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('<stdin>',t24_ordinal1) ).
fof(c_0_130_131,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_131_132,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
file('<stdin>',t32_wellord1) ).
fof(c_0_132_133,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
file('<stdin>',t31_wellord1) ).
fof(c_0_133_134,lemma,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('<stdin>',t25_wellord1) ).
fof(c_0_134_135,lemma,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
file('<stdin>',t24_wellord1) ).
fof(c_0_135_136,lemma,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
file('<stdin>',t23_wellord1) ).
fof(c_0_136_137,lemma,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
file('<stdin>',t22_wellord1) ).
fof(c_0_137_138,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_138_139,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('<stdin>',t8_wellord1) ).
fof(c_0_139_140,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('<stdin>',t5_wellord1) ).
fof(c_0_140_141,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_141_142,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('<stdin>',t35_funct_1) ).
fof(c_0_142_143,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_143_144,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_144_145,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_145_146,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
file('<stdin>',t26_finset_1) ).
fof(c_0_146_147,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('<stdin>',t94_relat_1) ).
fof(c_0_147_148,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_148_149,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_149_150,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_150_151,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_151_152,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_152_153,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_153_154,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_154_155,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_155_156,lemma,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('<stdin>',t15_finset_1) ).
fof(c_0_156_157,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_157_158,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_158_159,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_159_160,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_160_161,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('<stdin>',t23_ordinal1) ).
fof(c_0_161_162,lemma,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('<stdin>',t13_finset_1) ).
fof(c_0_162_163,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('<stdin>',t62_funct_1) ).
fof(c_0_163_164,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('<stdin>',t146_relat_1) ).
fof(c_0_164_165,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_165_166,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_166_167,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_167_168,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_168_169,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_169_170,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_170_171,lemma,
! [X1] :
? [X2] :
( relation(X2)
& well_orders(X2,X1) ),
file('<stdin>',t26_wellord2) ).
fof(c_0_171_172,lemma,
! [X1] : in(X1,succ(X1)),
file('<stdin>',t10_ordinal1) ).
fof(c_0_172_173,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('<stdin>',t65_relat_1) ).
fof(c_0_173_174,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_174_175,lemma,
! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
file('<stdin>',t7_wellord2) ).
fof(c_0_175_176,lemma,
! [X1] :
( ordinal(X1)
=> well_founded_relation(inclusion_relation(X1)) ),
file('<stdin>',t6_wellord2) ).
fof(c_0_176_177,lemma,
! [X1] :
( ordinal(X1)
=> connected(inclusion_relation(X1)) ),
file('<stdin>',t4_wellord2) ).
fof(c_0_177_178,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_178_179,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_179_180,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_180_181,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('<stdin>',t71_relat_1) ).
fof(c_0_181_182,lemma,
! [X1] : antisymmetric(inclusion_relation(X1)),
file('<stdin>',t5_wellord2) ).
fof(c_0_182_183,lemma,
! [X1] : transitive(inclusion_relation(X1)),
file('<stdin>',t3_wellord2) ).
fof(c_0_183_184,lemma,
! [X1] : reflexive(inclusion_relation(X1)),
file('<stdin>',t2_wellord2) ).
fof(c_0_184_185,conjecture,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('<stdin>',t12_pre_topc) ).
fof(c_0_185_186,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_186_187,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_187_188,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('<stdin>',t60_relat_1) ).
fof(c_0_188_189,plain,
( epred1_0
<=> ( ! [X4] :
( ordinal(X4)
=> ( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) )
=> ( in(succ(X4),omega)
=> ! [X8] :
( element(X8,powerset(powerset(succ(X4))))
=> ~ ( X8 != empty_set
& ! [X9] :
~ ( in(X9,X8)
& ! [X10] :
( ( in(X10,X8)
& subset(X9,X10) )
=> X10 = X9 ) ) ) ) ) ) )
& ! [X4] :
( ordinal(X4)
=> ( ( being_limit_ordinal(X4)
& ! [X11] :
( ordinal(X11)
=> ( in(X11,X4)
=> ( in(X11,omega)
=> ! [X12] :
( element(X12,powerset(powerset(X11)))
=> ~ ( X12 != empty_set
& ! [X13] :
~ ( in(X13,X12)
& ! [X14] :
( ( in(X14,X12)
& subset(X13,X14) )
=> X14 = X13 ) ) ) ) ) ) ) )
=> ( X4 = empty_set
| ( in(X4,omega)
=> ! [X15] :
( element(X15,powerset(powerset(X4)))
=> ~ ( X15 != empty_set
& ! [X16] :
~ ( in(X16,X15)
& ! [X17] :
( ( in(X17,X15)
& subset(X16,X17) )
=> X17 = X16 ) ) ) ) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_189_190,plain,
! [X1,X2] :
( epred2_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_190_191,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_191_192,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_192_193,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_193_194,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_194_195,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_195_196,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_196_197,lemma,
! [X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) ) ) ) ) ),
c_0_6 ).
fof(c_0_197_198,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_7 ).
fof(c_0_198_199,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_8 ).
fof(c_0_199_200,lemma,
( ! [X1] :
( ordinal(X1)
=> ( ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> ( in(X2,omega)
=> ! [X3] :
( element(X3,powerset(powerset(X2)))
=> ~ ( X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& ! [X5] :
( ( in(X5,X3)
& subset(X4,X5) )
=> X5 = X4 ) ) ) ) ) ) )
=> ( in(X1,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X1)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) ) )
=> ! [X1] :
( ordinal(X1)
=> ( in(X1,omega)
=> ! [X9] :
( element(X9,powerset(powerset(X1)))
=> ~ ( X9 != empty_set
& ! [X10] :
~ ( in(X10,X9)
& ! [X11] :
( ( in(X11,X9)
& subset(X10,X11) )
=> X11 = X10 ) ) ) ) ) ) ),
c_0_9 ).
fof(c_0_200_201,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_10 ).
fof(c_0_201_202,plain,
( ( ! [X4] :
( ordinal(X4)
=> ( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) )
=> ( in(succ(X4),omega)
=> ! [X8] :
( element(X8,powerset(powerset(succ(X4))))
=> ~ ( X8 != empty_set
& ! [X9] :
~ ( in(X9,X8)
& ! [X10] :
( ( in(X10,X8)
& subset(X9,X10) )
=> X10 = X9 ) ) ) ) ) ) )
& ! [X4] :
( ordinal(X4)
=> ( ( being_limit_ordinal(X4)
& ! [X11] :
( ordinal(X11)
=> ( in(X11,X4)
=> ( in(X11,omega)
=> ! [X12] :
( element(X12,powerset(powerset(X11)))
=> ~ ( X12 != empty_set
& ! [X13] :
~ ( in(X13,X12)
& ! [X14] :
( ( in(X14,X12)
& subset(X13,X14) )
=> X14 = X13 ) ) ) ) ) ) ) )
=> ( X4 = empty_set
| ( in(X4,omega)
=> ! [X15] :
( element(X15,powerset(powerset(X4)))
=> ~ ( X15 != empty_set
& ! [X16] :
~ ( in(X16,X15)
& ! [X17] :
( ( in(X17,X15)
& subset(X16,X17) )
=> X17 = X16 ) ) ) ) ) ) ) ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_188]) ).
fof(c_0_202_203,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_11 ).
fof(c_0_203_204,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_12 ).
fof(c_0_204_205,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_13 ).
fof(c_0_205_206,lemma,
! [X1,X2,X3] :
( ( element(X2,powerset(powerset(X1)))
& relation(X3)
& function(X3) )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,powerset(relation_dom(X3)))
& in(relation_image(X3,X5),X2) ) ) ),
c_0_14 ).
fof(c_0_206_207,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_15 ).
fof(c_0_207_208,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_16 ).
fof(c_0_208_209,lemma,
! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(X1))
& ? [X5] :
( in(X5,X2)
& X4 = set_difference(X5,singleton(X1)) ) ) ) ),
c_0_17 ).
fof(c_0_209_210,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_18 ).
fof(c_0_210_211,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_211_212,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_212_213,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_21 ).
fof(c_0_213_214,lemma,
( ( ( in(empty_set,omega)
=> ! [X1] :
( element(X1,powerset(powerset(empty_set)))
=> ~ ( X1 != empty_set
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
( ( in(X3,X1)
& subset(X2,X3) )
=> X3 = X2 ) ) ) ) )
& epred1_0 )
=> ! [X4] :
( ordinal(X4)
=> ( in(X4,omega)
=> ! [X18] :
( element(X18,powerset(powerset(X4)))
=> ~ ( X18 != empty_set
& ! [X19] :
~ ( in(X19,X18)
& ! [X20] :
( ( in(X20,X18)
& subset(X19,X20) )
=> X20 = X19 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_188,theory(equality,[symmetry])]) ).
fof(c_0_214_215,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_23 ).
fof(c_0_215_216,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_24 ).
fof(c_0_216_217,lemma,
! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,succ(X2))
& ? [X5] :
( ordinal(X5)
& X4 = X5
& in(X5,X1) ) ) ) ),
c_0_25 ).
fof(c_0_217_218,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_26 ).
fof(c_0_218_219,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_27 ).
fof(c_0_219_220,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_28 ).
fof(c_0_220_221,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_29 ).
fof(c_0_221_222,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_30 ).
fof(c_0_222_223,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_31 ).
fof(c_0_223_224,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_32 ).
fof(c_0_224_225,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(X1,X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
c_0_33 ).
fof(c_0_225_226,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_34]) ).
fof(c_0_226_227,lemma,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
( ( in(X4,X2)
& subset(X3,X4) )
=> X4 = X3 ) ) ) ) ),
c_0_35 ).
fof(c_0_227_228,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_36 ).
fof(c_0_228_229,lemma,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
c_0_37 ).
fof(c_0_229_230,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
c_0_38 ).
fof(c_0_230_231,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_39 ).
fof(c_0_231_232,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
c_0_40 ).
fof(c_0_232_233,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_41 ).
fof(c_0_233_234,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_42 ).
fof(c_0_234_235,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
c_0_43 ).
fof(c_0_235_236,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
c_0_44 ).
fof(c_0_236_237,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> epred2_2(X2,X1) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_45,c_0_189,theory(equality,[symmetry])]) ).
fof(c_0_237_238,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_46 ).
fof(c_0_238_239,lemma,
! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
c_0_47 ).
fof(c_0_239_240,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_48 ).
fof(c_0_240_241,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_49 ).
fof(c_0_241_242,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_50 ).
fof(c_0_242_243,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
c_0_51 ).
fof(c_0_243_244,lemma,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
c_0_52 ).
fof(c_0_244_245,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_53 ).
fof(c_0_245_246,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_54 ).
fof(c_0_246_247,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_55]) ).
fof(c_0_247_248,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_56 ).
fof(c_0_248_249,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_57 ).
fof(c_0_249_250,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
c_0_58 ).
fof(c_0_250_251,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
c_0_59 ).
fof(c_0_251_252,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_60 ).
fof(c_0_252_253,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_61]) ).
fof(c_0_253_254,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
c_0_62 ).
fof(c_0_254_255,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
c_0_63 ).
fof(c_0_255_256,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
c_0_64 ).
fof(c_0_256_257,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
c_0_65 ).
fof(c_0_257_258,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
c_0_66 ).
fof(c_0_258_259,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
c_0_67 ).
fof(c_0_259_260,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_68 ).
fof(c_0_260_261,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_69 ).
fof(c_0_261_262,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_70 ).
fof(c_0_262_263,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_71 ).
fof(c_0_263_264,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_72 ).
fof(c_0_264_265,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_73 ).
fof(c_0_265_266,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_74 ).
fof(c_0_266_267,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
c_0_75 ).
fof(c_0_267_268,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_76 ).
fof(c_0_268_269,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_77]) ).
fof(c_0_269_270,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_78]) ).
fof(c_0_270_271,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_79 ).
fof(c_0_271_272,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_80 ).
fof(c_0_272_273,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_81 ).
fof(c_0_273_274,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
c_0_82 ).
fof(c_0_274_275,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_83 ).
fof(c_0_275_276,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
c_0_84 ).
fof(c_0_276_277,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
c_0_85 ).
fof(c_0_277_278,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
c_0_86 ).
fof(c_0_278_279,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_87 ).
fof(c_0_279_280,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
c_0_88 ).
fof(c_0_280_281,lemma,
! [X1,X2] :
( relation(X2)
=> ( ( well_ordering(X2)
& subset(X1,relation_field(X2)) )
=> relation_field(relation_restriction(X2,X1)) = X1 ) ),
c_0_89 ).
fof(c_0_281_282,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
c_0_90 ).
fof(c_0_282_283,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_91]) ).
fof(c_0_283_284,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_284_285,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
c_0_93 ).
fof(c_0_285_286,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
c_0_94 ).
fof(c_0_286_287,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_95 ).
fof(c_0_287_288,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_96]) ).
fof(c_0_288_289,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
c_0_97 ).
fof(c_0_289_290,lemma,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
c_0_98 ).
fof(c_0_290_291,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
c_0_99 ).
fof(c_0_291_292,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_100 ).
fof(c_0_292_293,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_101 ).
fof(c_0_293_294,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
c_0_102 ).
fof(c_0_294_295,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_rng_restriction(X1,relation_dom_restriction(X2,X1)) ),
c_0_103 ).
fof(c_0_295_296,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_dom_restriction(relation_rng_restriction(X1,X2),X1) ),
c_0_104 ).
fof(c_0_296_297,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
c_0_105 ).
fof(c_0_297_298,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_orders(X2,X1)
=> ( relation_field(relation_restriction(X2,X1)) = X1
& well_ordering(relation_restriction(X2,X1)) ) ) ),
c_0_106 ).
fof(c_0_298_299,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_107 ).
fof(c_0_299_300,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_108 ).
fof(c_0_300_301,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
c_0_109 ).
fof(c_0_301_302,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
c_0_110 ).
fof(c_0_302_303,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_303_304,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_112 ).
fof(c_0_304_305,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_113 ).
fof(c_0_305_306,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_114 ).
fof(c_0_306_307,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_115 ).
fof(c_0_307_308,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
c_0_116 ).
fof(c_0_308_309,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
c_0_117 ).
fof(c_0_309_310,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
c_0_118 ).
fof(c_0_310_311,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( finite(X1)
=> finite(relation_image(X2,X1)) ) ),
c_0_119 ).
fof(c_0_311_312,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
c_0_120 ).
fof(c_0_312_313,lemma,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
c_0_121 ).
fof(c_0_313_314,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_122 ).
fof(c_0_314_315,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
c_0_123 ).
fof(c_0_315_316,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
c_0_124 ).
fof(c_0_316_317,lemma,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
c_0_125 ).
fof(c_0_317_318,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_126 ).
fof(c_0_318_319,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_127 ).
fof(c_0_319_320,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_128 ).
fof(c_0_320_321,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_321_322,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_130 ).
fof(c_0_322_323,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
c_0_131 ).
fof(c_0_323_324,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
c_0_132 ).
fof(c_0_324_325,lemma,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
c_0_133 ).
fof(c_0_325_326,lemma,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
c_0_134 ).
fof(c_0_326_327,lemma,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
c_0_135 ).
fof(c_0_327_328,lemma,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
c_0_136 ).
fof(c_0_328_329,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_137 ).
fof(c_0_329_330,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
c_0_138 ).
fof(c_0_330_331,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
c_0_139 ).
fof(c_0_331_332,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_140 ).
fof(c_0_332_333,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
c_0_141 ).
fof(c_0_333_334,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_142 ).
fof(c_0_334_335,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_143 ).
fof(c_0_335_336,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_144 ).
fof(c_0_336_337,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
c_0_145 ).
fof(c_0_337_338,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
c_0_146 ).
fof(c_0_338_339,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_147 ).
fof(c_0_339_340,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_148 ).
fof(c_0_340_341,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_149 ).
fof(c_0_341_342,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_150 ).
fof(c_0_342_343,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_151 ).
fof(c_0_343_344,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_152 ).
fof(c_0_344_345,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_153 ).
fof(c_0_345_346,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_154 ).
fof(c_0_346_347,lemma,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
c_0_155 ).
fof(c_0_347_348,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_156 ).
fof(c_0_348_349,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_157 ).
fof(c_0_349_350,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_158 ).
fof(c_0_350_351,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_351_352,plain,
! [X1,X2] :
( epred2_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_189]) ).
fof(c_0_352_353,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
c_0_160 ).
fof(c_0_353_354,lemma,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
c_0_161 ).
fof(c_0_354_355,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
c_0_162 ).
fof(c_0_355_356,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
c_0_163 ).
fof(c_0_356_357,lemma,
! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
c_0_164 ).
fof(c_0_357_358,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_165 ).
fof(c_0_358_359,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_166 ).
fof(c_0_359_360,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_167]) ).
fof(c_0_360_361,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_168 ).
fof(c_0_361_362,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
c_0_169 ).
fof(c_0_362_363,lemma,
! [X1] :
? [X2] :
( relation(X2)
& well_orders(X2,X1) ),
c_0_170 ).
fof(c_0_363_364,lemma,
! [X1] : in(X1,succ(X1)),
c_0_171 ).
fof(c_0_364_365,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
c_0_172 ).
fof(c_0_365_366,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_173 ).
fof(c_0_366_367,lemma,
! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
c_0_174 ).
fof(c_0_367_368,lemma,
! [X1] :
( ordinal(X1)
=> well_founded_relation(inclusion_relation(X1)) ),
c_0_175 ).
fof(c_0_368_369,lemma,
! [X1] :
( ordinal(X1)
=> connected(inclusion_relation(X1)) ),
c_0_176 ).
fof(c_0_369_370,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
c_0_177 ).
fof(c_0_370_371,lemma,
! [X1] : subset(empty_set,X1),
c_0_178 ).
fof(c_0_371_372,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_179 ).
fof(c_0_372_373,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
c_0_180 ).
fof(c_0_373_374,lemma,
! [X1] : antisymmetric(inclusion_relation(X1)),
c_0_181 ).
fof(c_0_374_375,lemma,
! [X1] : transitive(inclusion_relation(X1)),
c_0_182 ).
fof(c_0_375_376,lemma,
! [X1] : reflexive(inclusion_relation(X1)),
c_0_183 ).
fof(c_0_376_377,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(assume_negation,[status(cth)],[c_0_184]) ).
fof(c_0_377_378,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_185 ).
fof(c_0_378_379,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_186 ).
fof(c_0_379_380,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_187 ).
fof(c_0_380_381,lemma,
! [X10,X11,X12,X14,X18,X19,X20,X21,X22] :
( ( in(X14,cartesian_product2(X10,X12))
| ~ in(X14,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( ordered_pair(esk29_4(X10,X11,X12,X14),esk30_4(X10,X11,X12,X14)) = X14
| ~ in(X14,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( in(esk29_4(X10,X11,X12,X14),X10)
| ~ in(X14,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( esk29_4(X10,X11,X12,X14) = esk31_4(X10,X11,X12,X14)
| ~ in(X14,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( in(esk30_4(X10,X11,X12,X14),esk31_4(X10,X11,X12,X14))
| ~ in(X14,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( ~ in(X18,esk31_4(X10,X11,X12,X14))
| in(ordered_pair(esk30_4(X10,X11,X12,X14),X18),X11)
| ~ in(X14,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( in(esk32_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,esk28_3(X10,X11,X12))
| empty(X10)
| ~ relation(X11) )
& ( ~ in(ordered_pair(X21,esk32_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,esk28_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_190])])])])])]) ).
fof(c_0_381_382,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_191])])])])])]) ).
fof(c_0_382_383,lemma,
! [X8,X9,X10,X12,X15,X16,X17] :
( ( in(X12,cartesian_product2(X8,X8))
| ~ in(X12,esk43_3(X8,X9,X10))
| ~ relation(X9)
| ~ relation(X10)
| ~ function(X10) )
& ( X12 = ordered_pair(esk44_4(X8,X9,X10,X12),esk45_4(X8,X9,X10,X12))
| ~ in(X12,esk43_3(X8,X9,X10))
| ~ relation(X9)
| ~ relation(X10)
| ~ function(X10) )
& ( in(ordered_pair(apply(X10,esk44_4(X8,X9,X10,X12)),apply(X10,esk45_4(X8,X9,X10,X12))),X9)
| ~ in(X12,esk43_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,esk43_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_192])])])])])]) ).
fof(c_0_383_384,lemma,
! [X14,X15,X20,X22,X24,X25,X28,X30] :
( ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk50_2(X14,X15),X14)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk53_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk51_2(X14,X15),esk53_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X20,esk53_2(X14,X15))
| in(ordered_pair(esk51_2(X14,X15),X20),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk50_2(X14,X15) = esk54_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| in(esk52_2(X14,X15),esk54_2(X14,X15))
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| ~ in(X22,esk54_2(X14,X15))
| in(ordered_pair(esk52_2(X14,X15),X22),X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk55_2(X14,X15),X14)
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk55_2(X14,X15),X14)
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk55_2(X14,X15),X14)
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| in(esk56_4(X14,X15,X24,X25),X25)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( function(esk57_2(X14,X15))
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( relation_dom(esk57_2(X14,X15)) = X14
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( X28 = esk58_3(X14,X15,X28)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( in(apply(esk57_2(X14,X15),X28),esk58_3(X14,X15,X28))
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_2(X14,X15)
| empty(X14)
| ~ relation(X15) )
& ( ~ in(X30,esk58_3(X14,X15,X28))
| in(ordered_pair(apply(esk57_2(X14,X15),X28),X30),X15)
| ~ in(X28,X14)
| ~ in(ordered_pair(X24,esk56_4(X14,X15,X24,X25)),X15)
| ~ in(X24,X25)
| esk55_2(X14,X15) != X25
| esk51_2(X14,X15) != esk52_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_193])])])])]) ).
fof(c_0_384_385,lemma,
! [X6,X7,X8,X10,X11] :
( ( in(esk77_3(X6,X7,X8),X7)
| relation_rng_as_subset(X6,X7,X8) = X7
| ~ relation_of2_as_subset(X8,X6,X7) )
& ( ~ in(ordered_pair(X10,esk77_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(esk78_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_194])])])])]) ).
fof(c_0_385_386,lemma,
! [X6,X7,X8,X10,X11] :
( ( in(esk75_3(X6,X7,X8),X7)
| relation_dom_as_subset(X7,X6,X8) = X7
| ~ relation_of2_as_subset(X8,X7,X6) )
& ( ~ in(ordered_pair(esk75_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,esk76_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_195])])])])]) ).
fof(c_0_386_387,lemma,
! [X8,X10,X12,X14,X15,X16,X18] :
( ( in(X10,succ(X8))
| ~ in(X10,esk36_1(X8))
| ~ ordinal(X8) )
& ( ordinal(esk37_2(X8,X10))
| ~ in(X10,esk36_1(X8))
| ~ ordinal(X8) )
& ( X10 = esk37_2(X8,X10)
| ~ in(X10,esk36_1(X8))
| ~ ordinal(X8) )
& ( in(esk38_3(X8,X10,X12),X12)
| X12 = empty_set
| ~ element(X12,powerset(powerset(esk37_2(X8,X10))))
| ~ in(esk37_2(X8,X10),omega)
| ~ in(X10,esk36_1(X8))
| ~ ordinal(X8) )
& ( ~ in(X14,X12)
| ~ subset(esk38_3(X8,X10,X12),X14)
| X14 = esk38_3(X8,X10,X12)
| X12 = empty_set
| ~ element(X12,powerset(powerset(esk37_2(X8,X10))))
| ~ in(esk37_2(X8,X10),omega)
| ~ in(X10,esk36_1(X8))
| ~ ordinal(X8) )
& ( in(X16,omega)
| X15 != X16
| ~ ordinal(X16)
| ~ in(X15,succ(X8))
| in(X15,esk36_1(X8))
| ~ ordinal(X8) )
& ( element(esk39_3(X8,X15,X16),powerset(powerset(X16)))
| X15 != X16
| ~ ordinal(X16)
| ~ in(X15,succ(X8))
| in(X15,esk36_1(X8))
| ~ ordinal(X8) )
& ( esk39_3(X8,X15,X16) != empty_set
| X15 != X16
| ~ ordinal(X16)
| ~ in(X15,succ(X8))
| in(X15,esk36_1(X8))
| ~ ordinal(X8) )
& ( in(esk40_4(X8,X15,X16,X18),esk39_3(X8,X15,X16))
| ~ in(X18,esk39_3(X8,X15,X16))
| X15 != X16
| ~ ordinal(X16)
| ~ in(X15,succ(X8))
| in(X15,esk36_1(X8))
| ~ ordinal(X8) )
& ( subset(X18,esk40_4(X8,X15,X16,X18))
| ~ in(X18,esk39_3(X8,X15,X16))
| X15 != X16
| ~ ordinal(X16)
| ~ in(X15,succ(X8))
| in(X15,esk36_1(X8))
| ~ ordinal(X8) )
& ( esk40_4(X8,X15,X16,X18) != X18
| ~ in(X18,esk39_3(X8,X15,X16))
| X15 != X16
| ~ ordinal(X16)
| ~ in(X15,succ(X8))
| in(X15,esk36_1(X8))
| ~ ordinal(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_196])])])])])]) ).
fof(c_0_387_388,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(esk95_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,esk95_3(X5,X6,X7)) != apply(X7,esk95_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_197])])])])]) ).
fof(c_0_388_389,lemma,
! [X7,X8,X9,X11,X12,X13,X14] :
( ( relation(esk27_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(X9) )
& ( in(X11,X7)
| ~ in(ordered_pair(X11,X12),esk27_3(X7,X8,X9))
| ~ relation(X8)
| ~ relation(X9)
| ~ function(X9) )
& ( in(X12,X7)
| ~ in(ordered_pair(X11,X12),esk27_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),esk27_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),esk27_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_198])])])])])]) ).
fof(c_0_389_390,lemma,
! [X13,X14,X16,X18,X20,X21,X23] :
( ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| ordinal(esk64_0) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| ordinal(esk64_0) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| in(esk65_2(X13,X14),X14)
| X14 = empty_set
| ~ element(X14,powerset(powerset(X13)))
| ~ in(X13,omega)
| ~ in(X13,esk64_0)
| ~ ordinal(X13) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| in(esk65_2(X13,X14),X14)
| X14 = empty_set
| ~ element(X14,powerset(powerset(X13)))
| ~ in(X13,omega)
| ~ in(X13,esk64_0)
| ~ ordinal(X13) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| ~ in(X16,X14)
| ~ subset(esk65_2(X13,X14),X16)
| X16 = esk65_2(X13,X14)
| X14 = empty_set
| ~ element(X14,powerset(powerset(X13)))
| ~ in(X13,omega)
| ~ in(X13,esk64_0)
| ~ ordinal(X13) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| ~ in(X16,X14)
| ~ subset(esk65_2(X13,X14),X16)
| X16 = esk65_2(X13,X14)
| X14 = empty_set
| ~ element(X14,powerset(powerset(X13)))
| ~ in(X13,omega)
| ~ in(X13,esk64_0)
| ~ ordinal(X13) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| in(esk64_0,omega) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| in(esk64_0,omega) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| element(esk66_0,powerset(powerset(esk64_0))) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| element(esk66_0,powerset(powerset(esk64_0))) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| esk66_0 != empty_set )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| esk66_0 != empty_set )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| in(esk67_1(X18),esk66_0)
| ~ in(X18,esk66_0) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| in(esk67_1(X18),esk66_0)
| ~ in(X18,esk66_0) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| subset(X18,esk67_1(X18))
| ~ in(X18,esk66_0) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| subset(X18,esk67_1(X18))
| ~ in(X18,esk66_0) )
& ( in(esk68_2(X20,X21),X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| esk67_1(X18) != X18
| ~ in(X18,esk66_0) )
& ( ~ in(X23,X21)
| ~ subset(esk68_2(X20,X21),X23)
| X23 = esk68_2(X20,X21)
| X21 = empty_set
| ~ element(X21,powerset(powerset(X20)))
| ~ in(X20,omega)
| ~ ordinal(X20)
| esk67_1(X18) != X18
| ~ in(X18,esk66_0) ) ),
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_199])])])])]) ).
fof(c_0_390_391,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(esk92_2(X5,X6),relation_dom(X5))
| in(esk89_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) )
& ( esk91_2(X5,X6) = apply(X5,esk92_2(X5,X6))
| in(esk89_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(esk91_2(X5,X6),relation_rng(X5))
| esk92_2(X5,X6) != apply(X6,esk91_2(X5,X6))
| in(esk89_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(esk92_2(X5,X6),relation_dom(X5))
| esk90_2(X5,X6) = apply(X6,esk89_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) )
& ( esk91_2(X5,X6) = apply(X5,esk92_2(X5,X6))
| esk90_2(X5,X6) = apply(X6,esk89_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(esk91_2(X5,X6),relation_rng(X5))
| esk92_2(X5,X6) != apply(X6,esk91_2(X5,X6))
| esk90_2(X5,X6) = apply(X6,esk89_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(esk92_2(X5,X6),relation_dom(X5))
| ~ in(esk90_2(X5,X6),relation_dom(X5))
| esk89_2(X5,X6) != apply(X5,esk90_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) )
& ( esk91_2(X5,X6) = apply(X5,esk92_2(X5,X6))
| ~ in(esk90_2(X5,X6),relation_dom(X5))
| esk89_2(X5,X6) != apply(X5,esk90_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(esk91_2(X5,X6),relation_rng(X5))
| esk92_2(X5,X6) != apply(X6,esk91_2(X5,X6))
| ~ in(esk90_2(X5,X6),relation_dom(X5))
| esk89_2(X5,X6) != apply(X5,esk90_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_200])])])])])]) ).
fof(c_0_391_392,plain,
! [X19,X21,X23,X26,X27,X29,X31] :
( ( ordinal(esk100_0)
| ordinal(esk96_0)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| ordinal(esk96_0)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| ordinal(esk96_0)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| ordinal(esk96_0)
| epred1_0 )
& ( esk100_0 != empty_set
| ordinal(esk96_0)
| epred1_0 )
& ( in(esk100_0,omega)
| ordinal(esk96_0)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| ordinal(esk96_0)
| epred1_0 )
& ( esk102_0 != empty_set
| ordinal(esk96_0)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| ordinal(esk96_0)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| ordinal(esk96_0)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| ordinal(esk96_0)
| epred1_0 )
& ( ordinal(esk100_0)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( esk100_0 != empty_set
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( in(esk100_0,omega)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( esk102_0 != empty_set
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| in(esk97_1(X19),X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( ordinal(esk100_0)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( esk100_0 != empty_set
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( in(esk100_0,omega)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( esk102_0 != empty_set
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| ~ in(X21,X19)
| ~ subset(esk97_1(X19),X21)
| X21 = esk97_1(X19)
| X19 = empty_set
| ~ element(X19,powerset(powerset(esk96_0)))
| ~ in(esk96_0,omega)
| epred1_0 )
& ( ordinal(esk100_0)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( esk100_0 != empty_set
| in(succ(esk96_0),omega)
| epred1_0 )
& ( in(esk100_0,omega)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| in(succ(esk96_0),omega)
| epred1_0 )
& ( esk102_0 != empty_set
| in(succ(esk96_0),omega)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| in(succ(esk96_0),omega)
| epred1_0 )
& ( ordinal(esk100_0)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( esk100_0 != empty_set
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( in(esk100_0,omega)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( esk102_0 != empty_set
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| epred1_0 )
& ( ordinal(esk100_0)
| esk98_0 != empty_set
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| esk98_0 != empty_set
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| esk98_0 != empty_set
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| esk98_0 != empty_set
| epred1_0 )
& ( esk100_0 != empty_set
| esk98_0 != empty_set
| epred1_0 )
& ( in(esk100_0,omega)
| esk98_0 != empty_set
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| esk98_0 != empty_set
| epred1_0 )
& ( esk102_0 != empty_set
| esk98_0 != empty_set
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| esk98_0 != empty_set
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| esk98_0 != empty_set
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| esk98_0 != empty_set
| epred1_0 )
& ( ordinal(esk100_0)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk100_0 != empty_set
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk100_0,omega)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk102_0 != empty_set
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| in(esk99_1(X23),esk98_0)
| ~ in(X23,esk98_0)
| epred1_0 )
& ( ordinal(esk100_0)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk100_0 != empty_set
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk100_0,omega)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk102_0 != empty_set
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| subset(X23,esk99_1(X23))
| ~ in(X23,esk98_0)
| epred1_0 )
& ( ordinal(esk100_0)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( being_limit_ordinal(esk100_0)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk101_2(X26,X27),X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( ~ in(X29,X27)
| ~ subset(esk101_2(X26,X27),X29)
| X29 = esk101_2(X26,X27)
| X27 = empty_set
| ~ element(X27,powerset(powerset(X26)))
| ~ in(X26,omega)
| ~ in(X26,esk100_0)
| ~ ordinal(X26)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk100_0 != empty_set
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk100_0,omega)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( element(esk102_0,powerset(powerset(esk100_0)))
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk102_0 != empty_set
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( in(esk103_1(X31),esk102_0)
| ~ in(X31,esk102_0)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( subset(X31,esk103_1(X31))
| ~ in(X31,esk102_0)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 )
& ( esk103_1(X31) != X31
| ~ in(X31,esk102_0)
| esk99_1(X23) != X23
| ~ in(X23,esk98_0)
| epred1_0 ) ),
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_201])])])])]) ).
fof(c_0_392_393,lemma,
! [X5,X6,X7,X9] :
( ( in(esk73_3(X5,X6,X7),relation_rng(X7))
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(X5,esk73_3(X5,X6,X7)),X7)
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(esk73_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_202])])])])]) ).
fof(c_0_393_394,lemma,
! [X5,X6,X7,X9] :
( ( in(esk72_3(X5,X6,X7),relation_dom(X7))
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(esk72_3(X5,X6,X7),X5),X7)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(esk72_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_203])])])])]) ).
fof(c_0_394_395,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_204])])])])]) ).
fof(c_0_395_396,lemma,
! [X6,X7,X8,X10,X11] :
( ( in(X10,powerset(relation_dom(X8)))
| ~ in(X10,esk47_3(X6,X7,X8))
| ~ element(X7,powerset(powerset(X6)))
| ~ relation(X8)
| ~ function(X8) )
& ( in(relation_image(X8,X10),X7)
| ~ in(X10,esk47_3(X6,X7,X8))
| ~ element(X7,powerset(powerset(X6)))
| ~ relation(X8)
| ~ function(X8) )
& ( ~ in(X11,powerset(relation_dom(X8)))
| ~ in(relation_image(X8,X11),X7)
| in(X11,esk47_3(X6,X7,X8))
| ~ element(X7,powerset(powerset(X6)))
| ~ relation(X8)
| ~ function(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_205])])])])])]) ).
fof(c_0_396_397,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_206])])]) ).
fof(c_0_397_398,lemma,
! [X7,X8,X10,X13,X14,X15] :
( ( in(X10,cartesian_product2(X7,X8))
| ~ in(X10,esk33_2(X7,X8)) )
& ( ordered_pair(esk34_3(X7,X8,X10),esk35_3(X7,X8,X10)) = X10
| ~ in(X10,esk33_2(X7,X8)) )
& ( in(esk34_3(X7,X8,X10),X7)
| ~ in(X10,esk33_2(X7,X8)) )
& ( esk35_3(X7,X8,X10) = singleton(esk34_3(X7,X8,X10))
| ~ in(X10,esk33_2(X7,X8)) )
& ( ~ in(X13,cartesian_product2(X7,X8))
| ordered_pair(X14,X15) != X13
| ~ in(X14,X7)
| X15 != singleton(X14)
| in(X13,esk33_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_207])])])])])]) ).
fof(c_0_398_399,lemma,
! [X6,X7,X9,X11,X12] :
( ( in(X9,powerset(X6))
| ~ in(X9,esk41_2(X6,X7))
| ~ ordinal(X6)
| ~ element(X7,powerset(powerset(succ(X6)))) )
& ( in(esk42_3(X6,X7,X9),X7)
| ~ in(X9,esk41_2(X6,X7))
| ~ ordinal(X6)
| ~ element(X7,powerset(powerset(succ(X6)))) )
& ( X9 = set_difference(esk42_3(X6,X7,X9),singleton(X6))
| ~ in(X9,esk41_2(X6,X7))
| ~ ordinal(X6)
| ~ element(X7,powerset(powerset(succ(X6)))) )
& ( ~ in(X11,powerset(X6))
| ~ in(X12,X7)
| X11 != set_difference(X12,singleton(X6))
| in(X11,esk41_2(X6,X7))
| ~ ordinal(X6)
| ~ element(X7,powerset(powerset(succ(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_208])])])])])]) ).
fof(c_0_399_400,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_209])])]) ).
fof(c_0_400_401,lemma,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ join_commutative(X4)
| ~ join_semilatt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| ~ below(X4,X5,X6)
| ~ below(X4,X6,X5)
| X5 = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])])]) ).
fof(c_0_401_402,lemma,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_absorbing(X4)
| ~ latt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| below(X4,meet_commut(X4,X5,X6),X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])])]) ).
fof(c_0_402_403,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_212])]) ).
fof(c_0_403_404,lemma,
! [X22,X24,X25,X27] :
( ( in(esk26_2(X24,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| in(empty_set,omega)
| ~ epred1_0 )
& ( ~ in(X27,X25)
| ~ subset(esk26_2(X24,X25),X27)
| X27 = esk26_2(X24,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| in(empty_set,omega)
| ~ epred1_0 )
& ( in(esk26_2(X24,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| element(esk24_0,powerset(powerset(empty_set)))
| ~ epred1_0 )
& ( ~ in(X27,X25)
| ~ subset(esk26_2(X24,X25),X27)
| X27 = esk26_2(X24,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| element(esk24_0,powerset(powerset(empty_set)))
| ~ epred1_0 )
& ( in(esk26_2(X24,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| esk24_0 != empty_set
| ~ epred1_0 )
& ( ~ in(X27,X25)
| ~ subset(esk26_2(X24,X25),X27)
| X27 = esk26_2(X24,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| esk24_0 != empty_set
| ~ epred1_0 )
& ( in(esk26_2(X24,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| in(esk25_1(X22),esk24_0)
| ~ in(X22,esk24_0)
| ~ epred1_0 )
& ( ~ in(X27,X25)
| ~ subset(esk26_2(X24,X25),X27)
| X27 = esk26_2(X24,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| in(esk25_1(X22),esk24_0)
| ~ in(X22,esk24_0)
| ~ epred1_0 )
& ( in(esk26_2(X24,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| subset(X22,esk25_1(X22))
| ~ in(X22,esk24_0)
| ~ epred1_0 )
& ( ~ in(X27,X25)
| ~ subset(esk26_2(X24,X25),X27)
| X27 = esk26_2(X24,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| subset(X22,esk25_1(X22))
| ~ in(X22,esk24_0)
| ~ epred1_0 )
& ( in(esk26_2(X24,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| esk25_1(X22) != X22
| ~ in(X22,esk24_0)
| ~ epred1_0 )
& ( ~ in(X27,X25)
| ~ subset(esk26_2(X24,X25),X27)
| X27 = esk26_2(X24,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(X24)))
| ~ in(X24,omega)
| ~ ordinal(X24)
| esk25_1(X22) != X22
| ~ in(X22,esk24_0)
| ~ epred1_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_213])])])])]) ).
fof(c_0_404_405,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_214])])]) ).
fof(c_0_405_406,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_215])])])]) ).
fof(c_0_406_407,lemma,
! [X6,X7,X9,X11,X12] :
( ( in(X9,succ(X7))
| ~ in(X9,esk48_2(X6,X7))
| ~ ordinal(X7) )
& ( ordinal(esk49_3(X6,X7,X9))
| ~ in(X9,esk48_2(X6,X7))
| ~ ordinal(X7) )
& ( X9 = esk49_3(X6,X7,X9)
| ~ in(X9,esk48_2(X6,X7))
| ~ ordinal(X7) )
& ( in(esk49_3(X6,X7,X9),X6)
| ~ in(X9,esk48_2(X6,X7))
| ~ ordinal(X7) )
& ( ~ in(X11,succ(X7))
| ~ ordinal(X12)
| X11 != X12
| ~ in(X12,X6)
| in(X11,esk48_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_216])])])])])]) ).
fof(c_0_407_408,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_217])]) ).
fof(c_0_408_409,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_218])])])])]) ).
fof(c_0_409_410,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_219])]) ).
fof(c_0_410_411,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_220])]) ).
fof(c_0_411_412,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_221])])]) ).
fof(c_0_412_413,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_222])]) ).
fof(c_0_413_414,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_223])])]) ).
fof(c_0_414_415,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_224])]) ).
fof(c_0_415_416,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_225])])])])])]) ).
fof(c_0_416_417,lemma,
! [X5,X6,X8] :
( ( in(esk74_2(X5,X6),X6)
| X6 = empty_set
| ~ element(X6,powerset(powerset(X5)))
| ~ finite(X5) )
& ( ~ in(X8,X6)
| ~ subset(esk74_2(X5,X6),X8)
| X8 = esk74_2(X5,X6)
| X6 = empty_set
| ~ element(X6,powerset(powerset(X5)))
| ~ finite(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_226])])])])]) ).
fof(c_0_417_418,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_227])])]) ).
fof(c_0_418_419,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_228])])])])]) ).
fof(c_0_419_420,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_229])])])]) ).
fof(c_0_420_421,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_230])])]) ).
fof(c_0_421_422,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_231])])]) ).
fof(c_0_422_423,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_232])])]) ).
fof(c_0_423_424,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_233])])]) ).
fof(c_0_424_425,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_234])])]) ).
fof(c_0_425_426,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_235])]) ).
fof(c_0_426_427,lemma,
! [X4,X5,X6] :
( ~ relation(X4)
| ~ relation(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ relation_isomorphism(X4,X5,X6)
| epred2_2(X5,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_236])])]) ).
fof(c_0_427_428,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_237])])]) ).
fof(c_0_428_429,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_238])]) ).
fof(c_0_429_430,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_239])])])])])]) ).
fof(c_0_430_431,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_240])])])])]) ).
fof(c_0_431_432,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_241])])])])]) ).
fof(c_0_432_433,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_242])]) ).
fof(c_0_433_434,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_243])])])])]) ).
fof(c_0_434_435,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(esk84_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk84_2(X4,X5)) != esk84_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_244])])])])]) ).
fof(c_0_435_436,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_245])]) ).
fof(c_0_436_437,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_246])])]) ).
fof(c_0_437_438,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_247])])]) ).
fof(c_0_438_439,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_248])])]) ).
fof(c_0_439_440,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_249])])]) ).
fof(c_0_440_441,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_250])]) ).
fof(c_0_441_442,lemma,
! [X5,X6,X8] :
( ( ordinal(esk83_2(X5,X6))
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) )
& ( in(esk83_2(X5,X6),X5)
| X5 = empty_set
| ~ subset(X5,X6)
| ~ ordinal(X6) )
& ( ~ ordinal(X8)
| ~ in(X8,X5)
| ordinal_subset(esk83_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_251])])])])]) ).
fof(c_0_442_443,lemma,
! [X4,X7] :
( ( relation(esk81_1(X4))
| in(esk80_1(X4),X4)
| empty(X4) )
& ( function(esk81_1(X4))
| in(esk80_1(X4),X4)
| empty(X4) )
& ( relation_dom(esk81_1(X4)) = X4
| in(esk80_1(X4),X4)
| empty(X4) )
& ( ~ in(X7,X4)
| in(apply(esk81_1(X4),X7),X7)
| in(esk80_1(X4),X4)
| empty(X4) )
& ( relation(esk81_1(X4))
| esk80_1(X4) = empty_set
| empty(X4) )
& ( function(esk81_1(X4))
| esk80_1(X4) = empty_set
| empty(X4) )
& ( relation_dom(esk81_1(X4)) = X4
| esk80_1(X4) = empty_set
| empty(X4) )
& ( ~ in(X7,X4)
| in(apply(esk81_1(X4),X7),X7)
| esk80_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_252])])])])]) ).
fof(c_0_443_444,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_253])]) ).
fof(c_0_444_445,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_254])])]) ).
fof(c_0_445_446,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_255])])]) ).
fof(c_0_446_447,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_256])]) ).
fof(c_0_447_448,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_257])])]) ).
fof(c_0_448_449,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_258])])]) ).
fof(c_0_449_450,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_259])])]) ).
fof(c_0_450_451,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_260])])]) ).
fof(c_0_451_452,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_261])])])]) ).
fof(c_0_452_453,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_262])])])]) ).
fof(c_0_453_454,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_263])])])]) ).
fof(c_0_454_455,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_264])])])])]) ).
fof(c_0_455_456,lemma,
! [X5,X10,X12] :
( ( relation(esk63_1(X5))
| in(esk62_1(X5),X5)
| in(esk59_1(X5),X5) )
& ( function(esk63_1(X5))
| in(esk62_1(X5),X5)
| in(esk59_1(X5),X5) )
& ( relation_dom(esk63_1(X5)) = X5
| in(esk62_1(X5),X5)
| in(esk59_1(X5),X5) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| in(esk62_1(X5),X5)
| in(esk59_1(X5),X5) )
& ( relation(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| in(esk59_1(X5),X5) )
& ( function(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| in(esk59_1(X5),X5) )
& ( relation_dom(esk63_1(X5)) = X5
| X10 != singleton(esk62_1(X5))
| in(esk59_1(X5),X5) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| X10 != singleton(esk62_1(X5))
| in(esk59_1(X5),X5) )
& ( relation(esk63_1(X5))
| in(esk62_1(X5),X5)
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( function(esk63_1(X5))
| in(esk62_1(X5),X5)
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( relation_dom(esk63_1(X5)) = X5
| in(esk62_1(X5),X5)
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| in(esk62_1(X5),X5)
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( relation(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( function(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( relation_dom(esk63_1(X5)) = X5
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) = singleton(esk59_1(X5)) )
& ( relation(esk63_1(X5))
| in(esk62_1(X5),X5)
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( function(esk63_1(X5))
| in(esk62_1(X5),X5)
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( relation_dom(esk63_1(X5)) = X5
| in(esk62_1(X5),X5)
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| in(esk62_1(X5),X5)
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( relation(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( function(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( relation_dom(esk63_1(X5)) = X5
| X10 != singleton(esk62_1(X5))
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| X10 != singleton(esk62_1(X5))
| esk61_1(X5) = singleton(esk59_1(X5)) )
& ( relation(esk63_1(X5))
| in(esk62_1(X5),X5)
| esk60_1(X5) != esk61_1(X5) )
& ( function(esk63_1(X5))
| in(esk62_1(X5),X5)
| esk60_1(X5) != esk61_1(X5) )
& ( relation_dom(esk63_1(X5)) = X5
| in(esk62_1(X5),X5)
| esk60_1(X5) != esk61_1(X5) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| in(esk62_1(X5),X5)
| esk60_1(X5) != esk61_1(X5) )
& ( relation(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) != esk61_1(X5) )
& ( function(esk63_1(X5))
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) != esk61_1(X5) )
& ( relation_dom(esk63_1(X5)) = X5
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) != esk61_1(X5) )
& ( ~ in(X12,X5)
| apply(esk63_1(X5),X12) = singleton(X12)
| X10 != singleton(esk62_1(X5))
| esk60_1(X5) != esk61_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_265])])])])]) ).
fof(c_0_456_457,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_266])]) ).
fof(c_0_457_458,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_267])]) ).
fof(c_0_458_459,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_268])])])]) ).
fof(c_0_459_460,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk88_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_269])])])])]) ).
fof(c_0_460_461,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_270])]) ).
fof(c_0_461_462,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_271])])])])]) ).
fof(c_0_462_463,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_272])]) ).
fof(c_0_463_464,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_273])]) ).
fof(c_0_464_465,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_274])])]) ).
fof(c_0_465_466,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_275])]) ).
fof(c_0_466_467,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_276])]) ).
fof(c_0_467_468,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_277])])])]) ).
fof(c_0_468_469,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_278])])])])]) ).
fof(c_0_469_470,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_279])]) ).
fof(c_0_470_471,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_280])]) ).
fof(c_0_471_472,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_281])]) ).
fof(c_0_472_473,lemma,
! [X5,X7,X8,X9,X10] :
( in(X5,esk71_1(X5))
& ( ~ in(X7,esk71_1(X5))
| ~ subset(X8,X7)
| in(X8,esk71_1(X5)) )
& ( ~ in(X9,esk71_1(X5))
| in(powerset(X9),esk71_1(X5)) )
& ( ~ subset(X10,esk71_1(X5))
| are_equipotent(X10,esk71_1(X5))
| in(X10,esk71_1(X5)) ) ),
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_473_474,lemma,
! [X4] :
( ~ relation(X4)
| in(ordered_pair(esk93_1(X4),esk94_1(X4)),X4)
| X4 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_283])])]) ).
fof(c_0_474_475,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_284])]) ).
fof(c_0_475_476,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_285])]) ).
fof(c_0_476_477,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_286])])]) ).
fof(c_0_477_478,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk85_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk85_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_287])])])])])]) ).
fof(c_0_478_479,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_288])])])]) ).
fof(c_0_479_480,lemma,
! [X3,X4] :
( ( ~ being_limit_ordinal(X3)
| ~ ordinal(X4)
| ~ in(X4,X3)
| in(succ(X4),X3)
| ~ ordinal(X3) )
& ( ordinal(esk86_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( in(esk86_1(X3),X3)
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( ~ in(succ(esk86_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_289])])])])]) ).
fof(c_0_480_481,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_290])])]) ).
fof(c_0_481_482,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_291])]) ).
fof(c_0_482_483,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_292])])])]) ).
fof(c_0_483_484,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_293])]) ).
fof(c_0_484_485,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_294])]) ).
fof(c_0_485_486,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_295])]) ).
fof(c_0_486_487,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_296])])])]) ).
fof(c_0_487_488,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_297])])]) ).
fof(c_0_488_489,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_298])]) ).
fof(c_0_489_490,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_299])]) ).
fof(c_0_490_491,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_300])]) ).
fof(c_0_491_492,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_301])]) ).
fof(c_0_492_493,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_302])])])]) ).
fof(c_0_493_494,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_303])]) ).
fof(c_0_494_495,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_495_496,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_305]) ).
fof(c_0_496_497,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_306]) ).
fof(c_0_497_498,lemma,
! [X3] :
( ( in(esk82_1(X3),X3)
| ordinal(X3) )
& ( ~ ordinal(esk82_1(X3))
| ~ subset(esk82_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_307])])])]) ).
fof(c_0_498_499,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_308])]) ).
fof(c_0_499_500,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_309])]) ).
fof(c_0_500_501,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| ~ finite(X3)
| finite(relation_image(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_310])]) ).
fof(c_0_501_502,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_311])])]) ).
fof(c_0_502_503,lemma,
! [X4,X6,X7] :
( ( in(X6,X4)
| ~ in(X6,esk46_1(X4)) )
& ( ordinal(X6)
| ~ in(X6,esk46_1(X4)) )
& ( ~ in(X7,X4)
| ~ ordinal(X7)
| in(X7,esk46_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_312])])])])])]) ).
fof(c_0_503_504,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_313])]) ).
fof(c_0_504_505,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_dom_restriction(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_314])]) ).
fof(c_0_505_506,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng_restriction(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_315])]) ).
fof(c_0_506_507,lemma,
! [X4,X6] :
( relation(esk69_1(X4))
& function(esk69_1(X4))
& relation_dom(esk69_1(X4)) = X4
& ( ~ in(X6,X4)
| apply(esk69_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_316])])])]) ).
fof(c_0_507_508,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_317])])])]) ).
fof(c_0_508_509,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_318])])])]) ).
fof(c_0_509_510,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_319])])]) ).
fof(c_0_510_511,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_320])])]) ).
fof(c_0_511_512,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_321])]) ).
fof(c_0_512_513,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_322])]) ).
fof(c_0_513_514,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_323])]) ).
fof(c_0_514_515,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ antisymmetric(X4)
| antisymmetric(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_324])]) ).
fof(c_0_515_516,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ transitive(X4)
| transitive(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_325])]) ).
fof(c_0_516_517,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ connected(X4)
| connected(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_326])]) ).
fof(c_0_517_518,lemma,
! [X3,X4] :
( ~ relation(X4)
| ~ reflexive(X4)
| reflexive(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_327])]) ).
fof(c_0_518_519,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_328])]) ).
fof(c_0_519_520,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_329])])]) ).
fof(c_0_520_521,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_330])])]) ).
fof(c_0_521_522,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_331])]) ).
fof(c_0_522_523,lemma,
! [X3,X4] :
( ~ in(X4,X3)
| apply(identity_relation(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_332])]) ).
fof(c_0_523_524,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_333])]) ).
fof(c_0_524_525,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_334])]) ).
fof(c_0_525_526,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_335])]) ).
fof(c_0_526_527,lemma,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ finite(relation_dom(X2))
| finite(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_336])]) ).
fof(c_0_527_528,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_337])]) ).
fof(c_0_528_529,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_338]) ).
fof(c_0_529_530,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_339]) ).
fof(c_0_530_531,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_340]) ).
fof(c_0_531_532,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_341])])])])]) ).
fof(c_0_532_533,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_342])])])])]) ).
fof(c_0_533_534,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_343])])])]) ).
fof(c_0_534_535,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_344])]) ).
fof(c_0_535_536,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_345])]) ).
fof(c_0_536_537,lemma,
! [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_346])])])]) ).
fof(c_0_537_538,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_347])])])]) ).
fof(c_0_538_539,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_348])])])]) ).
fof(c_0_539_540,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_349])])]) ).
fof(c_0_540_541,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_350])]) ).
fof(c_0_541_542,plain,
! [X3,X4] :
( ( ~ reflexive(X3)
| reflexive(X4)
| ~ epred2_2(X4,X3) )
& ( ~ transitive(X3)
| transitive(X4)
| ~ epred2_2(X4,X3) )
& ( ~ connected(X3)
| connected(X4)
| ~ epred2_2(X4,X3) )
& ( ~ antisymmetric(X3)
| antisymmetric(X4)
| ~ epred2_2(X4,X3) )
& ( ~ well_founded_relation(X3)
| well_founded_relation(X4)
| ~ epred2_2(X4,X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_351])])]) ).
fof(c_0_542_543,lemma,
! [X3,X4] :
( ~ ordinal(X4)
| ~ in(X3,X4)
| ordinal(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_352])]) ).
fof(c_0_543_544,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_353])])])]) ).
fof(c_0_544_545,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_354])]) ).
fof(c_0_545_546,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_355])]) ).
fof(c_0_546_547,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_356])])]) ).
fof(c_0_547_548,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_357])]) ).
fof(c_0_548_549,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_358])])])]) ).
fof(c_0_549_550,lemma,
! [X3,X5] :
( ( ordinal(esk87_1(X3))
| being_limit_ordinal(X3)
| ~ ordinal(X3) )
& ( X3 = succ(esk87_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_359])])])])]) ).
fof(c_0_550_551,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_360])]) ).
fof(c_0_551_552,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_361])])]) ).
fof(c_0_552_553,lemma,
! [X3] :
( relation(esk79_1(X3))
& well_orders(esk79_1(X3),X3) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_362])]) ).
fof(c_0_553_554,lemma,
! [X2] : in(X2,succ(X2)),
inference(variable_rename,[status(thm)],[c_0_363]) ).
fof(c_0_554_555,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_364])])]) ).
fof(c_0_555_556,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_365]) ).
fof(c_0_556_557,lemma,
! [X2] :
( ~ ordinal(X2)
| well_ordering(inclusion_relation(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_366])]) ).
fof(c_0_557_558,lemma,
! [X2] :
( ~ ordinal(X2)
| well_founded_relation(inclusion_relation(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_367])]) ).
fof(c_0_558_559,lemma,
! [X2] :
( ~ ordinal(X2)
| connected(inclusion_relation(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_368])]) ).
fof(c_0_559_560,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_369])])]) ).
fof(c_0_560_561,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_370]) ).
fof(c_0_561_562,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_371]) ).
fof(c_0_562_563,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_372])])]) ).
fof(c_0_563_564,lemma,
! [X2] : antisymmetric(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_373]) ).
fof(c_0_564_565,lemma,
! [X2] : transitive(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_374]) ).
fof(c_0_565_566,lemma,
! [X2] : reflexive(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_375]) ).
fof(c_0_566_567,negated_conjecture,
( one_sorted_str(esk70_0)
& cast_as_carrier_subset(esk70_0) != the_carrier(esk70_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_376])])]) ).
fof(c_0_567_568,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_377]) ).
fof(c_0_568_569,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_378 ).
fof(c_0_569_570,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_379 ).
cnf(c_0_570_571,lemma,
( empty(X2)
| in(X3,esk28_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,esk32_7(X2,X1,X4,X3,X5,X6,X7)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_571_572,lemma,
( empty(X2)
| in(X3,esk28_3(X2,X1,X4))
| in(esk32_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_380]) ).
cnf(c_0_572_573,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_381]) ).
cnf(c_0_573_574,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_381]) ).
cnf(c_0_574_575,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_381]) ).
cnf(c_0_575_576,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_381]) ).
cnf(c_0_576_577,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_381]) ).
cnf(c_0_577_578,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_381]) ).
cnf(c_0_578_579,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_381]) ).
cnf(c_0_579_580,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_381]) ).
cnf(c_0_580_581,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_381]) ).
cnf(c_0_581_582,lemma,
( in(ordered_pair(apply(X1,esk44_4(X4,X2,X1,X3)),apply(X1,esk45_4(X4,X2,X1,X3))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk43_3(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_582_583,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_381]) ).
cnf(c_0_583_584,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_381]) ).
cnf(c_0_584_585,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_381]) ).
cnf(c_0_585_586,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_381]) ).
cnf(c_0_586_587,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_381]) ).
cnf(c_0_587_588,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_381]) ).
cnf(c_0_588_589,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_381]) ).
cnf(c_0_589_590,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_381]) ).
cnf(c_0_590_591,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_381]) ).
cnf(c_0_591_592,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_592_593,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_593_594,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_594_595,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_595_596,lemma,
( empty(X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_596_597,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_597_598,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_598_599,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_599_600,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_600_601,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_601_602,lemma,
( empty(X2)
| in(ordered_pair(esk30_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4))
| ~ in(X5,esk31_4(X2,X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_602_603,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_603_604,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_604_605,lemma,
( empty(X2)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_605_606,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_606_607,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_607_608,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_608_609,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| X6 = esk58_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_609_610,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| X6 = esk58_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_610_611,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_611_612,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_612_613,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_613_614,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_614_615,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_615_616,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_616_617,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_617_618,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_618_619,lemma,
( empty(X2)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_619_620,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_620_621,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_621_622,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_622_623,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_623_624,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_624_625,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_625_626,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_626_627,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_627_628,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_628_629,lemma,
( empty(X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_629_630,lemma,
( empty(X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_630_631,lemma,
( empty(X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_631_632,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_632_633,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_633_634,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_634_635,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_635_636,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_636_637,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_637_638,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_638_639,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_639_640,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_640_641,lemma,
( in(ordered_pair(esk78_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_384]) ).
cnf(c_0_641_642,lemma,
( in(ordered_pair(X4,esk76_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_385]) ).
cnf(c_0_642_643,lemma,
( X3 = ordered_pair(esk44_4(X4,X2,X1,X3),esk45_4(X4,X2,X1,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk43_3(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_643_644,lemma,
( empty(X2)
| ordered_pair(esk29_4(X2,X1,X4,X3),esk30_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_644_645,lemma,
( empty(X2)
| in(esk30_4(X2,X1,X4,X3),esk31_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_645_646,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_646_647,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_647_648,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_381]) ).
cnf(c_0_648_649,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_381]) ).
cnf(c_0_649_650,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_650_651,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_651_652,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_381]) ).
cnf(c_0_652_653,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_381]) ).
cnf(c_0_653_654,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_654_655,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_655_656,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_656_657,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_657_658,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_381]) ).
cnf(c_0_658_659,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_381]) ).
cnf(c_0_659_660,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_381]) ).
cnf(c_0_660_661,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_381]) ).
cnf(c_0_661_662,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_381]) ).
cnf(c_0_662_663,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_663_664,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_664_665,lemma,
( in(X2,esk36_1(X1))
| in(esk40_4(X1,X2,X3,X4),esk39_3(X1,X2,X3))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,esk39_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_665_666,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_666_667,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_667_668,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_668_669,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_669_670,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_670_671,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_671_672,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| X6 = esk58_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_672_673,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| X6 = esk58_3(X2,X1,X6)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_673_674,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_381]) ).
cnf(c_0_674_675,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_381]) ).
cnf(c_0_675_676,lemma,
( in(X2,esk36_1(X1))
| subset(X4,esk40_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,esk39_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_676_677,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_677_678,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_678_679,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_679_680,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_680_681,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_681_682,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_682_683,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_683_684,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_684_685,lemma,
( empty(X2)
| in(esk29_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_685_686,lemma,
( empty(X2)
| esk29_4(X2,X1,X4,X3) = esk31_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_686_687,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_381]) ).
cnf(c_0_687_688,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_381]) ).
cnf(c_0_688_689,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_689_690,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_690_691,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_691_692,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| X5 = esk58_3(X2,X1,X5)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_692_693,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_381]) ).
cnf(c_0_693_694,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_381]) ).
cnf(c_0_694_695,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_381]) ).
cnf(c_0_695_696,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_696_697,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_697_698,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_698_699,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_699_700,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_700_701,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_701_702,lemma,
( in(X2,esk36_1(X1))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,esk39_3(X1,X2,X3))
| esk40_4(X1,X2,X3,X4) != X4 ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_702_703,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_381]) ).
cnf(c_0_703_704,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_381]) ).
cnf(c_0_704_705,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_705_706,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_706_707,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_707_708,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_708_709,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_709_710,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_710_711,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_711_712,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_712_713,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_713_714,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_714_715,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_715_716,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_716_717,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk58_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_717_718,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk58_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_718_719,lemma,
( X3 = empty_set
| X4 = esk38_3(X1,X2,X3)
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1))
| ~ in(esk37_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk37_2(X1,X2))))
| ~ subset(esk38_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_719_720,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(X4,esk77_3(X2,X3,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_720_721,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(esk75_3(X3,X2,X1),X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_721_722,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_722_723,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_723_724,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_381]) ).
cnf(c_0_724_725,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_381]) ).
cnf(c_0_725_726,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_726_727,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_727_728,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_728_729,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_729_730,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,esk95_3(X3,X1,X2)) != apply(X2,esk95_3(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_730_731,lemma,
( in(X3,esk43_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_382]) ).
cnf(c_0_731_732,lemma,
( in(ordered_pair(X3,X4),esk27_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_388]) ).
cnf(c_0_732_733,lemma,
( X3 = empty_set
| in(esk38_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1))
| ~ in(esk37_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk37_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_733_734,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_381]) ).
cnf(c_0_734_735,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_381]) ).
cnf(c_0_735_736,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X4),esk58_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_736_737,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X4),esk58_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_737_738,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_381]) ).
cnf(c_0_738_739,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_381]) ).
cnf(c_0_739_740,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_381]) ).
cnf(c_0_740_741,lemma,
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk27_3(X5,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_741_742,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_381]) ).
cnf(c_0_742_743,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_381]) ).
cnf(c_0_743_744,lemma,
( X2 = empty_set
| X3 = esk65_2(X1,X2)
| X5 = empty_set
| X6 = esk68_2(X4,X5)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk65_2(X1,X2),X3)
| ~ in(X3,X2)
| ~ ordinal(X4)
| ~ in(X4,omega)
| ~ element(X5,powerset(powerset(X4)))
| ~ subset(esk68_2(X4,X5),X6)
| ~ in(X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_744_745,lemma,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk89_2(X1,X2) != apply(X1,esk90_2(X1,X2))
| ~ in(esk90_2(X1,X2),relation_dom(X1))
| esk92_2(X1,X2) != apply(X2,esk91_2(X1,X2))
| ~ in(esk91_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_745_746,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_746_747,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_747_748,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| X4 = empty_set
| X5 = esk101_2(X3,X4)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ ordinal(X3)
| ~ in(X3,esk100_0)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3)))
| ~ subset(esk101_2(X3,X4),X5)
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_748_749,lemma,
( in(ordered_pair(X2,esk73_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_749_750,lemma,
( in(ordered_pair(esk72_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_750_751,lemma,
( X2 = empty_set
| in(esk65_2(X1,X2),X2)
| X4 = empty_set
| X5 = esk68_2(X3,X4)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ ordinal(X3)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3)))
| ~ subset(esk68_2(X3,X4),X5)
| ~ in(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_751_752,lemma,
( X2 = empty_set
| X3 = esk65_2(X1,X2)
| X5 = empty_set
| in(esk68_2(X4,X5),X5)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk65_2(X1,X2),X3)
| ~ in(X3,X2)
| ~ ordinal(X4)
| ~ in(X4,omega)
| ~ element(X5,powerset(powerset(X4))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_752_753,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_753_754,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_754_755,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_394]) ).
cnf(c_0_755_756,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_756_757,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_757_758,lemma,
( in(X4,esk47_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| ~ in(X4,powerset(relation_dom(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_758_759,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_396]) ).
cnf(c_0_759_760,lemma,
( in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk47_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_760_761,lemma,
( ordered_pair(esk34_3(X2,X3,X1),esk35_3(X2,X3,X1)) = X1
| ~ in(X1,esk33_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_761_762,lemma,
( in(X4,powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk47_3(X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_762_763,lemma,
( X3 = set_difference(esk42_3(X2,X1,X3),singleton(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk41_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_763_764,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| X4 = esk58_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_764_765,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| X4 = esk58_3(X2,X1,X4)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_765_766,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_381]) ).
cnf(c_0_766_767,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_381]) ).
cnf(c_0_767_768,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_381]) ).
cnf(c_0_768_769,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_381]) ).
cnf(c_0_769_770,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_770_771,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_394]) ).
cnf(c_0_771_772,lemma,
( in(esk42_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk41_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_772_773,lemma,
( in(X3,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk27_3(X5,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_773_774,lemma,
( in(X4,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk27_3(X5,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_774_775,lemma,
( X2 = function_inverse(X1)
| esk90_2(X1,X2) = apply(X2,esk89_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk92_2(X1,X2) != apply(X2,esk91_2(X1,X2))
| ~ in(esk91_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_775_776,lemma,
( X2 = function_inverse(X1)
| esk91_2(X1,X2) = apply(X1,esk92_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk89_2(X1,X2) != apply(X1,esk90_2(X1,X2))
| ~ in(esk90_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_776_777,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| X4 = empty_set
| in(esk101_2(X3,X4),X4)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ ordinal(X3)
| ~ in(X3,esk100_0)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_777_778,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| in(esk77_3(X2,X3,X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_778_779,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| in(esk75_3(X3,X2,X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_779_780,lemma,
( X2 = empty_set
| in(esk65_2(X1,X2),X2)
| X4 = empty_set
| in(esk68_2(X3,X4),X4)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ ordinal(X3)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_780_781,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_399]) ).
cnf(c_0_781_782,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_399]) ).
cnf(c_0_782_783,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_394]) ).
cnf(c_0_783_784,lemma,
( X2 = function_inverse(X1)
| in(esk89_2(X1,X2),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk92_2(X1,X2) != apply(X2,esk91_2(X1,X2))
| ~ in(esk91_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_784_785,lemma,
( X2 = function_inverse(X1)
| in(esk92_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk89_2(X1,X2) != apply(X1,esk90_2(X1,X2))
| ~ in(esk90_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_785_786,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_399]) ).
cnf(c_0_786_787,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_399]) ).
cnf(c_0_787_788,lemma,
( X1 = X2
| empty_carrier(X3)
| ~ below(X3,X2,X1)
| ~ below(X3,X1,X2)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ join_semilatt_str(X3)
| ~ join_commutative(X3) ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_788_789,lemma,
( below(X1,meet_commut(X1,X2,X3),X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_789_790,lemma,
( in(X3,cartesian_product2(X4,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk43_3(X4,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_790_791,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_402]) ).
cnf(c_0_791_792,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_792_793,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_793_794,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_794_795,lemma,
( empty(X2)
| in(X3,cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_795_796,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_796_797,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_797_798,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_798_799,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_799_800,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_800_801,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_801_802,plain,
( epred1_0
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_802_803,lemma,
( esk35_3(X2,X3,X1) = singleton(esk34_3(X2,X3,X1))
| ~ in(X1,esk33_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_803_804,lemma,
( in(X3,esk41_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| ~ in(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_804_805,lemma,
( subset(X1,esk25_1(X1))
| X3 = empty_set
| X4 = esk26_2(X2,X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk26_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_805_806,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_806_807,lemma,
( subset(X1,esk67_1(X1))
| X3 = empty_set
| X4 = esk68_2(X2,X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk68_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_807_808,lemma,
( in(esk25_1(X1),esk24_0)
| X3 = empty_set
| X4 = esk26_2(X2,X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk26_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_808_809,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_404]) ).
cnf(c_0_809_810,lemma,
( in(esk67_1(X1),esk66_0)
| X3 = empty_set
| X4 = esk68_2(X2,X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk68_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_810_811,plain,
( epred1_0
| in(succ(esk96_0),omega)
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_811_812,lemma,
( X3 = empty_set
| X4 = esk26_2(X2,X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| esk25_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk26_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_812_813,lemma,
( X3 = empty_set
| X4 = esk68_2(X2,X3)
| ~ in(X1,esk66_0)
| esk67_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk68_2(X2,X3),X4)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_813_814,lemma,
( in(X2,esk36_1(X1))
| element(esk39_3(X1,X2,X3),powerset(powerset(X3)))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_814_815,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk95_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_387]) ).
cnf(c_0_815_816,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_399]) ).
cnf(c_0_816_817,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_399]) ).
cnf(c_0_817_818,lemma,
( element(esk24_0,powerset(powerset(empty_set)))
| X2 = empty_set
| X3 = esk26_2(X1,X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk26_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_818_819,lemma,
( element(esk66_0,powerset(powerset(esk64_0)))
| X2 = empty_set
| X3 = esk68_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_819_820,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_405]) ).
cnf(c_0_820_821,plain,
( epred1_0
| ordinal(esk96_0)
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_821_822,plain,
( epred1_0
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| esk98_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_822_823,lemma,
( in(esk73_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_823_824,lemma,
( in(esk72_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_824_825,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_381]) ).
cnf(c_0_825_826,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_381]) ).
cnf(c_0_826_827,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_381]) ).
cnf(c_0_827_828,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_381]) ).
cnf(c_0_828_829,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| X3 = esk58_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_829_830,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| X3 = esk58_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_830_831,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_381]) ).
cnf(c_0_831_832,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_381]) ).
cnf(c_0_832_833,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_381]) ).
cnf(c_0_833_834,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_381]) ).
cnf(c_0_834_835,lemma,
( in(empty_set,omega)
| X2 = empty_set
| X3 = esk26_2(X1,X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk26_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_835_836,lemma,
( in(esk64_0,omega)
| X2 = empty_set
| X3 = esk68_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_836_837,lemma,
( in(esk73_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_837_838,lemma,
( in(esk72_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_838_839,lemma,
( in(esk49_3(X3,X1,X2),X3)
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_839_840,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_405]) ).
cnf(c_0_840_841,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_841_842,lemma,
( ordinal(esk64_0)
| X2 = empty_set
| X3 = esk68_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_842_843,lemma,
( in(esk34_3(X2,X3,X1),X2)
| ~ in(X1,esk33_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_843_844,lemma,
( X2 = empty_set
| X3 = esk26_2(X1,X2)
| ~ epred1_0
| esk24_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk26_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_844_845,lemma,
( X2 = empty_set
| X3 = esk68_2(X1,X2)
| esk66_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_845_846,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_846_847,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_407]) ).
cnf(c_0_847_848,lemma,
( ordinal(esk49_3(X3,X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_848_849,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_408]) ).
cnf(c_0_849_850,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_850_851,lemma,
( in(X3,powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk41_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_851_852,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_409]) ).
cnf(c_0_852_853,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_410]) ).
cnf(c_0_853_854,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_411]) ).
cnf(c_0_854_855,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| X3 = esk58_3(X2,X1,X3)
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_855_856,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_381]) ).
cnf(c_0_856_857,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_381]) ).
cnf(c_0_857_858,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_412]) ).
cnf(c_0_858_859,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_413]) ).
cnf(c_0_859_860,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_413]) ).
cnf(c_0_860_861,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| X3 = esk58_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_861_862,plain,
( epred1_0
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_862_863,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_381]) ).
cnf(c_0_863_864,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_381]) ).
cnf(c_0_864_865,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_381]) ).
cnf(c_0_865_866,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_381]) ).
cnf(c_0_866_867,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_392]) ).
cnf(c_0_867_868,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_393]) ).
cnf(c_0_868_869,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_414]) ).
cnf(c_0_869_870,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| subset(X3,esk103_1(X3))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ in(X3,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_870_871,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_405]) ).
cnf(c_0_871_872,lemma,
( subset(X1,esk25_1(X1))
| X3 = empty_set
| in(esk26_2(X2,X3),X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_872_873,lemma,
( X2 = function_inverse(X1)
| esk90_2(X1,X2) = apply(X2,esk89_2(X1,X2))
| esk91_2(X1,X2) = apply(X1,esk92_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_390]) ).
cnf(c_0_873_874,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_415]) ).
cnf(c_0_874_875,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| in(esk103_1(X3),esk102_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ in(X3,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_875_876,lemma,
( subset(X1,esk67_1(X1))
| X3 = empty_set
| in(esk68_2(X2,X3),X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_876_877,lemma,
( X2 = empty_set
| X3 = esk74_2(X1,X2)
| ~ finite(X1)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk74_2(X1,X2),X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_877_878,lemma,
( in(esk25_1(X1),esk24_0)
| X3 = empty_set
| in(esk26_2(X2,X3),X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_878_879,lemma,
( in(esk67_1(X1),esk66_0)
| X3 = empty_set
| in(esk68_2(X2,X3),X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_879_880,lemma,
( in(X1,esk33_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_397]) ).
cnf(c_0_880_881,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| X3 = esk58_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_881_882,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| X3 = esk58_3(X2,X1,X3)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_882_883,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_381]) ).
cnf(c_0_883_884,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_381]) ).
cnf(c_0_884_885,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_381]) ).
cnf(c_0_885_886,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_381]) ).
cnf(c_0_886_887,plain,
( epred1_0
| in(succ(esk96_0),omega)
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_887_888,lemma,
( in(X2,esk36_1(X1))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| esk39_3(X1,X2,X3) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_888_889,lemma,
( X2 = function_inverse(X1)
| in(esk89_2(X1,X2),relation_rng(X1))
| esk91_2(X1,X2) = apply(X1,esk92_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_390]) ).
cnf(c_0_889_890,lemma,
( X2 = function_inverse(X1)
| esk90_2(X1,X2) = apply(X2,esk89_2(X1,X2))
| in(esk92_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_390]) ).
cnf(c_0_890_891,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ in(X3,esk102_0)
| esk103_1(X3) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_891_892,lemma,
( X3 = empty_set
| in(esk26_2(X2,X3),X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| esk25_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_892_893,lemma,
( X3 = empty_set
| in(esk68_2(X2,X3),X3)
| ~ in(X1,esk66_0)
| esk67_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_893_894,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_894_895,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_895_896,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_896_897,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_897_898,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_898_899,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_899_900,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_417]) ).
cnf(c_0_900_901,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_901_902,lemma,
( X2 = function_inverse(X1)
| in(esk89_2(X1,X2),relation_rng(X1))
| in(esk92_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_390]) ).
cnf(c_0_902_903,lemma,
( element(esk24_0,powerset(powerset(empty_set)))
| X2 = empty_set
| in(esk26_2(X1,X2),X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_903_904,lemma,
( element(esk66_0,powerset(powerset(esk64_0)))
| X2 = empty_set
| in(esk68_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_904_905,plain,
( epred1_0
| ordinal(esk96_0)
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_905_906,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_906_907,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_418]) ).
cnf(c_0_907_908,plain,
( epred1_0
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| esk98_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_908_909,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_419]) ).
cnf(c_0_909_910,lemma,
( in(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_910_911,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_417]) ).
cnf(c_0_911_912,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_912_913,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_913_914,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_914_915,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_423]) ).
cnf(c_0_915_916,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_916_917,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_917_918,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_918_919,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_420]) ).
cnf(c_0_919_920,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_422]) ).
cnf(c_0_920_921,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| in(esk100_0,omega)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_921_922,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_424]) ).
cnf(c_0_922_923,lemma,
( in(empty_set,omega)
| X2 = empty_set
| in(esk26_2(X1,X2),X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_923_924,lemma,
( relation(esk27_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_924_925,lemma,
( in(esk64_0,omega)
| X2 = empty_set
| in(esk68_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_925_926,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_425]) ).
cnf(c_0_926_927,lemma,
( epred2_2(X1,X2)
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_927_928,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_419]) ).
cnf(c_0_928_929,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_929_930,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_930_931,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk51_2(X2,X1) != esk52_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_931_932,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_427]) ).
cnf(c_0_932_933,lemma,
( X2 = esk49_3(X3,X1,X2)
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_933_934,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_934_935,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| being_limit_ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_935_936,lemma,
( subset(fiber(relation_restriction(X1,X2),X3),fiber(X1,X3))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_936_937,lemma,
( ordinal(esk64_0)
| X2 = empty_set
| in(esk68_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_937_938,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_938_939,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_939_940,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_940_941,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| subset(X2,esk103_1(X2))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_941_942,lemma,
( X2 = empty_set
| in(esk26_2(X1,X2),X2)
| ~ epred1_0
| esk24_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_942_943,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_943_944,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_944_945,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| in(esk103_1(X2),esk102_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_945_946,lemma,
( X2 = empty_set
| in(esk68_2(X1,X2),X2)
| esk66_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_946_947,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_390]) ).
cnf(c_0_947_948,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_390]) ).
cnf(c_0_948_949,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_429]) ).
cnf(c_0_949_950,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_429]) ).
cnf(c_0_950_951,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_951_952,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_952_953,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_953_954,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_954_955,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_955_956,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_390]) ).
cnf(c_0_956_957,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_390]) ).
cnf(c_0_957_958,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_429]) ).
cnf(c_0_958_959,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_429]) ).
cnf(c_0_959_960,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_429]) ).
cnf(c_0_960_961,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk8_1(X1),esk9_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_961_962,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk9_1(X1),esk8_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_962_963,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk2_1(X1),esk4_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_963_964,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk1_1(X1),esk1_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_964_965,lemma,
( in(X2,esk48_2(X3,X1))
| ~ ordinal(X1)
| ~ in(X4,X3)
| X2 != X4
| ~ ordinal(X4)
| ~ in(X2,succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_965_966,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_387]) ).
cnf(c_0_966_967,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk84_2(X2,X1)) != esk84_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_967_968,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_968_969,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_969_970,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_970_971,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_971_972,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_972_973,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_973_974,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_436]) ).
cnf(c_0_974_975,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_437]) ).
cnf(c_0_975_976,lemma,
( in(X2,cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_976_977,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_977_978,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk53_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_978_979,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_979_980,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_980_981,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_381]) ).
cnf(c_0_981_982,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_381]) ).
cnf(c_0_982_983,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_381]) ).
cnf(c_0_983_984,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_381]) ).
cnf(c_0_984_985,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_985_986,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_986_987,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_987_988,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_988_989,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_989_990,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_438]) ).
cnf(c_0_990_991,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_438]) ).
cnf(c_0_991_992,lemma,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_992_993,lemma,
( subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_993_994,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_994_995,lemma,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk33_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_995_996,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_429]) ).
cnf(c_0_996_997,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_429]) ).
cnf(c_0_997_998,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_429]) ).
cnf(c_0_998_999,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_429]) ).
cnf(c_0_999_1000,lemma,
( X2 = empty_set
| ordinal_subset(esk83_2(X2,X1),X3)
| ~ ordinal(X1)
| ~ subset(X2,X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_1000_1001,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_429]) ).
cnf(c_0_1001_1002,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_429]) ).
cnf(c_0_1002_1003,lemma,
( X2 = empty_set
| in(esk74_2(X1,X2),X2)
| ~ finite(X1)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_1003_1004,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| in(apply(esk81_1(X1),X2),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1004_1005,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1005_1006,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1006_1007,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_1007_1008,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_1008_1009,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| in(esk100_0,omega)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1009_1010,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_1010_1011,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_1011_1012,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_1012_1013,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_429]) ).
cnf(c_0_1013_1014,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_429]) ).
cnf(c_0_1014_1015,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_429]) ).
cnf(c_0_1015_1016,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_446]) ).
cnf(c_0_1016_1017,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_1017_1018,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_1018_1019,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_1019_1020,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_1020_1021,lemma,
( in(X2,succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_1021_1022,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_449]) ).
cnf(c_0_1022_1023,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_450]) ).
cnf(c_0_1023_1024,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_1024_1025,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_1025_1026,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_1026_1027,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_1027_1028,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_1028_1029,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1029_1030,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_456]) ).
cnf(c_0_1030_1031,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_457]) ).
cnf(c_0_1031_1032,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_458]) ).
cnf(c_0_1032_1033,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_1033_1034,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_381]) ).
cnf(c_0_1034_1035,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_381]) ).
cnf(c_0_1035_1036,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_1036_1037,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_1037_1038,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_1038_1039,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_1039_1040,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1040_1041,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| being_limit_ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1041_1042,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_1042_1043,lemma,
( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1043_1044,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_1044_1045,lemma,
( in(esk59_1(X1),X1)
| apply(esk63_1(X1),X3) = singleton(X3)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1045_1046,lemma,
( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_1046_1047,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| subset(X1,esk103_1(X1))
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1047_1048,lemma,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_1048_1049,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| in(apply(esk81_1(X1),X2),X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1049_1050,lemma,
( element(X1,powerset(X2))
| ~ in(esk10_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_1050_1051,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1051_1052,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1052_1053,lemma,
( in(X2,esk36_1(X1))
| in(X3,omega)
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_1053_1054,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| in(esk103_1(X1),esk102_0)
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1054_1055,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| subset(X2,esk103_1(X2))
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1055_1056,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_1056_1057,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_1057_1058,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_1058_1059,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_1059_1060,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1060_1061,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1061_1062,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| subset(X2,esk103_1(X2))
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1062_1063,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| in(esk103_1(X2),esk102_0)
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1063_1064,lemma,
( in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| esk60_1(X1) != esk61_1(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1064_1065,lemma,
( in(esk88_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_1065_1066,lemma,
( ordinal_subset(esk23_1(X2),X3)
| ~ in(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1066_1067,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| in(esk103_1(X2),esk102_0)
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1067_1068,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_1068_1069,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_1069_1070,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| apply(esk63_1(X1),X3) = singleton(X3)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1070_1071,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| apply(esk63_1(X1),X3) = singleton(X3)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1071_1072,lemma,
( apply(esk63_1(X1),X3) = singleton(X3)
| esk60_1(X1) != esk61_1(X1)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1072_1073,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_470]) ).
cnf(c_0_1073_1074,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_1074_1075,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_1075_1076,lemma,
( relation(esk5_2(X2,X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_1076_1077,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_387]) ).
cnf(c_0_1077_1078,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk6_1(X1),esk7_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_1078_1079,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk7_1(X1),esk6_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_1079_1080,lemma,
( transitive(X1)
| in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_1080_1081,lemma,
( transitive(X1)
| in(ordered_pair(esk3_1(X1),esk4_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_1081_1082,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_1082_1083,lemma,
( in(X1,esk71_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk71_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1083_1084,lemma,
( X1 = empty_set
| in(ordered_pair(esk93_1(X1),esk94_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_1084_1085,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_1085_1086,lemma,
( in(X1,esk71_1(X2))
| are_equipotent(X1,esk71_1(X2))
| ~ subset(X1,esk71_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1086_1087,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1087_1088,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_1088_1089,lemma,
( X2 = empty_set
| in(esk83_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_1089_1090,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1090_1091,plain,
( epred1_0
| subset(X2,esk103_1(X2))
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1091_1092,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_381]) ).
cnf(c_0_1092_1093,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_381]) ).
cnf(c_0_1093_1094,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_381]) ).
cnf(c_0_1094_1095,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_381]) ).
cnf(c_0_1095_1096,lemma,
( ordinal(esk37_2(X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_1096_1097,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_1097_1098,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| element(esk102_0,powerset(powerset(esk100_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1098_1099,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1099_1100,plain,
( epred1_0
| in(esk103_1(X2),esk102_0)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ in(X2,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1100_1101,lemma,
( X1 = identity_relation(X2)
| in(esk84_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_1101_1102,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_1102_1103,lemma,
( ~ in(X1,X2)
| ~ in(X3,X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_1103_1104,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1104_1105,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1105_1106,lemma,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_1106_1107,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_1107_1108,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_1108_1109,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1109_1110,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_1110_1111,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_483]) ).
cnf(c_0_1111_1112,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk86_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_1112_1113,lemma,
( X2 = empty_set
| ordinal(esk83_2(X2,X1))
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_1113_1114,lemma,
( relation_restriction(X1,X2) = relation_rng_restriction(X2,relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_1114_1115,lemma,
( relation_restriction(X1,X2) = relation_dom_restriction(relation_rng_restriction(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_1115_1116,lemma,
( in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(succ(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1116_1117,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1117_1118,lemma,
( element(X1,powerset(X2))
| in(esk10_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_1118_1119,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_1119_1120,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_1120_1121,lemma,
( in(X2,succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_1121_1122,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_1122_1123,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_1123_1124,lemma,
( in(powerset(X1),esk71_1(X2))
| ~ in(X1,esk71_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1124_1125,plain,
( epred1_0
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1125_1126,plain,
( epred1_0
| in(succ(esk96_0),omega)
| subset(X1,esk103_1(X1))
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1126_1127,lemma,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_1127_1128,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_1128_1129,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_1129_1130,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_1130_1131,plain,
( epred1_0
| in(succ(esk96_0),omega)
| in(esk103_1(X1),esk102_0)
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1131_1132,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| in(esk100_0,omega) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1132_1133,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_1133_1134,lemma,
( disjoint(X1,X2)
| in(esk85_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_1134_1135,lemma,
( disjoint(X1,X2)
| in(esk85_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_1135_1136,lemma,
( X2 = esk37_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_1136_1137,plain,
( epred1_0
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1137_1138,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_1138_1139,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_1139_1140,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_1140_1141,lemma,
( ordinal(X1)
| ~ subset(esk82_1(X1),X1)
| ~ ordinal(esk82_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1141_1142,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_1142_1143,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_1143_1144,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| in(esk100_0,omega)
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1144_1145,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_390]) ).
cnf(c_0_1145_1146,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1146_1147,lemma,
( finite(relation_image(X1,X2))
| ~ finite(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_1147_1148,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| relation(esk63_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1148_1149,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| function(esk63_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1149_1150,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| in(esk100_0,omega)
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1150_1151,lemma,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_1151_1152,lemma,
( in(X1,esk46_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1152_1153,lemma,
( in(esk23_1(X2),X2)
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1153_1154,lemma,
( in(esk59_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1154_1155,lemma,
( in(esk59_1(X1),X1)
| relation(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1155_1156,lemma,
( in(esk59_1(X1),X1)
| function(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1156_1157,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_1157_1158,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_1158_1159,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_1159_1160,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| ordinal(esk100_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1160_1161,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| being_limit_ordinal(esk100_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1161_1162,lemma,
( apply(esk69_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1162_1163,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1163_1164,lemma,
( in(X1,X2)
| ~ in(X1,esk46_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1164_1165,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_1165_1166,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1166_1167,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_1167_1168,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1168_1169,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1169_1170,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| relation(esk63_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1170_1171,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| function(esk63_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1171_1172,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| relation(esk63_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1172_1173,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| in(esk62_1(X1),X1)
| function(esk63_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1173_1174,lemma,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_510]) ).
cnf(c_0_1174_1175,plain,
( epred1_0
| in(succ(esk96_0),omega)
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1175_1176,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_1176_1177,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1177_1178,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1178_1179,lemma,
( in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1
| esk60_1(X1) != esk61_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1179_1180,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_512]) ).
cnf(c_0_1180_1181,lemma,
( well_founded_relation(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_1181_1182,lemma,
( antisymmetric(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_1182_1183,lemma,
( transitive(relation_restriction(X1,X2))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_1183_1184,lemma,
( connected(relation_restriction(X1,X2))
| ~ connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_1184_1185,lemma,
( reflexive(relation_restriction(X1,X2))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_1185_1186,plain,
( epred1_0
| ordinal(esk96_0)
| subset(X1,esk103_1(X1))
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1186_1187,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1187_1188,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| being_limit_ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1188_1189,lemma,
( in(esk62_1(X1),X1)
| relation(esk63_1(X1))
| esk60_1(X1) != esk61_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1189_1190,lemma,
( in(esk62_1(X1),X1)
| function(esk63_1(X1))
| esk60_1(X1) != esk61_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1190_1191,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_518]) ).
cnf(c_0_1191_1192,lemma,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_orders(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_1192_1193,lemma,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_1193_1194,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_521]) ).
cnf(c_0_1194_1195,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_522]) ).
cnf(c_0_1195_1196,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_1196_1197,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| relation_dom(esk63_1(X1)) = X1
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1197_1198,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| relation_dom(esk63_1(X1)) = X1
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1198_1199,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_1199_1200,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_1200_1201,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_1201_1202,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_1202_1203,plain,
( epred1_0
| ordinal(esk96_0)
| in(esk103_1(X1),esk102_0)
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1203_1204,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1204_1205,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| being_limit_ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1205_1206,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| relation(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1206_1207,lemma,
( esk60_1(X1) = singleton(esk59_1(X1))
| function(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1207_1208,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| relation(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1208_1209,lemma,
( esk61_1(X1) = singleton(esk59_1(X1))
| function(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1209_1210,plain,
( epred1_0
| subset(X1,esk103_1(X1))
| esk98_0 != empty_set
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1210_1211,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ~ in(X1,esk98_0)
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1211_1212,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ~ in(X1,esk98_0)
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1212_1213,lemma,
( relation_dom(esk63_1(X1)) = X1
| esk60_1(X1) != esk61_1(X1)
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1213_1214,plain,
( epred1_0
| in(succ(esk96_0),omega)
| element(esk102_0,powerset(powerset(esk100_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1214_1215,lemma,
( finite(relation_rng(X1))
| ~ finite(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_1215_1216,lemma,
( relation(esk63_1(X1))
| esk60_1(X1) != esk61_1(X1)
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1216_1217,lemma,
( function(esk63_1(X1))
| esk60_1(X1) != esk61_1(X1)
| X2 != singleton(esk62_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_1217_1218,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_1218_1219,plain,
( epred1_0
| in(esk103_1(X1),esk102_0)
| esk98_0 != empty_set
| ~ in(X1,esk102_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1219_1220,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ~ in(X1,esk98_0)
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1220_1221,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ~ in(X1,esk98_0)
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1221_1222,plain,
( epred1_0
| in(esk100_0,omega)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1222_1223,lemma,
( ordinal(esk23_1(X2))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_1223_1224,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_528]) ).
cnf(c_0_1224_1225,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_529]) ).
cnf(c_0_1225_1226,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_530]) ).
cnf(c_0_1226_1227,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1227_1228,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1228_1229,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_1229_1230,lemma,
( connected(X1)
| in(esk8_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_1230_1231,lemma,
( connected(X1)
| in(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_1231_1232,lemma,
( reflexive(X1)
| in(esk1_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_1232_1233,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_1233_1234,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_534]) ).
cnf(c_0_1234_1235,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_535]) ).
cnf(c_0_1235_1236,lemma,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_536]) ).
cnf(c_0_1236_1237,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_537]) ).
cnf(c_0_1237_1238,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_537]) ).
cnf(c_0_1238_1239,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_538]) ).
cnf(c_0_1239_1240,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_538]) ).
cnf(c_0_1240_1241,lemma,
( ordinal(X1)
| ~ in(X1,esk46_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_1241_1242,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| relation_dom(esk81_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1242_1243,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_539]) ).
cnf(c_0_1243_1244,lemma,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_539]) ).
cnf(c_0_1244_1245,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_1245_1246,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| relation(esk81_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1246_1247,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| function(esk81_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1247_1248,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_540]) ).
cnf(c_0_1248_1249,lemma,
( well_orders(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_1249_1250,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_1250_1251,plain,
( reflexive(X1)
| ~ epred2_2(X1,X2)
| ~ reflexive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_1251_1252,plain,
( transitive(X1)
| ~ epred2_2(X1,X2)
| ~ transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_1252_1253,plain,
( connected(X1)
| ~ epred2_2(X1,X2)
| ~ connected(X2) ),
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_1253_1254,plain,
( antisymmetric(X1)
| ~ epred2_2(X1,X2)
| ~ antisymmetric(X2) ),
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_1254_1255,plain,
( well_founded_relation(X1)
| ~ epred2_2(X1,X2)
| ~ well_founded_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_1255_1256,lemma,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_542]) ).
cnf(c_0_1256_1257,lemma,
( finite(X1)
| ~ finite(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_543]) ).
cnf(c_0_1257_1258,plain,
( epred1_0
| ordinal(esk96_0)
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1258_1259,plain,
( epred1_0
| ordinal(esk100_0)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1259_1260,plain,
( epred1_0
| being_limit_ordinal(esk100_0)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1260_1261,lemma,
( being_limit_ordinal(X1)
| in(esk86_1(X1),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_1261_1262,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_544]) ).
cnf(c_0_1262_1263,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_545]) ).
cnf(c_0_1263_1264,lemma,
pair_first(ordered_pair(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_546]) ).
cnf(c_0_1264_1265,lemma,
pair_second(ordered_pair(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_546]) ).
cnf(c_0_1265_1266,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1266_1267,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1267_1268,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1268_1269,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1269_1270,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_547]) ).
cnf(c_0_1270_1271,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_548]) ).
cnf(c_0_1271_1272,plain,
( epred1_0
| esk98_0 != empty_set
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1272_1273,plain,
( epred1_0
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1273_1274,plain,
( epred1_0
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1274_1275,lemma,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| X1 != succ(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_1275_1276,plain,
( epred1_0
| ordinal(esk96_0)
| element(esk102_0,powerset(powerset(esk100_0))) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1276_1277,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1277_1278,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1278_1279,plain,
( epred1_0
| in(succ(esk96_0),omega)
| in(esk100_0,omega) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1279_1280,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_1280_1281,plain,
( epred1_0
| element(esk102_0,powerset(powerset(esk100_0)))
| esk98_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1281_1282,lemma,
( ordinal(X1)
| in(esk82_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_1282_1283,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1283_1284,lemma,
( esk20_1(X1) = singleton(esk19_1(X1))
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1284_1285,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| relation(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1285_1286,lemma,
( esk21_1(X1) = singleton(esk19_1(X1))
| function(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1286_1287,lemma,
( connected(X1)
| ~ relation(X1)
| esk8_1(X1) != esk9_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_1287_1288,lemma,
( antisymmetric(X1)
| ~ relation(X1)
| esk6_1(X1) != esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_1288_1289,lemma,
( relation(esk22_1(X1))
| esk20_1(X1) != esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1289_1290,lemma,
( function(esk22_1(X1))
| esk20_1(X1) != esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_1290_1291,lemma,
( being_limit_ordinal(X1)
| X1 = succ(esk87_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_1291_1292,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_1292_1293,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_1293_1294,lemma,
( being_limit_ordinal(X1)
| ordinal(esk87_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_1294_1295,lemma,
( being_limit_ordinal(X1)
| ordinal(esk86_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_1295_1296,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_550]) ).
cnf(c_0_1296_1297,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_1297_1298,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_1298_1299,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| relation_dom(esk81_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1299_1300,lemma,
well_orders(esk79_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_552]) ).
cnf(c_0_1300_1301,lemma,
in(X1,esk71_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_1301_1302,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_1302_1303,plain,
( epred1_0
| in(succ(esk96_0),omega)
| ordinal(esk100_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1303_1304,plain,
( epred1_0
| in(succ(esk96_0),omega)
| being_limit_ordinal(esk100_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1304_1305,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| relation(esk81_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1305_1306,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| function(esk81_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_1306_1307,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_1307_1308,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_1308_1309,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_555]) ).
cnf(c_0_1309_1310,plain,
( epred1_0
| in(succ(esk96_0),omega)
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1310_1311,plain,
( epred1_0
| in(succ(esk96_0),omega)
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1311_1312,lemma,
( well_ordering(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_556]) ).
cnf(c_0_1312_1313,lemma,
( well_founded_relation(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_557]) ).
cnf(c_0_1313_1314,lemma,
( connected(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_558]) ).
cnf(c_0_1314_1315,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_559]) ).
cnf(c_0_1315_1316,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_559]) ).
cnf(c_0_1316_1317,plain,
( epred1_0
| ordinal(esk96_0)
| in(esk100_0,omega) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1317_1318,plain,
( epred1_0
| in(esk100_0,omega)
| esk98_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1318_1319,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_560]) ).
cnf(c_0_1319_1320,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_561]) ).
cnf(c_0_1320_1321,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_562]) ).
cnf(c_0_1321_1322,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_562]) ).
cnf(c_0_1322_1323,lemma,
relation_dom(esk69_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1323_1324,lemma,
antisymmetric(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_563]) ).
cnf(c_0_1324_1325,lemma,
transitive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_564]) ).
cnf(c_0_1325_1326,lemma,
reflexive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_565]) ).
cnf(c_0_1326_1327,lemma,
relation(esk79_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_552]) ).
cnf(c_0_1327_1328,lemma,
relation(esk69_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1328_1329,lemma,
function(esk69_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_1329_1330,negated_conjecture,
cast_as_carrier_subset(esk70_0) != the_carrier(esk70_0),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_1330_1331,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_567]) ).
cnf(c_0_1331_1332,plain,
( epred1_0
| ordinal(esk96_0)
| ordinal(esk100_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1332_1333,plain,
( epred1_0
| ordinal(esk96_0)
| being_limit_ordinal(esk100_0) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1333_1334,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_1334_1335,plain,
( epred1_0
| ordinal(esk96_0)
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1335_1336,plain,
( epred1_0
| ordinal(esk96_0)
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1336_1337,plain,
( epred1_0
| ordinal(esk100_0)
| esk98_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1337_1338,plain,
( epred1_0
| being_limit_ordinal(esk100_0)
| esk98_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1338_1339,plain,
( epred1_0
| esk98_0 != empty_set
| esk100_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1339_1340,plain,
( epred1_0
| esk98_0 != empty_set
| esk102_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_1340_1341,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_569]) ).
cnf(c_0_1341_1342,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_569]) ).
cnf(c_0_1342_1343,negated_conjecture,
one_sorted_str(esk70_0),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_1343_1344,lemma,
( empty(X2)
| in(X3,esk28_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,esk32_7(X2,X1,X4,X3,X5,X6,X7)),X1) ),
c_0_570,
[final] ).
cnf(c_0_1344_1345,lemma,
( empty(X2)
| in(X3,esk28_3(X2,X1,X4))
| in(esk32_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_571,
[final] ).
cnf(c_0_1345_1346,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_572,
[final] ).
cnf(c_0_1346_1347,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_573,
[final] ).
cnf(c_0_1347_1348,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_574,
[final] ).
cnf(c_0_1348_1349,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_575,
[final] ).
cnf(c_0_1349_1350,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_576,
[final] ).
cnf(c_0_1350_1351,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_577,
[final] ).
cnf(c_0_1351_1352,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_578,
[final] ).
cnf(c_0_1352_1353,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_579,
[final] ).
cnf(c_0_1353_1354,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_580,
[final] ).
cnf(c_0_1354_1355,lemma,
( in(ordered_pair(apply(X1,esk44_4(X4,X2,X1,X3)),apply(X1,esk45_4(X4,X2,X1,X3))),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk43_3(X4,X2,X1)) ),
c_0_581,
[final] ).
cnf(c_0_1355_1356,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_582,
[final] ).
cnf(c_0_1356_1357,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_583,
[final] ).
cnf(c_0_1357_1358,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_584,
[final] ).
cnf(c_0_1358_1359,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_585,
[final] ).
cnf(c_0_1359_1360,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_586,
[final] ).
cnf(c_0_1360_1361,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_587,
[final] ).
cnf(c_0_1361_1362,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_588,
[final] ).
cnf(c_0_1362_1363,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_589,
[final] ).
cnf(c_0_1363_1364,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_590,
[final] ).
cnf(c_0_1364_1365,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
c_0_591,
[final] ).
cnf(c_0_1365_1366,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
c_0_592,
[final] ).
cnf(c_0_1366_1367,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_593,
[final] ).
cnf(c_0_1367_1368,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_594,
[final] ).
cnf(c_0_1368_1369,lemma,
( empty(X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_595,
[final] ).
cnf(c_0_1369_1370,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_596,
[final] ).
cnf(c_0_1370_1371,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_597,
[final] ).
cnf(c_0_1371_1372,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_598,
[final] ).
cnf(c_0_1372_1373,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_599,
[final] ).
cnf(c_0_1373_1374,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_600,
[final] ).
cnf(c_0_1374_1375,lemma,
( empty(X2)
| in(ordered_pair(esk30_4(X2,X1,X4,X3),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4))
| ~ in(X5,esk31_4(X2,X1,X4,X3)) ),
c_0_601,
[final] ).
cnf(c_0_1375_1376,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_602,
[final] ).
cnf(c_0_1376_1377,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_603,
[final] ).
cnf(c_0_1377_1378,lemma,
( empty(X2)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_604,
[final] ).
cnf(c_0_1378_1379,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_605,
[final] ).
cnf(c_0_1379_1380,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_606,
[final] ).
cnf(c_0_1380_1381,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_607,
[final] ).
cnf(c_0_1381_1382,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| esk58_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_608,
[final] ).
cnf(c_0_1382_1383,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| esk58_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1)
| ~ in(X6,X2) ),
c_0_609,
[final] ).
cnf(c_0_1383_1384,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
c_0_610,
[final] ).
cnf(c_0_1384_1385,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
c_0_611,
[final] ).
cnf(c_0_1385_1386,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
c_0_612,
[final] ).
cnf(c_0_1386_1387,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
c_0_613,
[final] ).
cnf(c_0_1387_1388,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
c_0_614,
[final] ).
cnf(c_0_1388_1389,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(ordered_pair(X5,esk56_4(X2,X1,X5,X4)),X1) ),
c_0_615,
[final] ).
cnf(c_0_1389_1390,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_616,
[final] ).
cnf(c_0_1390_1391,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_617,
[final] ).
cnf(c_0_1391_1392,lemma,
( empty(X2)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_618,
[final] ).
cnf(c_0_1392_1393,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_619,
[final] ).
cnf(c_0_1393_1394,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_620,
[final] ).
cnf(c_0_1394_1395,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1)
| ~ in(X5,X2) ),
c_0_621,
[final] ).
cnf(c_0_1395_1396,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_622,
[final] ).
cnf(c_0_1396_1397,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_623,
[final] ).
cnf(c_0_1397_1398,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_624,
[final] ).
cnf(c_0_1398_1399,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_625,
[final] ).
cnf(c_0_1399_1400,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_626,
[final] ).
cnf(c_0_1400_1401,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_627,
[final] ).
cnf(c_0_1401_1402,lemma,
( empty(X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_628,
[final] ).
cnf(c_0_1402_1403,lemma,
( empty(X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_629,
[final] ).
cnf(c_0_1403_1404,lemma,
( empty(X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_630,
[final] ).
cnf(c_0_1404_1405,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_631,
[final] ).
cnf(c_0_1405_1406,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_632,
[final] ).
cnf(c_0_1406_1407,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_633,
[final] ).
cnf(c_0_1407_1408,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_634,
[final] ).
cnf(c_0_1408_1409,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_635,
[final] ).
cnf(c_0_1409_1410,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_636,
[final] ).
cnf(c_0_1410_1411,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_637,
[final] ).
cnf(c_0_1411_1412,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_638,
[final] ).
cnf(c_0_1412_1413,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk56_4(X2,X1,X4,X3)),X1) ),
c_0_639,
[final] ).
cnf(c_0_1413_1414,lemma,
( in(ordered_pair(esk78_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_640,
[final] ).
cnf(c_0_1414_1415,lemma,
( in(ordered_pair(X4,esk76_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_641,
[final] ).
cnf(c_0_1415_1416,lemma,
( ordered_pair(esk44_4(X4,X2,X1,X3),esk45_4(X4,X2,X1,X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk43_3(X4,X2,X1)) ),
c_0_642,
[final] ).
cnf(c_0_1416_1417,lemma,
( empty(X2)
| ordered_pair(esk29_4(X2,X1,X4,X3),esk30_4(X2,X1,X4,X3)) = X3
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
c_0_643,
[final] ).
cnf(c_0_1417_1418,lemma,
( empty(X2)
| in(esk30_4(X2,X1,X4,X3),esk31_4(X2,X1,X4,X3))
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
c_0_644,
[final] ).
cnf(c_0_1418_1419,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
c_0_645,
[final] ).
cnf(c_0_1419_1420,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(ordered_pair(apply(esk57_2(X2,X1),X6),X7),X1)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2)
| ~ in(X7,esk58_3(X2,X1,X6)) ),
c_0_646,
[final] ).
cnf(c_0_1420_1421,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_647,
[final] ).
cnf(c_0_1421_1422,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_648,
[final] ).
cnf(c_0_1422_1423,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_649,
[final] ).
cnf(c_0_1423_1424,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_650,
[final] ).
cnf(c_0_1424_1425,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_651,
[final] ).
cnf(c_0_1425_1426,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_652,
[final] ).
cnf(c_0_1426_1427,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_653,
[final] ).
cnf(c_0_1427_1428,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_654,
[final] ).
cnf(c_0_1428_1429,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_655,
[final] ).
cnf(c_0_1429_1430,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(ordered_pair(apply(esk57_2(X2,X1),X5),X6),X1)
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2)
| ~ in(X6,esk58_3(X2,X1,X5)) ),
c_0_656,
[final] ).
cnf(c_0_1430_1431,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_657,
[final] ).
cnf(c_0_1431_1432,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_658,
[final] ).
cnf(c_0_1432_1433,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_659,
[final] ).
cnf(c_0_1433_1434,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_660,
[final] ).
cnf(c_0_1434_1435,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_661,
[final] ).
cnf(c_0_1435_1436,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_662,
[final] ).
cnf(c_0_1436_1437,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| in(apply(esk57_2(X2,X1),X6),esk58_3(X2,X1,X6))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_663,
[final] ).
cnf(c_0_1437_1438,lemma,
( in(X2,esk36_1(X1))
| in(esk40_4(X1,X2,X3,X4),esk39_3(X1,X2,X3))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,esk39_3(X1,X2,X3)) ),
c_0_664,
[final] ).
cnf(c_0_1438_1439,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_665,
[final] ).
cnf(c_0_1439_1440,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_666,
[final] ).
cnf(c_0_1440_1441,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_667,
[final] ).
cnf(c_0_1441_1442,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_668,
[final] ).
cnf(c_0_1442_1443,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_669,
[final] ).
cnf(c_0_1443_1444,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| in(apply(esk57_2(X2,X1),X5),esk58_3(X2,X1,X5))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_670,
[final] ).
cnf(c_0_1444_1445,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| esk58_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_671,
[final] ).
cnf(c_0_1445_1446,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| esk58_3(X2,X1,X6) = X6
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4)
| ~ in(X6,X2) ),
c_0_672,
[final] ).
cnf(c_0_1446_1447,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_673,
[final] ).
cnf(c_0_1447_1448,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_674,
[final] ).
cnf(c_0_1448_1449,lemma,
( in(X2,esk36_1(X1))
| subset(X4,esk40_4(X1,X2,X3,X4))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,esk39_3(X1,X2,X3)) ),
c_0_675,
[final] ).
cnf(c_0_1449_1450,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_676,
[final] ).
cnf(c_0_1450_1451,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_677,
[final] ).
cnf(c_0_1451_1452,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_678,
[final] ).
cnf(c_0_1452_1453,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_679,
[final] ).
cnf(c_0_1453_1454,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_680,
[final] ).
cnf(c_0_1454_1455,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk56_4(X2,X1,X5,X4),X4)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| esk55_2(X2,X1) != X4
| ~ in(X5,X4) ),
c_0_681,
[final] ).
cnf(c_0_1455_1456,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_682,
[final] ).
cnf(c_0_1456_1457,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_683,
[final] ).
cnf(c_0_1457_1458,lemma,
( empty(X2)
| in(esk29_4(X2,X1,X4,X3),X2)
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
c_0_684,
[final] ).
cnf(c_0_1458_1459,lemma,
( empty(X2)
| esk29_4(X2,X1,X4,X3) = esk31_4(X2,X1,X4,X3)
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
c_0_685,
[final] ).
cnf(c_0_1459_1460,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_686,
[final] ).
cnf(c_0_1460_1461,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_687,
[final] ).
cnf(c_0_1461_1462,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_688,
[final] ).
cnf(c_0_1462_1463,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_689,
[final] ).
cnf(c_0_1463_1464,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_690,
[final] ).
cnf(c_0_1464_1465,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| esk58_3(X2,X1,X5) = X5
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3)
| ~ in(X5,X2) ),
c_0_691,
[final] ).
cnf(c_0_1465_1466,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_692,
[final] ).
cnf(c_0_1466_1467,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_693,
[final] ).
cnf(c_0_1467_1468,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_694,
[final] ).
cnf(c_0_1468_1469,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_695,
[final] ).
cnf(c_0_1469_1470,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_696,
[final] ).
cnf(c_0_1470_1471,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_697,
[final] ).
cnf(c_0_1471_1472,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_698,
[final] ).
cnf(c_0_1472_1473,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_699,
[final] ).
cnf(c_0_1473_1474,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_700,
[final] ).
cnf(c_0_1474_1475,lemma,
( in(X2,esk36_1(X1))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,esk39_3(X1,X2,X3))
| esk40_4(X1,X2,X3,X4) != X4 ),
c_0_701,
[final] ).
cnf(c_0_1475_1476,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_702,
[final] ).
cnf(c_0_1476_1477,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_703,
[final] ).
cnf(c_0_1477_1478,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_704,
[final] ).
cnf(c_0_1478_1479,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_705,
[final] ).
cnf(c_0_1479_1480,lemma,
( empty(X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_706,
[final] ).
cnf(c_0_1480_1481,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_707,
[final] ).
cnf(c_0_1481_1482,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_708,
[final] ).
cnf(c_0_1482_1483,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_709,
[final] ).
cnf(c_0_1483_1484,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_710,
[final] ).
cnf(c_0_1484_1485,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_711,
[final] ).
cnf(c_0_1485_1486,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_712,
[final] ).
cnf(c_0_1486_1487,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_713,
[final] ).
cnf(c_0_1487_1488,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_714,
[final] ).
cnf(c_0_1488_1489,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk56_4(X2,X1,X4,X3),X3)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk55_2(X2,X1) != X3
| ~ in(X4,X3) ),
c_0_715,
[final] ).
cnf(c_0_1489_1490,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk58_3(X2,X1,X4)) ),
c_0_716,
[final] ).
cnf(c_0_1490_1491,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X4),X5),X1)
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| ~ in(X4,X2)
| ~ in(X5,esk58_3(X2,X1,X4)) ),
c_0_717,
[final] ).
cnf(c_0_1491_1492,lemma,
( X3 = empty_set
| X4 = esk38_3(X1,X2,X3)
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1))
| ~ in(esk37_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk37_2(X1,X2))))
| ~ subset(esk38_3(X1,X2,X3),X4)
| ~ in(X4,X3) ),
c_0_718,
[final] ).
cnf(c_0_1492_1493,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(X4,esk77_3(X2,X3,X1)),X1) ),
c_0_719,
[final] ).
cnf(c_0_1493_1494,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(ordered_pair(esk75_3(X3,X2,X1),X4),X1) ),
c_0_720,
[final] ).
cnf(c_0_1494_1495,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
c_0_721,
[final] ).
cnf(c_0_1495_1496,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
c_0_722,
[final] ).
cnf(c_0_1496_1497,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_723,
[final] ).
cnf(c_0_1497_1498,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_724,
[final] ).
cnf(c_0_1498_1499,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
c_0_725,
[final] ).
cnf(c_0_1499_1500,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
c_0_726,
[final] ).
cnf(c_0_1500_1501,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
c_0_727,
[final] ).
cnf(c_0_1501_1502,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(ordered_pair(apply(esk57_2(X2,X1),X3),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(X4,esk58_3(X2,X1,X3)) ),
c_0_728,
[final] ).
cnf(c_0_1502_1503,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,esk95_3(X3,X1,X2)) != apply(X2,esk95_3(X3,X1,X2)) ),
c_0_729,
[final] ).
cnf(c_0_1503_1504,lemma,
( in(X3,esk43_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_730,
[final] ).
cnf(c_0_1504_1505,lemma,
( in(ordered_pair(X3,X4),esk27_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_731,
[final] ).
cnf(c_0_1505_1506,lemma,
( X3 = empty_set
| in(esk38_3(X1,X2,X3),X3)
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1))
| ~ in(esk37_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk37_2(X1,X2)))) ),
c_0_732,
[final] ).
cnf(c_0_1506_1507,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_733,
[final] ).
cnf(c_0_1507_1508,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_734,
[final] ).
cnf(c_0_1508_1509,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X4),esk58_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| ~ in(X4,X2) ),
c_0_735,
[final] ).
cnf(c_0_1509_1510,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X4),esk58_3(X2,X1,X4))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| ~ in(X4,X2) ),
c_0_736,
[final] ).
cnf(c_0_1510_1511,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_737,
[final] ).
cnf(c_0_1511_1512,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_738,
[final] ).
cnf(c_0_1512_1513,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_739,
[final] ).
cnf(c_0_1513_1514,lemma,
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk27_3(X5,X2,X1)) ),
c_0_740,
[final] ).
cnf(c_0_1514_1515,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_741,
[final] ).
cnf(c_0_1515_1516,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_742,
[final] ).
cnf(c_0_1516_1517,lemma,
( X2 = empty_set
| X3 = esk65_2(X1,X2)
| X5 = empty_set
| X6 = esk68_2(X4,X5)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk65_2(X1,X2),X3)
| ~ in(X3,X2)
| ~ ordinal(X4)
| ~ in(X4,omega)
| ~ element(X5,powerset(powerset(X4)))
| ~ subset(esk68_2(X4,X5),X6)
| ~ in(X6,X5) ),
c_0_743,
[final] ).
cnf(c_0_1517_1518,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,esk90_2(X1,X2)) != esk89_2(X1,X2)
| ~ in(esk90_2(X1,X2),relation_dom(X1))
| apply(X2,esk91_2(X1,X2)) != esk92_2(X1,X2)
| ~ in(esk91_2(X1,X2),relation_rng(X1)) ),
c_0_744,
[final] ).
cnf(c_0_1518_1519,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_745,
[final] ).
cnf(c_0_1519_1520,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_746,
[final] ).
cnf(c_0_1520_1521,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| X4 = empty_set
| X5 = esk101_2(X3,X4)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ ordinal(X3)
| ~ in(X3,esk100_0)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3)))
| ~ subset(esk101_2(X3,X4),X5)
| ~ in(X5,X4) ),
c_0_747,
[final] ).
cnf(c_0_1521_1522,lemma,
( in(ordered_pair(X2,esk73_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_748,
[final] ).
cnf(c_0_1522_1523,lemma,
( in(ordered_pair(esk72_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_749,
[final] ).
cnf(c_0_1523_1524,lemma,
( X2 = empty_set
| in(esk65_2(X1,X2),X2)
| X4 = empty_set
| X5 = esk68_2(X3,X4)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ ordinal(X3)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3)))
| ~ subset(esk68_2(X3,X4),X5)
| ~ in(X5,X4) ),
c_0_750,
[final] ).
cnf(c_0_1524_1525,lemma,
( X2 = empty_set
| X3 = esk65_2(X1,X2)
| X5 = empty_set
| in(esk68_2(X4,X5),X5)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk65_2(X1,X2),X3)
| ~ in(X3,X2)
| ~ ordinal(X4)
| ~ in(X4,omega)
| ~ element(X5,powerset(powerset(X4))) ),
c_0_751,
[final] ).
cnf(c_0_1525_1526,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| ~ in(X3,X2) ),
c_0_752,
[final] ).
cnf(c_0_1526_1527,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_753,
[final] ).
cnf(c_0_1527_1528,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_754,
[final] ).
cnf(c_0_1528_1529,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_755,
[final] ).
cnf(c_0_1529_1530,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| in(apply(esk57_2(X2,X1),X3),esk58_3(X2,X1,X3))
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_756,
[final] ).
cnf(c_0_1530_1531,lemma,
( in(X4,esk47_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(relation_image(X1,X4),X2)
| ~ in(X4,powerset(relation_dom(X1))) ),
c_0_757,
[final] ).
cnf(c_0_1531_1532,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_758,
[final] ).
cnf(c_0_1532_1533,lemma,
( in(relation_image(X1,X4),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk47_3(X3,X2,X1)) ),
c_0_759,
[final] ).
cnf(c_0_1533_1534,lemma,
( ordered_pair(esk34_3(X2,X3,X1),esk35_3(X2,X3,X1)) = X1
| ~ in(X1,esk33_2(X2,X3)) ),
c_0_760,
[final] ).
cnf(c_0_1534_1535,lemma,
( in(X4,powerset(relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X4,esk47_3(X3,X2,X1)) ),
c_0_761,
[final] ).
cnf(c_0_1535_1536,lemma,
( set_difference(esk42_3(X2,X1,X3),singleton(X2)) = X3
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk41_2(X2,X1)) ),
c_0_762,
[final] ).
cnf(c_0_1536_1537,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1))
| ~ in(X4,X2) ),
c_0_763,
[final] ).
cnf(c_0_1537_1538,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X4) = X4
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1))
| ~ in(X4,X2) ),
c_0_764,
[final] ).
cnf(c_0_1538_1539,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_765,
[final] ).
cnf(c_0_1539_1540,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_766,
[final] ).
cnf(c_0_1540_1541,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_767,
[final] ).
cnf(c_0_1541_1542,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_768,
[final] ).
cnf(c_0_1542_1543,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_769,
[final] ).
cnf(c_0_1543_1544,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_770,
[final] ).
cnf(c_0_1544_1545,lemma,
( in(esk42_3(X2,X1,X3),X1)
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk41_2(X2,X1)) ),
c_0_771,
[final] ).
cnf(c_0_1545_1546,lemma,
( in(X3,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk27_3(X5,X2,X1)) ),
c_0_772,
[final] ).
cnf(c_0_1546_1547,lemma,
( in(X4,X5)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),esk27_3(X5,X2,X1)) ),
c_0_773,
[final] ).
cnf(c_0_1547_1548,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk89_2(X1,X2)) = esk90_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X2,esk91_2(X1,X2)) != esk92_2(X1,X2)
| ~ in(esk91_2(X1,X2),relation_rng(X1)) ),
c_0_774,
[final] ).
cnf(c_0_1548_1549,lemma,
( X2 = function_inverse(X1)
| apply(X1,esk92_2(X1,X2)) = esk91_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk90_2(X1,X2)) != esk89_2(X1,X2)
| ~ in(esk90_2(X1,X2),relation_dom(X1)) ),
c_0_775,
[final] ).
cnf(c_0_1549_1550,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| X4 = empty_set
| in(esk101_2(X3,X4),X4)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ ordinal(X3)
| ~ in(X3,esk100_0)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3))) ),
c_0_776,
[final] ).
cnf(c_0_1550_1551,lemma,
( relation_rng_as_subset(X2,X3,X1) = X3
| in(esk77_3(X2,X3,X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_777,
[final] ).
cnf(c_0_1551_1552,lemma,
( relation_dom_as_subset(X2,X3,X1) = X2
| in(esk75_3(X3,X2,X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_778,
[final] ).
cnf(c_0_1552_1553,lemma,
( X2 = empty_set
| in(esk65_2(X1,X2),X2)
| X4 = empty_set
| in(esk68_2(X3,X4),X4)
| ~ ordinal(X1)
| ~ in(X1,esk64_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ ordinal(X3)
| ~ in(X3,omega)
| ~ element(X4,powerset(powerset(X3))) ),
c_0_779,
[final] ).
cnf(c_0_1553_1554,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_780,
[final] ).
cnf(c_0_1554_1555,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_781,
[final] ).
cnf(c_0_1555_1556,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_782,
[final] ).
cnf(c_0_1556_1557,lemma,
( X2 = function_inverse(X1)
| in(esk89_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,esk91_2(X1,X2)) != esk92_2(X1,X2)
| ~ in(esk91_2(X1,X2),relation_rng(X1)) ),
c_0_783,
[final] ).
cnf(c_0_1557_1558,lemma,
( X2 = function_inverse(X1)
| in(esk92_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,esk90_2(X1,X2)) != esk89_2(X1,X2)
| ~ in(esk90_2(X1,X2),relation_dom(X1)) ),
c_0_784,
[final] ).
cnf(c_0_1558_1559,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_785,
[final] ).
cnf(c_0_1559_1560,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_786,
[final] ).
cnf(c_0_1560_1561,lemma,
( X1 = X2
| empty_carrier(X3)
| ~ below(X3,X2,X1)
| ~ below(X3,X1,X2)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ join_semilatt_str(X3)
| ~ join_commutative(X3) ),
c_0_787,
[final] ).
cnf(c_0_1561_1562,lemma,
( below(X1,meet_commut(X1,X2,X3),X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1) ),
c_0_788,
[final] ).
cnf(c_0_1562_1563,lemma,
( in(X3,cartesian_product2(X4,X4))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X3,esk43_3(X4,X2,X1)) ),
c_0_789,
[final] ).
cnf(c_0_1563_1564,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_790,
[final] ).
cnf(c_0_1564_1565,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_791,
[final] ).
cnf(c_0_1565_1566,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_792,
[final] ).
cnf(c_0_1566_1567,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_793,
[final] ).
cnf(c_0_1567_1568,lemma,
( empty(X2)
| in(X3,cartesian_product2(X2,X4))
| ~ relation(X1)
| ~ in(X3,esk28_3(X2,X1,X4)) ),
c_0_794,
[final] ).
cnf(c_0_1568_1569,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1)) ),
c_0_795,
[final] ).
cnf(c_0_1569_1570,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1)) ),
c_0_796,
[final] ).
cnf(c_0_1570_1571,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1)) ),
c_0_797,
[final] ).
cnf(c_0_1571_1572,lemma,
( empty(X2)
| in(ordered_pair(esk51_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk53_2(X2,X1)) ),
c_0_798,
[final] ).
cnf(c_0_1572_1573,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1)) ),
c_0_799,
[final] ).
cnf(c_0_1573_1574,lemma,
( empty(X2)
| in(ordered_pair(esk52_2(X2,X1),X3),X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| ~ in(X3,esk54_2(X2,X1)) ),
c_0_800,
[final] ).
cnf(c_0_1574_1575,plain,
( epred1_0
| X3 = empty_set
| X4 = esk101_2(X2,X3)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk101_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_801,
[final] ).
cnf(c_0_1575_1576,lemma,
( singleton(esk34_3(X2,X3,X1)) = esk35_3(X2,X3,X1)
| ~ in(X1,esk33_2(X2,X3)) ),
c_0_802,
[final] ).
cnf(c_0_1576_1577,lemma,
( in(X3,esk41_2(X2,X1))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| X3 != set_difference(X4,singleton(X2))
| ~ in(X4,X1)
| ~ in(X3,powerset(X2)) ),
c_0_803,
[final] ).
cnf(c_0_1577_1578,lemma,
( subset(X1,esk25_1(X1))
| X3 = empty_set
| X4 = esk26_2(X2,X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk26_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_804,
[final] ).
cnf(c_0_1578_1579,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_805,
[final] ).
cnf(c_0_1579_1580,lemma,
( subset(X1,esk67_1(X1))
| X3 = empty_set
| X4 = esk68_2(X2,X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk68_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_806,
[final] ).
cnf(c_0_1580_1581,lemma,
( in(esk25_1(X1),esk24_0)
| X3 = empty_set
| X4 = esk26_2(X2,X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk26_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_807,
[final] ).
cnf(c_0_1581_1582,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_808,
[final] ).
cnf(c_0_1582_1583,lemma,
( in(esk67_1(X1),esk66_0)
| X3 = empty_set
| X4 = esk68_2(X2,X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk68_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_809,
[final] ).
cnf(c_0_1583_1584,plain,
( epred1_0
| in(succ(esk96_0),omega)
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_810,
[final] ).
cnf(c_0_1584_1585,lemma,
( X3 = empty_set
| X4 = esk26_2(X2,X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| esk25_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk26_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_811,
[final] ).
cnf(c_0_1585_1586,lemma,
( X3 = empty_set
| X4 = esk68_2(X2,X3)
| ~ in(X1,esk66_0)
| esk67_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2)))
| ~ subset(esk68_2(X2,X3),X4)
| ~ in(X4,X3) ),
c_0_812,
[final] ).
cnf(c_0_1586_1587,lemma,
( in(X2,esk36_1(X1))
| element(esk39_3(X1,X2,X3),powerset(powerset(X3)))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3 ),
c_0_813,
[final] ).
cnf(c_0_1587_1588,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk95_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_814,
[final] ).
cnf(c_0_1588_1589,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_815,
[final] ).
cnf(c_0_1589_1590,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_816,
[final] ).
cnf(c_0_1590_1591,lemma,
( element(esk24_0,powerset(powerset(empty_set)))
| X2 = empty_set
| X3 = esk26_2(X1,X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk26_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_817,
[final] ).
cnf(c_0_1591_1592,lemma,
( element(esk66_0,powerset(powerset(esk64_0)))
| X2 = empty_set
| X3 = esk68_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_818,
[final] ).
cnf(c_0_1592_1593,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_819,
[final] ).
cnf(c_0_1593_1594,plain,
( epred1_0
| ordinal(esk96_0)
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_820,
[final] ).
cnf(c_0_1594_1595,plain,
( epred1_0
| X2 = empty_set
| X3 = esk101_2(X1,X2)
| esk98_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk101_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_821,
[final] ).
cnf(c_0_1595_1596,lemma,
( in(esk73_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_822,
[final] ).
cnf(c_0_1596_1597,lemma,
( in(esk72_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_823,
[final] ).
cnf(c_0_1597_1598,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_824,
[final] ).
cnf(c_0_1598_1599,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_825,
[final] ).
cnf(c_0_1599_1600,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_826,
[final] ).
cnf(c_0_1600_1601,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_827,
[final] ).
cnf(c_0_1601_1602,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_828,
[final] ).
cnf(c_0_1602_1603,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_829,
[final] ).
cnf(c_0_1603_1604,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_830,
[final] ).
cnf(c_0_1604_1605,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_831,
[final] ).
cnf(c_0_1605_1606,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_832,
[final] ).
cnf(c_0_1606_1607,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_833,
[final] ).
cnf(c_0_1607_1608,lemma,
( in(empty_set,omega)
| X2 = empty_set
| X3 = esk26_2(X1,X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk26_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_834,
[final] ).
cnf(c_0_1608_1609,lemma,
( in(esk64_0,omega)
| X2 = empty_set
| X3 = esk68_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_835,
[final] ).
cnf(c_0_1609_1610,lemma,
( in(esk73_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_836,
[final] ).
cnf(c_0_1610_1611,lemma,
( in(esk72_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_837,
[final] ).
cnf(c_0_1611_1612,lemma,
( in(esk49_3(X3,X1,X2),X3)
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
c_0_838,
[final] ).
cnf(c_0_1612_1613,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_839,
[final] ).
cnf(c_0_1613_1614,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_840,
[final] ).
cnf(c_0_1614_1615,lemma,
( ordinal(esk64_0)
| X2 = empty_set
| X3 = esk68_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_841,
[final] ).
cnf(c_0_1615_1616,lemma,
( in(esk34_3(X2,X3,X1),X2)
| ~ in(X1,esk33_2(X2,X3)) ),
c_0_842,
[final] ).
cnf(c_0_1616_1617,lemma,
( X2 = empty_set
| X3 = esk26_2(X1,X2)
| ~ epred1_0
| esk24_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk26_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_843,
[final] ).
cnf(c_0_1617_1618,lemma,
( X2 = empty_set
| X3 = esk68_2(X1,X2)
| esk66_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk68_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_844,
[final] ).
cnf(c_0_1618_1619,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_845,
[final] ).
cnf(c_0_1619_1620,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_846,
[final] ).
cnf(c_0_1620_1621,lemma,
( ordinal(esk49_3(X3,X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
c_0_847,
[final] ).
cnf(c_0_1621_1622,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_848,
[final] ).
cnf(c_0_1622_1623,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(X1,esk98_0)
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_849,
[final] ).
cnf(c_0_1623_1624,lemma,
( in(X3,powerset(X2))
| ~ element(X1,powerset(powerset(succ(X2))))
| ~ ordinal(X2)
| ~ in(X3,esk41_2(X2,X1)) ),
c_0_850,
[final] ).
cnf(c_0_1624_1625,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_851,
[final] ).
cnf(c_0_1625_1626,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_852,
[final] ).
cnf(c_0_1626_1627,lemma,
( relation_isomorphism(X1,X2,function_inverse(X3))
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_853,
[final] ).
cnf(c_0_1627_1628,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X3) = X3
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1)
| ~ in(X3,X2) ),
c_0_854,
[final] ).
cnf(c_0_1628_1629,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_855,
[final] ).
cnf(c_0_1629_1630,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_856,
[final] ).
cnf(c_0_1630_1631,lemma,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X4) ),
c_0_857,
[final] ).
cnf(c_0_1631_1632,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_858,
[final] ).
cnf(c_0_1632_1633,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_859,
[final] ).
cnf(c_0_1633_1634,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_860,
[final] ).
cnf(c_0_1634_1635,plain,
( epred1_0
| X3 = empty_set
| in(esk101_2(X2,X3),X3)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,esk100_0)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_861,
[final] ).
cnf(c_0_1635_1636,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_862,
[final] ).
cnf(c_0_1636_1637,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_863,
[final] ).
cnf(c_0_1637_1638,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_864,
[final] ).
cnf(c_0_1638_1639,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_865,
[final] ).
cnf(c_0_1639_1640,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_866,
[final] ).
cnf(c_0_1640_1641,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_867,
[final] ).
cnf(c_0_1641_1642,lemma,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(X4,X3)
| ~ relation_of2_as_subset(X1,X2,X4) ),
c_0_868,
[final] ).
cnf(c_0_1642_1643,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| subset(X3,esk103_1(X3))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ in(X3,esk102_0) ),
c_0_869,
[final] ).
cnf(c_0_1643_1644,lemma,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
c_0_870,
[final] ).
cnf(c_0_1644_1645,lemma,
( subset(X1,esk25_1(X1))
| X3 = empty_set
| in(esk26_2(X2,X3),X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_871,
[final] ).
cnf(c_0_1645_1646,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk89_2(X1,X2)) = esk90_2(X1,X2)
| apply(X1,esk92_2(X1,X2)) = esk91_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_872,
[final] ).
cnf(c_0_1646_1647,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_873,
[final] ).
cnf(c_0_1647_1648,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| in(esk103_1(X3),esk102_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ in(X3,esk102_0) ),
c_0_874,
[final] ).
cnf(c_0_1648_1649,lemma,
( subset(X1,esk67_1(X1))
| X3 = empty_set
| in(esk68_2(X2,X3),X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_875,
[final] ).
cnf(c_0_1649_1650,lemma,
( X2 = empty_set
| X3 = esk74_2(X1,X2)
| ~ finite(X1)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(esk74_2(X1,X2),X3)
| ~ in(X3,X2) ),
c_0_876,
[final] ).
cnf(c_0_1650_1651,lemma,
( in(esk25_1(X1),esk24_0)
| X3 = empty_set
| in(esk26_2(X2,X3),X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_877,
[final] ).
cnf(c_0_1651_1652,lemma,
( in(esk67_1(X1),esk66_0)
| X3 = empty_set
| in(esk68_2(X2,X3),X3)
| ~ in(X1,esk66_0)
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_878,
[final] ).
cnf(c_0_1652_1653,lemma,
( in(X1,esk33_2(X2,X3))
| X4 != singleton(X5)
| ~ in(X5,X2)
| ordered_pair(X5,X4) != X1
| ~ in(X1,cartesian_product2(X2,X3)) ),
c_0_879,
[final] ).
cnf(c_0_1653_1654,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_880,
[final] ).
cnf(c_0_1654_1655,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| esk58_3(X2,X1,X3) = X3
| ~ relation(X1)
| ~ in(X3,X2) ),
c_0_881,
[final] ).
cnf(c_0_1655_1656,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_882,
[final] ).
cnf(c_0_1656_1657,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_883,
[final] ).
cnf(c_0_1657_1658,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_884,
[final] ).
cnf(c_0_1658_1659,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_885,
[final] ).
cnf(c_0_1659_1660,plain,
( epred1_0
| in(succ(esk96_0),omega)
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_886,
[final] ).
cnf(c_0_1660_1661,lemma,
( in(X2,esk36_1(X1))
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3
| esk39_3(X1,X2,X3) != empty_set ),
c_0_887,
[final] ).
cnf(c_0_1661_1662,lemma,
( X2 = function_inverse(X1)
| in(esk89_2(X1,X2),relation_rng(X1))
| apply(X1,esk92_2(X1,X2)) = esk91_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_888,
[final] ).
cnf(c_0_1662_1663,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk89_2(X1,X2)) = esk90_2(X1,X2)
| in(esk92_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_889,
[final] ).
cnf(c_0_1663_1664,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| ~ in(X3,esk102_0)
| esk103_1(X3) != X3 ),
c_0_890,
[final] ).
cnf(c_0_1664_1665,lemma,
( X3 = empty_set
| in(esk26_2(X2,X3),X3)
| ~ epred1_0
| ~ in(X1,esk24_0)
| esk25_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_891,
[final] ).
cnf(c_0_1665_1666,lemma,
( X3 = empty_set
| in(esk68_2(X2,X3),X3)
| ~ in(X1,esk66_0)
| esk67_1(X1) != X1
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ element(X3,powerset(powerset(X2))) ),
c_0_892,
[final] ).
cnf(c_0_1666_1667,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_893,
[final] ).
cnf(c_0_1667_1668,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_894,
[final] ).
cnf(c_0_1668_1669,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_895,
[final] ).
cnf(c_0_1669_1670,lemma,
( empty(X2)
| in(esk51_2(X2,X1),esk53_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_896,
[final] ).
cnf(c_0_1670_1671,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_897,
[final] ).
cnf(c_0_1671_1672,lemma,
( empty(X2)
| in(esk52_2(X2,X1),esk54_2(X2,X1))
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_898,
[final] ).
cnf(c_0_1672_1673,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_899,
[final] ).
cnf(c_0_1673_1674,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
c_0_900,
[final] ).
cnf(c_0_1674_1675,lemma,
( X2 = function_inverse(X1)
| in(esk89_2(X1,X2),relation_rng(X1))
| in(esk92_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_901,
[final] ).
cnf(c_0_1675_1676,lemma,
( element(esk24_0,powerset(powerset(empty_set)))
| X2 = empty_set
| in(esk26_2(X1,X2),X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_902,
[final] ).
cnf(c_0_1676_1677,lemma,
( element(esk66_0,powerset(powerset(esk64_0)))
| X2 = empty_set
| in(esk68_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_903,
[final] ).
cnf(c_0_1677_1678,plain,
( epred1_0
| ordinal(esk96_0)
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_904,
[final] ).
cnf(c_0_1678_1679,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_905,
[final] ).
cnf(c_0_1679_1680,lemma,
( X2 = X3
| ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ antisymmetric(X1) ),
c_0_906,
[final] ).
cnf(c_0_1680_1681,plain,
( epred1_0
| X2 = empty_set
| in(esk101_2(X1,X2),X2)
| esk98_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,esk100_0)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_907,
[final] ).
cnf(c_0_1681_1682,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
c_0_908,
[final] ).
cnf(c_0_1682_1683,lemma,
( in(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_909,
[final] ).
cnf(c_0_1683_1684,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X2,relation_dom(X1)) ),
c_0_910,
[final] ).
cnf(c_0_1684_1685,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_911,
[final] ).
cnf(c_0_1685_1686,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
c_0_912,
[final] ).
cnf(c_0_1686_1687,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_913,
[final] ).
cnf(c_0_1687_1688,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_914,
[final] ).
cnf(c_0_1688_1689,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_915,
[final] ).
cnf(c_0_1689_1690,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_field(relation_restriction(X1,X3))) ),
c_0_916,
[final] ).
cnf(c_0_1690_1691,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_917,
[final] ).
cnf(c_0_1691_1692,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
c_0_918,
[final] ).
cnf(c_0_1692_1693,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
c_0_919,
[final] ).
cnf(c_0_1693_1694,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| in(esk100_0,omega)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
c_0_920,
[final] ).
cnf(c_0_1694_1695,lemma,
( in(X2,relation_restriction(X1,X3))
| ~ relation(X1)
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
c_0_921,
[final] ).
cnf(c_0_1695_1696,lemma,
( in(empty_set,omega)
| X2 = empty_set
| in(esk26_2(X1,X2),X2)
| ~ epred1_0
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_922,
[final] ).
cnf(c_0_1696_1697,lemma,
( relation(esk27_3(X3,X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_923,
[final] ).
cnf(c_0_1697_1698,lemma,
( in(esk64_0,omega)
| X2 = empty_set
| in(esk68_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_924,
[final] ).
cnf(c_0_1698_1699,lemma,
( subset(X1,relation_inverse_image(X2,relation_image(X2,X1)))
| ~ subset(X1,relation_dom(X2))
| ~ relation(X2) ),
c_0_925,
[final] ).
cnf(c_0_1699_1700,lemma,
( epred2_2(X1,X2)
| ~ relation_isomorphism(X2,X1,X3)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_926,
[final] ).
cnf(c_0_1700_1701,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
c_0_927,
[final] ).
cnf(c_0_1701_1702,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1) ),
c_0_928,
[final] ).
cnf(c_0_1702_1703,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1) ),
c_0_929,
[final] ).
cnf(c_0_1703_1704,lemma,
( empty(X2)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1)
| esk52_2(X2,X1) != esk51_2(X2,X1) ),
c_0_930,
[final] ).
cnf(c_0_1704_1705,lemma,
( well_ordering(X1)
| ~ relation_isomorphism(X2,X1,X3)
| ~ well_ordering(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_931,
[final] ).
cnf(c_0_1705_1706,lemma,
( esk49_3(X3,X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
c_0_932,
[final] ).
cnf(c_0_1706_1707,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
c_0_933,
[final] ).
cnf(c_0_1707_1708,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| being_limit_ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1) ),
c_0_934,
[final] ).
cnf(c_0_1708_1709,lemma,
( subset(fiber(relation_restriction(X1,X2),X3),fiber(X1,X3))
| ~ relation(X1) ),
c_0_935,
[final] ).
cnf(c_0_1709_1710,lemma,
( ordinal(esk64_0)
| X2 = empty_set
| in(esk68_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_936,
[final] ).
cnf(c_0_1710_1711,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| esk100_0 != empty_set ),
c_0_937,
[final] ).
cnf(c_0_1711_1712,plain,
( epred1_0
| X1 = empty_set
| X2 = esk97_1(X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ subset(esk97_1(X1),X2)
| ~ in(X2,X1)
| esk102_0 != empty_set ),
c_0_938,
[final] ).
cnf(c_0_1712_1713,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_939,
[final] ).
cnf(c_0_1713_1714,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| subset(X2,esk103_1(X2))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ in(X2,esk102_0) ),
c_0_940,
[final] ).
cnf(c_0_1714_1715,lemma,
( X2 = empty_set
| in(esk26_2(X1,X2),X2)
| ~ epred1_0
| esk24_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_941,
[final] ).
cnf(c_0_1715_1716,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_942,
[final] ).
cnf(c_0_1716_1717,lemma,
( empty(X2)
| in(esk50_2(X2,X1),X2)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_943,
[final] ).
cnf(c_0_1717_1718,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| in(esk103_1(X2),esk102_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ in(X2,esk102_0) ),
c_0_944,
[final] ).
cnf(c_0_1718_1719,lemma,
( X2 = empty_set
| in(esk68_2(X1,X2),X2)
| esk66_0 != empty_set
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_945,
[final] ).
cnf(c_0_1719_1720,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_946,
[final] ).
cnf(c_0_1720_1721,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_947,
[final] ).
cnf(c_0_1721_1722,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_948,
[final] ).
cnf(c_0_1722_1723,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_949,
[final] ).
cnf(c_0_1723_1724,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_950,
[final] ).
cnf(c_0_1724_1725,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_951,
[final] ).
cnf(c_0_1725_1726,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_952,
[final] ).
cnf(c_0_1726_1727,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_953,
[final] ).
cnf(c_0_1727_1728,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
c_0_954,
[final] ).
cnf(c_0_1728_1729,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_955,
[final] ).
cnf(c_0_1729_1730,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_956,
[final] ).
cnf(c_0_1730_1731,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_957,
[final] ).
cnf(c_0_1731_1732,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_958,
[final] ).
cnf(c_0_1732_1733,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_959,
[final] ).
cnf(c_0_1733_1734,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk8_1(X1),esk9_1(X1)),X1) ),
c_0_960,
[final] ).
cnf(c_0_1734_1735,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk9_1(X1),esk8_1(X1)),X1) ),
c_0_961,
[final] ).
cnf(c_0_1735_1736,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk2_1(X1),esk4_1(X1)),X1) ),
c_0_962,
[final] ).
cnf(c_0_1736_1737,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk1_1(X1),esk1_1(X1)),X1) ),
c_0_963,
[final] ).
cnf(c_0_1737_1738,lemma,
( in(X2,esk48_2(X3,X1))
| ~ ordinal(X1)
| ~ in(X4,X3)
| X2 != X4
| ~ ordinal(X4)
| ~ in(X2,succ(X1)) ),
c_0_964,
[final] ).
cnf(c_0_1738_1739,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_965,
[final] ).
cnf(c_0_1739_1740,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk84_2(X2,X1)) != esk84_2(X2,X1) ),
c_0_966,
[final] ).
cnf(c_0_1740_1741,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_967,
[final] ).
cnf(c_0_1741_1742,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_968,
[final] ).
cnf(c_0_1742_1743,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_969,
[final] ).
cnf(c_0_1743_1744,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_970,
[final] ).
cnf(c_0_1744_1745,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation_dom(esk57_2(X2,X1)) = X2
| ~ relation(X1) ),
c_0_971,
[final] ).
cnf(c_0_1745_1746,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
c_0_972,
[final] ).
cnf(c_0_1746_1747,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
c_0_973,
[final] ).
cnf(c_0_1747_1748,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1)) ),
c_0_974,
[final] ).
cnf(c_0_1748_1749,lemma,
( in(X2,cartesian_product2(X3,X3))
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_975,
[final] ).
cnf(c_0_1749_1750,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_976,
[final] ).
cnf(c_0_1750_1751,lemma,
( empty(X2)
| esk53_2(X2,X1) = esk50_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_977,
[final] ).
cnf(c_0_1751_1752,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| relation(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_978,
[final] ).
cnf(c_0_1752_1753,lemma,
( empty(X2)
| esk50_2(X2,X1) = esk54_2(X2,X1)
| in(esk55_2(X2,X1),X2)
| function(esk57_2(X2,X1))
| ~ relation(X1) ),
c_0_979,
[final] ).
cnf(c_0_1753_1754,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_980,
[final] ).
cnf(c_0_1754_1755,lemma,
( empty(X2)
| in(esk12_2(X2,X1),esk14_2(X2,X1))
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_981,
[final] ).
cnf(c_0_1755_1756,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_982,
[final] ).
cnf(c_0_1756_1757,lemma,
( empty(X2)
| in(esk13_2(X2,X1),esk15_2(X2,X1))
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_983,
[final] ).
cnf(c_0_1757_1758,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_984,
[final] ).
cnf(c_0_1758_1759,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_985,
[final] ).
cnf(c_0_1759_1760,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_986,
[final] ).
cnf(c_0_1760_1761,lemma,
( in(esk19_1(X1),X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_987,
[final] ).
cnf(c_0_1761_1762,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
c_0_988,
[final] ).
cnf(c_0_1762_1763,lemma,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
c_0_989,
[final] ).
cnf(c_0_1763_1764,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_990,
[final] ).
cnf(c_0_1764_1765,lemma,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_991,
[final] ).
cnf(c_0_1765_1766,lemma,
( subset(relation_rng(X1),X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
c_0_992,
[final] ).
cnf(c_0_1766_1767,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_993,
[final] ).
cnf(c_0_1767_1768,lemma,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk33_2(X2,X3)) ),
c_0_994,
[final] ).
cnf(c_0_1768_1769,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_995,
[final] ).
cnf(c_0_1769_1770,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_996,
[final] ).
cnf(c_0_1770_1771,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_997,
[final] ).
cnf(c_0_1771_1772,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_998,
[final] ).
cnf(c_0_1772_1773,lemma,
( X2 = empty_set
| ordinal_subset(esk83_2(X2,X1),X3)
| ~ ordinal(X1)
| ~ subset(X2,X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
c_0_999,
[final] ).
cnf(c_0_1773_1774,lemma,
( in(X2,X1)
| esk21_1(X1) != esk20_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1000,
[final] ).
cnf(c_0_1774_1775,lemma,
( in(X2,X1)
| esk21_1(X1) != esk20_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1001,
[final] ).
cnf(c_0_1775_1776,lemma,
( X2 = empty_set
| in(esk74_2(X1,X2),X2)
| ~ finite(X1)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1002,
[final] ).
cnf(c_0_1776_1777,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| in(apply(esk81_1(X1),X2),X2)
| ~ in(X2,X1) ),
c_0_1003,
[final] ).
cnf(c_0_1777_1778,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1004,
[final] ).
cnf(c_0_1778_1779,lemma,
( in(esk19_1(X1),X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1005,
[final] ).
cnf(c_0_1779_1780,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1006,
[final] ).
cnf(c_0_1780_1781,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
c_0_1007,
[final] ).
cnf(c_0_1781_1782,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| in(esk100_0,omega)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
c_0_1008,
[final] ).
cnf(c_0_1782_1783,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1009,
[final] ).
cnf(c_0_1783_1784,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1010,
[final] ).
cnf(c_0_1784_1785,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1011,
[final] ).
cnf(c_0_1785_1786,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1012,
[final] ).
cnf(c_0_1786_1787,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| X3 = singleton(X2)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1013,
[final] ).
cnf(c_0_1787_1788,lemma,
( X3 = singleton(X2)
| esk21_1(X1) != esk20_1(X1)
| ~ in(ordered_pair(X2,X3),esk22_1(X1)) ),
c_0_1014,
[final] ).
cnf(c_0_1788_1789,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1015,
[final] ).
cnf(c_0_1789_1790,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1016,
[final] ).
cnf(c_0_1790_1791,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1017,
[final] ).
cnf(c_0_1791_1792,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1018,
[final] ).
cnf(c_0_1792_1793,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_1019,
[final] ).
cnf(c_0_1793_1794,lemma,
( in(X2,succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk48_2(X3,X1)) ),
c_0_1020,
[final] ).
cnf(c_0_1794_1795,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
c_0_1021,
[final] ).
cnf(c_0_1795_1796,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1022,
[final] ).
cnf(c_0_1796_1797,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_1023,
[final] ).
cnf(c_0_1797_1798,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_1024,
[final] ).
cnf(c_0_1798_1799,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_1025,
[final] ).
cnf(c_0_1799_1800,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_1026,
[final] ).
cnf(c_0_1800_1801,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_1027,
[final] ).
cnf(c_0_1801_1802,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_1028,
[final] ).
cnf(c_0_1802_1803,lemma,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ subset(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1029,
[final] ).
cnf(c_0_1803_1804,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
c_0_1030,
[final] ).
cnf(c_0_1804_1805,lemma,
( well_orders(esk5_2(X2,X1),X2)
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
c_0_1031,
[final] ).
cnf(c_0_1805_1806,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
c_0_1032,
[final] ).
cnf(c_0_1806_1807,lemma,
( empty(X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1) ),
c_0_1033,
[final] ).
cnf(c_0_1807_1808,lemma,
( empty(X2)
| function(esk16_2(X2,X1))
| ~ relation(X1)
| esk13_2(X2,X1) != esk12_2(X2,X1) ),
c_0_1034,
[final] ).
cnf(c_0_1808_1809,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_1035,
[final] ).
cnf(c_0_1809_1810,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_1036,
[final] ).
cnf(c_0_1810_1811,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_1037,
[final] ).
cnf(c_0_1811_1812,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_1038,
[final] ).
cnf(c_0_1812_1813,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
c_0_1039,
[final] ).
cnf(c_0_1813_1814,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| being_limit_ordinal(esk100_0)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0))) ),
c_0_1040,
[final] ).
cnf(c_0_1814_1815,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
c_0_1041,
[final] ).
cnf(c_0_1815_1816,lemma,
( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
c_0_1042,
[final] ).
cnf(c_0_1816_1817,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
c_0_1043,
[final] ).
cnf(c_0_1817_1818,lemma,
( in(esk59_1(X1),X1)
| apply(esk63_1(X1),X3) = singleton(X3)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
c_0_1044,
[final] ).
cnf(c_0_1818_1819,lemma,
( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(X2) ),
c_0_1045,
[final] ).
cnf(c_0_1819_1820,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| subset(X1,esk103_1(X1))
| ~ in(X1,esk102_0) ),
c_0_1046,
[final] ).
cnf(c_0_1820_1821,lemma,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_1047,
[final] ).
cnf(c_0_1821_1822,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| in(apply(esk81_1(X1),X2),X2)
| ~ in(X2,X1) ),
c_0_1048,
[final] ).
cnf(c_0_1822_1823,lemma,
( element(X1,powerset(X2))
| ~ in(esk10_2(X1,X2),X2) ),
c_0_1049,
[final] ).
cnf(c_0_1823_1824,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| esk100_0 != empty_set ),
c_0_1050,
[final] ).
cnf(c_0_1824_1825,plain,
( epred1_0
| X1 = empty_set
| in(esk97_1(X1),X1)
| ~ in(esk96_0,omega)
| ~ element(X1,powerset(powerset(esk96_0)))
| esk102_0 != empty_set ),
c_0_1051,
[final] ).
cnf(c_0_1825_1826,lemma,
( in(X2,esk36_1(X1))
| in(X3,omega)
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X3)
| X2 != X3 ),
c_0_1052,
[final] ).
cnf(c_0_1826_1827,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| in(esk103_1(X1),esk102_0)
| ~ in(X1,esk102_0) ),
c_0_1053,
[final] ).
cnf(c_0_1827_1828,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| subset(X2,esk103_1(X2))
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
c_0_1054,
[final] ).
cnf(c_0_1828_1829,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1055,
[final] ).
cnf(c_0_1829_1830,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1056,
[final] ).
cnf(c_0_1830_1831,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1057,
[final] ).
cnf(c_0_1831_1832,lemma,
( empty(X2)
| in(esk11_2(X2,X1),X2)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1058,
[final] ).
cnf(c_0_1832_1833,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_1059,
[final] ).
cnf(c_0_1833_1834,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_1060,
[final] ).
cnf(c_0_1834_1835,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| subset(X2,esk103_1(X2))
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
c_0_1061,
[final] ).
cnf(c_0_1835_1836,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| in(esk103_1(X2),esk102_0)
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
c_0_1062,
[final] ).
cnf(c_0_1836_1837,lemma,
( in(esk62_1(X1),X1)
| apply(esk63_1(X1),X2) = singleton(X2)
| esk61_1(X1) != esk60_1(X1)
| ~ in(X2,X1) ),
c_0_1063,
[final] ).
cnf(c_0_1837_1838,lemma,
( in(esk88_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_1064,
[final] ).
cnf(c_0_1838_1839,lemma,
( ordinal_subset(esk23_1(X2),X3)
| ~ in(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,X2)
| ~ ordinal(X3) ),
c_0_1065,
[final] ).
cnf(c_0_1839_1840,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| in(esk103_1(X2),esk102_0)
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0) ),
c_0_1066,
[final] ).
cnf(c_0_1840_1841,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
c_0_1067,
[final] ).
cnf(c_0_1841_1842,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
c_0_1068,
[final] ).
cnf(c_0_1842_1843,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| apply(esk63_1(X1),X3) = singleton(X3)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
c_0_1069,
[final] ).
cnf(c_0_1843_1844,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| apply(esk63_1(X1),X3) = singleton(X3)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
c_0_1070,
[final] ).
cnf(c_0_1844_1845,lemma,
( apply(esk63_1(X1),X3) = singleton(X3)
| esk61_1(X1) != esk60_1(X1)
| X2 != singleton(esk62_1(X1))
| ~ in(X3,X1) ),
c_0_1071,
[final] ).
cnf(c_0_1845_1846,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ subset(X2,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
c_0_1072,
[final] ).
cnf(c_0_1846_1847,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_1073,
[final] ).
cnf(c_0_1847_1848,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_1074,
[final] ).
cnf(c_0_1848_1849,lemma,
( relation(esk5_2(X2,X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ equipotent(X2,relation_field(X1)) ),
c_0_1075,
[final] ).
cnf(c_0_1849_1850,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_1076,
[final] ).
cnf(c_0_1850_1851,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk6_1(X1),esk7_1(X1)),X1)
| ~ relation(X1) ),
c_0_1077,
[final] ).
cnf(c_0_1851_1852,lemma,
( antisymmetric(X1)
| in(ordered_pair(esk7_1(X1),esk6_1(X1)),X1)
| ~ relation(X1) ),
c_0_1078,
[final] ).
cnf(c_0_1852_1853,lemma,
( transitive(X1)
| in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| ~ relation(X1) ),
c_0_1079,
[final] ).
cnf(c_0_1853_1854,lemma,
( transitive(X1)
| in(ordered_pair(esk3_1(X1),esk4_1(X1)),X1)
| ~ relation(X1) ),
c_0_1080,
[final] ).
cnf(c_0_1854_1855,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_1081,
[final] ).
cnf(c_0_1855_1856,lemma,
( in(X1,esk71_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk71_1(X2)) ),
c_0_1082,
[final] ).
cnf(c_0_1856_1857,lemma,
( X1 = empty_set
| in(ordered_pair(esk93_1(X1),esk94_1(X1)),X1)
| ~ relation(X1) ),
c_0_1083,
[final] ).
cnf(c_0_1857_1858,lemma,
( relation_image(X1,set_intersection2(relation_dom(X1),X2)) = relation_image(X1,X2)
| ~ relation(X1) ),
c_0_1084,
[final] ).
cnf(c_0_1858_1859,lemma,
( in(X1,esk71_1(X2))
| are_equipotent(X1,esk71_1(X2))
| ~ subset(X1,esk71_1(X2)) ),
c_0_1085,
[final] ).
cnf(c_0_1859_1860,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
c_0_1086,
[final] ).
cnf(c_0_1860_1861,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
c_0_1087,
[final] ).
cnf(c_0_1861_1862,lemma,
( X2 = empty_set
| in(esk83_2(X2,X1),X2)
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
c_0_1088,
[final] ).
cnf(c_0_1862_1863,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
c_0_1089,
[final] ).
cnf(c_0_1863_1864,plain,
( epred1_0
| subset(X2,esk103_1(X2))
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ in(X2,esk102_0) ),
c_0_1090,
[final] ).
cnf(c_0_1864_1865,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1091,
[final] ).
cnf(c_0_1865_1866,lemma,
( empty(X2)
| esk14_2(X2,X1) = esk11_2(X2,X1)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1092,
[final] ).
cnf(c_0_1866_1867,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| relation(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1093,
[final] ).
cnf(c_0_1867_1868,lemma,
( empty(X2)
| esk11_2(X2,X1) = esk15_2(X2,X1)
| function(esk16_2(X2,X1))
| ~ relation(X1) ),
c_0_1094,
[final] ).
cnf(c_0_1868_1869,lemma,
( ordinal(esk37_2(X1,X2))
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1)) ),
c_0_1095,
[final] ).
cnf(c_0_1869_1870,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
c_0_1096,
[final] ).
cnf(c_0_1870_1871,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| element(esk102_0,powerset(powerset(esk100_0))) ),
c_0_1097,
[final] ).
cnf(c_0_1871_1872,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ~ in(X1,esk98_0)
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
c_0_1098,
[final] ).
cnf(c_0_1872_1873,plain,
( epred1_0
| in(esk103_1(X2),esk102_0)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ in(X2,esk102_0) ),
c_0_1099,
[final] ).
cnf(c_0_1873_1874,lemma,
( X1 = identity_relation(X2)
| in(esk84_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
c_0_1100,
[final] ).
cnf(c_0_1874_1875,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_1101,
[final] ).
cnf(c_0_1875_1876,lemma,
( ~ in(X1,X2)
| ~ in(X3,X1)
| ~ in(X2,X3) ),
c_0_1102,
[final] ).
cnf(c_0_1876_1877,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X1,esk98_0) ),
c_0_1103,
[final] ).
cnf(c_0_1877_1878,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X1,esk98_0) ),
c_0_1104,
[final] ).
cnf(c_0_1878_1879,lemma,
( in(succ(X2),X1)
| ~ ordinal(X1)
| ~ in(X2,X1)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X1) ),
c_0_1105,
[final] ).
cnf(c_0_1879_1880,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_1106,
[final] ).
cnf(c_0_1880_1881,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_1107,
[final] ).
cnf(c_0_1881_1882,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_1108,
[final] ).
cnf(c_0_1882_1883,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_1109,
[final] ).
cnf(c_0_1883_1884,lemma,
( X2 = empty_set
| relation_inverse_image(X1,X2) != empty_set
| ~ subset(X2,relation_rng(X1))
| ~ relation(X1) ),
c_0_1110,
[final] ).
cnf(c_0_1884_1885,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(succ(esk86_1(X1)),X1) ),
c_0_1111,
[final] ).
cnf(c_0_1885_1886,lemma,
( X2 = empty_set
| ordinal(esk83_2(X2,X1))
| ~ ordinal(X1)
| ~ subset(X2,X1) ),
c_0_1112,
[final] ).
cnf(c_0_1886_1887,lemma,
( relation_rng_restriction(X2,relation_dom_restriction(X1,X2)) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_1113,
[final] ).
cnf(c_0_1887_1888,lemma,
( relation_dom_restriction(relation_rng_restriction(X2,X1),X2) = relation_restriction(X1,X2)
| ~ relation(X1) ),
c_0_1114,
[final] ).
cnf(c_0_1888_1889,lemma,
( in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(succ(X1),X2) ),
c_0_1115,
[final] ).
cnf(c_0_1889_1890,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1116,
[final] ).
cnf(c_0_1890_1891,lemma,
( element(X1,powerset(X2))
| in(esk10_2(X1,X2),X1) ),
c_0_1117,
[final] ).
cnf(c_0_1891_1892,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
c_0_1118,
[final] ).
cnf(c_0_1892_1893,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
c_0_1119,
[final] ).
cnf(c_0_1893_1894,lemma,
( in(X2,succ(X1))
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1)) ),
c_0_1120,
[final] ).
cnf(c_0_1894_1895,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_1121,
[final] ).
cnf(c_0_1895_1896,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_1122,
[final] ).
cnf(c_0_1896_1897,lemma,
( in(powerset(X1),esk71_1(X2))
| ~ in(X1,esk71_1(X2)) ),
c_0_1123,
[final] ).
cnf(c_0_1897_1898,plain,
( epred1_0
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| ~ in(X2,esk102_0)
| esk103_1(X2) != X2 ),
c_0_1124,
[final] ).
cnf(c_0_1898_1899,plain,
( epred1_0
| in(succ(esk96_0),omega)
| subset(X1,esk103_1(X1))
| ~ in(X1,esk102_0) ),
c_0_1125,
[final] ).
cnf(c_0_1899_1900,lemma,
( ordinal_subset(succ(X1),X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X2) ),
c_0_1126,
[final] ).
cnf(c_0_1900_1901,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
c_0_1127,
[final] ).
cnf(c_0_1901_1902,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
c_0_1128,
[final] ).
cnf(c_0_1902_1903,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_1129,
[final] ).
cnf(c_0_1903_1904,plain,
( epred1_0
| in(succ(esk96_0),omega)
| in(esk103_1(X1),esk102_0)
| ~ in(X1,esk102_0) ),
c_0_1130,
[final] ).
cnf(c_0_1904_1905,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| in(esk100_0,omega) ),
c_0_1131,
[final] ).
cnf(c_0_1905_1906,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_1132,
[final] ).
cnf(c_0_1906_1907,lemma,
( disjoint(X1,X2)
| in(esk85_2(X1,X2),X1) ),
c_0_1133,
[final] ).
cnf(c_0_1907_1908,lemma,
( disjoint(X1,X2)
| in(esk85_2(X1,X2),X2) ),
c_0_1134,
[final] ).
cnf(c_0_1908_1909,lemma,
( esk37_2(X1,X2) = X2
| ~ ordinal(X1)
| ~ in(X2,esk36_1(X1)) ),
c_0_1135,
[final] ).
cnf(c_0_1909_1910,plain,
( epred1_0
| element(esk102_0,powerset(powerset(esk100_0)))
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
c_0_1136,
[final] ).
cnf(c_0_1910_1911,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_1137,
[final] ).
cnf(c_0_1911_1912,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_1138,
[final] ).
cnf(c_0_1912_1913,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_1139,
[final] ).
cnf(c_0_1913_1914,lemma,
( ordinal(X1)
| ~ subset(esk82_1(X1),X1)
| ~ ordinal(esk82_1(X1)) ),
c_0_1140,
[final] ).
cnf(c_0_1914_1915,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
c_0_1141,
[final] ).
cnf(c_0_1915_1916,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
c_0_1142,
[final] ).
cnf(c_0_1916_1917,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| in(esk100_0,omega)
| ~ in(X1,esk98_0) ),
c_0_1143,
[final] ).
cnf(c_0_1917_1918,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_1144,
[final] ).
cnf(c_0_1918_1919,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1 ),
c_0_1145,
[final] ).
cnf(c_0_1919_1920,lemma,
( finite(relation_image(X1,X2))
| ~ finite(X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1146,
[final] ).
cnf(c_0_1920_1921,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| relation(esk63_1(X1)) ),
c_0_1147,
[final] ).
cnf(c_0_1921_1922,lemma,
( in(esk59_1(X1),X1)
| in(esk62_1(X1),X1)
| function(esk63_1(X1)) ),
c_0_1148,
[final] ).
cnf(c_0_1922_1923,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| in(esk100_0,omega)
| ~ in(X1,esk98_0) ),
c_0_1149,
[final] ).
cnf(c_0_1923_1924,lemma,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
c_0_1150,
[final] ).
cnf(c_0_1924_1925,lemma,
( in(X1,esk46_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
c_0_1151,
[final] ).
cnf(c_0_1925_1926,lemma,
( in(esk23_1(X2),X2)
| ~ in(X1,X2)
| ~ ordinal(X1) ),
c_0_1152,
[final] ).
cnf(c_0_1926_1927,lemma,
( in(esk59_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1
| X2 != singleton(esk62_1(X1)) ),
c_0_1153,
[final] ).
cnf(c_0_1927_1928,lemma,
( in(esk59_1(X1),X1)
| relation(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
c_0_1154,
[final] ).
cnf(c_0_1928_1929,lemma,
( in(esk59_1(X1),X1)
| function(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
c_0_1155,
[final] ).
cnf(c_0_1929_1930,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_1156,
[final] ).
cnf(c_0_1930_1931,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
c_0_1157,
[final] ).
cnf(c_0_1931_1932,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
c_0_1158,
[final] ).
cnf(c_0_1932_1933,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| ordinal(esk100_0) ),
c_0_1159,
[final] ).
cnf(c_0_1933_1934,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| being_limit_ordinal(esk100_0) ),
c_0_1160,
[final] ).
cnf(c_0_1934_1935,lemma,
( apply(esk69_1(X1),X2) = singleton(X2)
| ~ in(X2,X1) ),
c_0_1161,
[final] ).
cnf(c_0_1935_1936,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_1162,
[final] ).
cnf(c_0_1936_1937,lemma,
( in(X1,X2)
| ~ in(X1,esk46_1(X2)) ),
c_0_1163,
[final] ).
cnf(c_0_1937_1938,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_1164,
[final] ).
cnf(c_0_1938_1939,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_1165,
[final] ).
cnf(c_0_1939_1940,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_1166,
[final] ).
cnf(c_0_1940_1941,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1 ),
c_0_1167,
[final] ).
cnf(c_0_1941_1942,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1 ),
c_0_1168,
[final] ).
cnf(c_0_1942_1943,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| in(esk62_1(X1),X1)
| relation(esk63_1(X1)) ),
c_0_1169,
[final] ).
cnf(c_0_1943_1944,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| in(esk62_1(X1),X1)
| function(esk63_1(X1)) ),
c_0_1170,
[final] ).
cnf(c_0_1944_1945,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| in(esk62_1(X1),X1)
| relation(esk63_1(X1)) ),
c_0_1171,
[final] ).
cnf(c_0_1945_1946,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| in(esk62_1(X1),X1)
| function(esk63_1(X1)) ),
c_0_1172,
[final] ).
cnf(c_0_1946_1947,lemma,
( in(X1,X2)
| X2 = X1
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
c_0_1173,
[final] ).
cnf(c_0_1947_1948,plain,
( epred1_0
| in(succ(esk96_0),omega)
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
c_0_1174,
[final] ).
cnf(c_0_1948_1949,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_1175,
[final] ).
cnf(c_0_1949_1950,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| esk100_0 != empty_set ),
c_0_1176,
[final] ).
cnf(c_0_1950_1951,plain,
( epred1_0
| element(esk98_0,powerset(powerset(succ(esk96_0))))
| esk102_0 != empty_set ),
c_0_1177,
[final] ).
cnf(c_0_1951_1952,lemma,
( in(esk62_1(X1),X1)
| relation_dom(esk63_1(X1)) = X1
| esk61_1(X1) != esk60_1(X1) ),
c_0_1178,
[final] ).
cnf(c_0_1952_1953,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ well_ordering(X1)
| ~ relation(X1) ),
c_0_1179,
[final] ).
cnf(c_0_1953_1954,lemma,
( well_founded_relation(relation_restriction(X1,X2))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
c_0_1180,
[final] ).
cnf(c_0_1954_1955,lemma,
( antisymmetric(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
c_0_1181,
[final] ).
cnf(c_0_1955_1956,lemma,
( transitive(relation_restriction(X1,X2))
| ~ transitive(X1)
| ~ relation(X1) ),
c_0_1182,
[final] ).
cnf(c_0_1956_1957,lemma,
( connected(relation_restriction(X1,X2))
| ~ connected(X1)
| ~ relation(X1) ),
c_0_1183,
[final] ).
cnf(c_0_1957_1958,lemma,
( reflexive(relation_restriction(X1,X2))
| ~ reflexive(X1)
| ~ relation(X1) ),
c_0_1184,
[final] ).
cnf(c_0_1958_1959,plain,
( epred1_0
| ordinal(esk96_0)
| subset(X1,esk103_1(X1))
| ~ in(X1,esk102_0) ),
c_0_1185,
[final] ).
cnf(c_0_1959_1960,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
c_0_1186,
[final] ).
cnf(c_0_1960_1961,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| being_limit_ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
c_0_1187,
[final] ).
cnf(c_0_1961_1962,lemma,
( in(esk62_1(X1),X1)
| relation(esk63_1(X1))
| esk61_1(X1) != esk60_1(X1) ),
c_0_1188,
[final] ).
cnf(c_0_1962_1963,lemma,
( in(esk62_1(X1),X1)
| function(esk63_1(X1))
| esk61_1(X1) != esk60_1(X1) ),
c_0_1189,
[final] ).
cnf(c_0_1963_1964,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_1190,
[final] ).
cnf(c_0_1964_1965,lemma,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_orders(X1,relation_field(X1)) ),
c_0_1191,
[final] ).
cnf(c_0_1965_1966,lemma,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
c_0_1192,
[final] ).
cnf(c_0_1966_1967,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_1193,
[final] ).
cnf(c_0_1967_1968,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
c_0_1194,
[final] ).
cnf(c_0_1968_1969,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_1195,
[final] ).
cnf(c_0_1969_1970,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| relation_dom(esk63_1(X1)) = X1
| X2 != singleton(esk62_1(X1)) ),
c_0_1196,
[final] ).
cnf(c_0_1970_1971,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| relation_dom(esk63_1(X1)) = X1
| X2 != singleton(esk62_1(X1)) ),
c_0_1197,
[final] ).
cnf(c_0_1971_1972,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_1198,
[final] ).
cnf(c_0_1972_1973,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_1199,
[final] ).
cnf(c_0_1973_1974,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_1200,
[final] ).
cnf(c_0_1974_1975,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_1201,
[final] ).
cnf(c_0_1975_1976,plain,
( epred1_0
| ordinal(esk96_0)
| in(esk103_1(X1),esk102_0)
| ~ in(X1,esk102_0) ),
c_0_1202,
[final] ).
cnf(c_0_1976_1977,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
c_0_1203,
[final] ).
cnf(c_0_1977_1978,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| being_limit_ordinal(esk100_0)
| ~ in(X1,esk98_0) ),
c_0_1204,
[final] ).
cnf(c_0_1978_1979,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| relation(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
c_0_1205,
[final] ).
cnf(c_0_1979_1980,lemma,
( singleton(esk59_1(X1)) = esk60_1(X1)
| function(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
c_0_1206,
[final] ).
cnf(c_0_1980_1981,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| relation(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
c_0_1207,
[final] ).
cnf(c_0_1981_1982,lemma,
( singleton(esk59_1(X1)) = esk61_1(X1)
| function(esk63_1(X1))
| X2 != singleton(esk62_1(X1)) ),
c_0_1208,
[final] ).
cnf(c_0_1982_1983,plain,
( epred1_0
| subset(X1,esk103_1(X1))
| esk98_0 != empty_set
| ~ in(X1,esk102_0) ),
c_0_1209,
[final] ).
cnf(c_0_1983_1984,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ~ in(X1,esk98_0)
| esk100_0 != empty_set ),
c_0_1210,
[final] ).
cnf(c_0_1984_1985,plain,
( epred1_0
| subset(X1,esk99_1(X1))
| ~ in(X1,esk98_0)
| esk102_0 != empty_set ),
c_0_1211,
[final] ).
cnf(c_0_1985_1986,lemma,
( relation_dom(esk63_1(X1)) = X1
| esk61_1(X1) != esk60_1(X1)
| X2 != singleton(esk62_1(X1)) ),
c_0_1212,
[final] ).
cnf(c_0_1986_1987,plain,
( epred1_0
| in(succ(esk96_0),omega)
| element(esk102_0,powerset(powerset(esk100_0))) ),
c_0_1213,
[final] ).
cnf(c_0_1987_1988,lemma,
( finite(relation_rng(X1))
| ~ finite(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_1214,
[final] ).
cnf(c_0_1988_1989,lemma,
( relation(esk63_1(X1))
| esk61_1(X1) != esk60_1(X1)
| X2 != singleton(esk62_1(X1)) ),
c_0_1215,
[final] ).
cnf(c_0_1989_1990,lemma,
( function(esk63_1(X1))
| esk61_1(X1) != esk60_1(X1)
| X2 != singleton(esk62_1(X1)) ),
c_0_1216,
[final] ).
cnf(c_0_1990_1991,lemma,
( relation_composition(identity_relation(X2),X1) = relation_dom_restriction(X1,X2)
| ~ relation(X1) ),
c_0_1217,
[final] ).
cnf(c_0_1991_1992,plain,
( epred1_0
| in(esk103_1(X1),esk102_0)
| esk98_0 != empty_set
| ~ in(X1,esk102_0) ),
c_0_1218,
[final] ).
cnf(c_0_1992_1993,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ~ in(X1,esk98_0)
| esk100_0 != empty_set ),
c_0_1219,
[final] ).
cnf(c_0_1993_1994,plain,
( epred1_0
| in(esk99_1(X1),esk98_0)
| ~ in(X1,esk98_0)
| esk102_0 != empty_set ),
c_0_1220,
[final] ).
cnf(c_0_1994_1995,plain,
( epred1_0
| in(esk100_0,omega)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
c_0_1221,
[final] ).
cnf(c_0_1995_1996,lemma,
( ordinal(esk23_1(X2))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
c_0_1222,
[final] ).
cnf(c_0_1996_1997,lemma,
subset(X1,set_union2(X1,X2)),
c_0_1223,
[final] ).
cnf(c_0_1997_1998,lemma,
subset(set_difference(X1,X2),X1),
c_0_1224,
[final] ).
cnf(c_0_1998_1999,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_1225,
[final] ).
cnf(c_0_1999_2000,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_1226,
[final] ).
cnf(c_0_2000_2001,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_1227,
[final] ).
cnf(c_0_2001_2002,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_1228,
[final] ).
cnf(c_0_2002_2003,lemma,
( connected(X1)
| in(esk8_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1229,
[final] ).
cnf(c_0_2003_2004,lemma,
( connected(X1)
| in(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1230,
[final] ).
cnf(c_0_2004_2005,lemma,
( reflexive(X1)
| in(esk1_1(X1),relation_field(X1))
| ~ relation(X1) ),
c_0_1231,
[final] ).
cnf(c_0_2005_2006,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_1232,
[final] ).
cnf(c_0_2006_2007,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_1233,
[final] ).
cnf(c_0_2007_2008,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_1234,
[final] ).
cnf(c_0_2008_2009,lemma,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
c_0_1235,
[final] ).
cnf(c_0_2009_2010,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_1236,
[final] ).
cnf(c_0_2010_2011,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_1237,
[final] ).
cnf(c_0_2011_2012,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_1238,
[final] ).
cnf(c_0_2012_2013,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_1239,
[final] ).
cnf(c_0_2013_2014,lemma,
( ordinal(X1)
| ~ in(X1,esk46_1(X2)) ),
c_0_1240,
[final] ).
cnf(c_0_2014_2015,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| relation_dom(esk81_1(X1)) = X1 ),
c_0_1241,
[final] ).
cnf(c_0_2015_2016,lemma,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_1242,
[final] ).
cnf(c_0_2016_2017,lemma,
( relation_rng(function_inverse(X1)) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_1243,
[final] ).
cnf(c_0_2017_2018,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_1244,
[final] ).
cnf(c_0_2018_2019,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| relation(esk81_1(X1)) ),
c_0_1245,
[final] ).
cnf(c_0_2019_2020,lemma,
( empty(X1)
| in(esk80_1(X1),X1)
| function(esk81_1(X1)) ),
c_0_1246,
[final] ).
cnf(c_0_2020_2021,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_1247,
[final] ).
cnf(c_0_2021_2022,lemma,
( well_orders(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1) ),
c_0_1248,
[final] ).
cnf(c_0_2022_2023,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
c_0_1249,
[final] ).
cnf(c_0_2023_2024,plain,
( reflexive(X1)
| ~ epred2_2(X1,X2)
| ~ reflexive(X2) ),
c_0_1250,
[final] ).
cnf(c_0_2024_2025,plain,
( transitive(X1)
| ~ epred2_2(X1,X2)
| ~ transitive(X2) ),
c_0_1251,
[final] ).
cnf(c_0_2025_2026,plain,
( connected(X1)
| ~ epred2_2(X1,X2)
| ~ connected(X2) ),
c_0_1252,
[final] ).
cnf(c_0_2026_2027,plain,
( antisymmetric(X1)
| ~ epred2_2(X1,X2)
| ~ antisymmetric(X2) ),
c_0_1253,
[final] ).
cnf(c_0_2027_2028,plain,
( well_founded_relation(X1)
| ~ epred2_2(X1,X2)
| ~ well_founded_relation(X2) ),
c_0_1254,
[final] ).
cnf(c_0_2028_2029,lemma,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
c_0_1255,
[final] ).
cnf(c_0_2029_2030,lemma,
( finite(X1)
| ~ finite(X2)
| ~ subset(X1,X2) ),
c_0_1256,
[final] ).
cnf(c_0_2030_2031,plain,
( epred1_0
| ordinal(esk96_0)
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
c_0_1257,
[final] ).
cnf(c_0_2031_2032,plain,
( epred1_0
| ordinal(esk100_0)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
c_0_1258,
[final] ).
cnf(c_0_2032_2033,plain,
( epred1_0
| being_limit_ordinal(esk100_0)
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1 ),
c_0_1259,
[final] ).
cnf(c_0_2033_2034,lemma,
( being_limit_ordinal(X1)
| in(esk86_1(X1),X1)
| ~ ordinal(X1) ),
c_0_1260,
[final] ).
cnf(c_0_2034_2035,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_1261,
[final] ).
cnf(c_0_2035_2036,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_1262,
[final] ).
cnf(c_0_2036_2037,lemma,
pair_first(ordered_pair(X1,X2)) = X1,
c_0_1263,
[final] ).
cnf(c_0_2037_2038,lemma,
pair_second(ordered_pair(X1,X2)) = X2,
c_0_1264,
[final] ).
cnf(c_0_2038_2039,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
c_0_1265,
[final] ).
cnf(c_0_2039_2040,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
c_0_1266,
[final] ).
cnf(c_0_2040_2041,lemma,
( in(esk19_1(X1),X1)
| relation(esk22_1(X1)) ),
c_0_1267,
[final] ).
cnf(c_0_2041_2042,lemma,
( in(esk19_1(X1),X1)
| function(esk22_1(X1)) ),
c_0_1268,
[final] ).
cnf(c_0_2042_2043,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_1269,
[final] ).
cnf(c_0_2043_2044,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_1270,
[final] ).
cnf(c_0_2044_2045,plain,
( epred1_0
| esk98_0 != empty_set
| ~ in(X1,esk102_0)
| esk103_1(X1) != X1 ),
c_0_1271,
[final] ).
cnf(c_0_2045_2046,plain,
( epred1_0
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| esk100_0 != empty_set ),
c_0_1272,
[final] ).
cnf(c_0_2046_2047,plain,
( epred1_0
| ~ in(X1,esk98_0)
| esk99_1(X1) != X1
| esk102_0 != empty_set ),
c_0_1273,
[final] ).
cnf(c_0_2047_2048,lemma,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| X1 != succ(X2)
| ~ ordinal(X2) ),
c_0_1274,
[final] ).
cnf(c_0_2048_2049,plain,
( epred1_0
| ordinal(esk96_0)
| element(esk102_0,powerset(powerset(esk100_0))) ),
c_0_1275,
[final] ).
cnf(c_0_2049_2050,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_1276,
[final] ).
cnf(c_0_2050_2051,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_1277,
[final] ).
cnf(c_0_2051_2052,plain,
( epred1_0
| in(succ(esk96_0),omega)
| in(esk100_0,omega) ),
c_0_1278,
[final] ).
cnf(c_0_2052_2053,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
c_0_1279,
[final] ).
cnf(c_0_2053_2054,plain,
( epred1_0
| element(esk102_0,powerset(powerset(esk100_0)))
| esk98_0 != empty_set ),
c_0_1280,
[final] ).
cnf(c_0_2054_2055,lemma,
( ordinal(X1)
| in(esk82_1(X1),X1) ),
c_0_1281,
[final] ).
cnf(c_0_2055_2056,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| relation(esk22_1(X1)) ),
c_0_1282,
[final] ).
cnf(c_0_2056_2057,lemma,
( singleton(esk19_1(X1)) = esk20_1(X1)
| function(esk22_1(X1)) ),
c_0_1283,
[final] ).
cnf(c_0_2057_2058,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| relation(esk22_1(X1)) ),
c_0_1284,
[final] ).
cnf(c_0_2058_2059,lemma,
( singleton(esk19_1(X1)) = esk21_1(X1)
| function(esk22_1(X1)) ),
c_0_1285,
[final] ).
cnf(c_0_2059_2060,lemma,
( connected(X1)
| ~ relation(X1)
| esk8_1(X1) != esk9_1(X1) ),
c_0_1286,
[final] ).
cnf(c_0_2060_2061,lemma,
( antisymmetric(X1)
| ~ relation(X1)
| esk7_1(X1) != esk6_1(X1) ),
c_0_1287,
[final] ).
cnf(c_0_2061_2062,lemma,
( relation(esk22_1(X1))
| esk21_1(X1) != esk20_1(X1) ),
c_0_1288,
[final] ).
cnf(c_0_2062_2063,lemma,
( function(esk22_1(X1))
| esk21_1(X1) != esk20_1(X1) ),
c_0_1289,
[final] ).
cnf(c_0_2063_2064,lemma,
( being_limit_ordinal(X1)
| succ(esk87_1(X1)) = X1
| ~ ordinal(X1) ),
c_0_1290,
[final] ).
cnf(c_0_2064_2065,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_1291,
[final] ).
cnf(c_0_2065_2066,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_1292,
[final] ).
cnf(c_0_2066_2067,lemma,
( being_limit_ordinal(X1)
| ordinal(esk87_1(X1))
| ~ ordinal(X1) ),
c_0_1293,
[final] ).
cnf(c_0_2067_2068,lemma,
( being_limit_ordinal(X1)
| ordinal(esk86_1(X1))
| ~ ordinal(X1) ),
c_0_1294,
[final] ).
cnf(c_0_2068_2069,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_1295,
[final] ).
cnf(c_0_2069_2070,lemma,
( relation_dom(relation_inverse(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_1296,
[final] ).
cnf(c_0_2070_2071,lemma,
( relation_rng(relation_inverse(X1)) = relation_dom(X1)
| ~ relation(X1) ),
c_0_1297,
[final] ).
cnf(c_0_2071_2072,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| relation_dom(esk81_1(X1)) = X1 ),
c_0_1298,
[final] ).
cnf(c_0_2072_2073,lemma,
well_orders(esk79_1(X1),X1),
c_0_1299,
[final] ).
cnf(c_0_2073_2074,lemma,
in(X1,esk71_1(X1)),
c_0_1300,
[final] ).
cnf(c_0_2074_2075,lemma,
in(X1,succ(X1)),
c_0_1301,
[final] ).
cnf(c_0_2075_2076,plain,
( epred1_0
| in(succ(esk96_0),omega)
| ordinal(esk100_0) ),
c_0_1302,
[final] ).
cnf(c_0_2076_2077,plain,
( epred1_0
| in(succ(esk96_0),omega)
| being_limit_ordinal(esk100_0) ),
c_0_1303,
[final] ).
cnf(c_0_2077_2078,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| relation(esk81_1(X1)) ),
c_0_1304,
[final] ).
cnf(c_0_2078_2079,lemma,
( empty(X1)
| esk80_1(X1) = empty_set
| function(esk81_1(X1)) ),
c_0_1305,
[final] ).
cnf(c_0_2079_2080,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_1306,
[final] ).
cnf(c_0_2080_2081,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_1307,
[final] ).
cnf(c_0_2081_2082,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_1308,
[final] ).
cnf(c_0_2082_2083,plain,
( epred1_0
| in(succ(esk96_0),omega)
| esk100_0 != empty_set ),
c_0_1309,
[final] ).
cnf(c_0_2083_2084,plain,
( epred1_0
| in(succ(esk96_0),omega)
| esk102_0 != empty_set ),
c_0_1310,
[final] ).
cnf(c_0_2084_2085,lemma,
( well_ordering(inclusion_relation(X1))
| ~ ordinal(X1) ),
c_0_1311,
[final] ).
cnf(c_0_2085_2086,lemma,
( well_founded_relation(inclusion_relation(X1))
| ~ ordinal(X1) ),
c_0_1312,
[final] ).
cnf(c_0_2086_2087,lemma,
( connected(inclusion_relation(X1))
| ~ ordinal(X1) ),
c_0_1313,
[final] ).
cnf(c_0_2087_2088,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_1314,
[final] ).
cnf(c_0_2088_2089,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_1315,
[final] ).
cnf(c_0_2089_2090,plain,
( epred1_0
| ordinal(esk96_0)
| in(esk100_0,omega) ),
c_0_1316,
[final] ).
cnf(c_0_2090_2091,plain,
( epred1_0
| in(esk100_0,omega)
| esk98_0 != empty_set ),
c_0_1317,
[final] ).
cnf(c_0_2091_2092,lemma,
subset(empty_set,X1),
c_0_1318,
[final] ).
cnf(c_0_2092_2093,lemma,
union(powerset(X1)) = X1,
c_0_1319,
[final] ).
cnf(c_0_2093_2094,lemma,
relation_dom(identity_relation(X1)) = X1,
c_0_1320,
[final] ).
cnf(c_0_2094_2095,lemma,
relation_rng(identity_relation(X1)) = X1,
c_0_1321,
[final] ).
cnf(c_0_2095_2096,lemma,
relation_dom(esk69_1(X1)) = X1,
c_0_1322,
[final] ).
cnf(c_0_2096_2097,lemma,
antisymmetric(inclusion_relation(X1)),
c_0_1323,
[final] ).
cnf(c_0_2097_2098,lemma,
transitive(inclusion_relation(X1)),
c_0_1324,
[final] ).
cnf(c_0_2098_2099,lemma,
reflexive(inclusion_relation(X1)),
c_0_1325,
[final] ).
cnf(c_0_2099_2100,lemma,
relation(esk79_1(X1)),
c_0_1326,
[final] ).
cnf(c_0_2100_2101,lemma,
relation(esk69_1(X1)),
c_0_1327,
[final] ).
cnf(c_0_2101_2102,lemma,
function(esk69_1(X1)),
c_0_1328,
[final] ).
cnf(c_0_2102_2103,negated_conjecture,
the_carrier(esk70_0) != cast_as_carrier_subset(esk70_0),
c_0_1329,
[final] ).
cnf(c_0_2103_2104,lemma,
singleton(X1) != empty_set,
c_0_1330,
[final] ).
cnf(c_0_2104_2105,plain,
( epred1_0
| ordinal(esk96_0)
| ordinal(esk100_0) ),
c_0_1331,
[final] ).
cnf(c_0_2105_2106,plain,
( epred1_0
| ordinal(esk96_0)
| being_limit_ordinal(esk100_0) ),
c_0_1332,
[final] ).
cnf(c_0_2106_2107,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_1333,
[final] ).
cnf(c_0_2107_2108,plain,
( epred1_0
| ordinal(esk96_0)
| esk100_0 != empty_set ),
c_0_1334,
[final] ).
cnf(c_0_2108_2109,plain,
( epred1_0
| ordinal(esk96_0)
| esk102_0 != empty_set ),
c_0_1335,
[final] ).
cnf(c_0_2109_2110,plain,
( epred1_0
| ordinal(esk100_0)
| esk98_0 != empty_set ),
c_0_1336,
[final] ).
cnf(c_0_2110_2111,plain,
( epred1_0
| being_limit_ordinal(esk100_0)
| esk98_0 != empty_set ),
c_0_1337,
[final] ).
cnf(c_0_2111_2112,plain,
( epred1_0
| esk98_0 != empty_set
| esk100_0 != empty_set ),
c_0_1338,
[final] ).
cnf(c_0_2112_2113,plain,
( epred1_0
| esk98_0 != empty_set
| esk102_0 != empty_set ),
c_0_1339,
[final] ).
cnf(c_0_2113_2114,lemma,
relation_dom(empty_set) = empty_set,
c_0_1340,
[final] ).
cnf(c_0_2114_2115,lemma,
relation_rng(empty_set) = empty_set,
c_0_1341,
[final] ).
cnf(c_0_2115_2116,negated_conjecture,
one_sorted_str(esk70_0),
c_0_1342,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_5247,negated_conjecture,
one_sorted_str(sk2_esk70_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p',c_0_2115) ).
cnf(c_8546,negated_conjecture,
one_sorted_str(sk2_esk70_0),
inference(copy,[status(esa)],[c_5247]) ).
cnf(c_9173,negated_conjecture,
one_sorted_str(sk2_esk70_0),
inference(copy,[status(esa)],[c_8546]) ).
cnf(c_9436,negated_conjecture,
one_sorted_str(sk2_esk70_0),
inference(copy,[status(esa)],[c_9173]) ).
cnf(c_14999,negated_conjecture,
one_sorted_str(sk2_esk70_0),
inference(copy,[status(esa)],[c_9436]) ).
cnf(c_29983,negated_conjecture,
one_sorted_str(sk2_esk70_0),
inference(copy,[status(esa)],[c_14999]) ).
cnf(c_236,plain,
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p',c_0_2931_1) ).
cnf(c_20461,plain,
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(copy,[status(esa)],[c_236]) ).
cnf(c_20462,plain,
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(rewriting,[status(thm)],[c_20461]) ).
cnf(c_29990,plain,
cast_as_carrier_subset(sk2_esk70_0) = the_carrier(sk2_esk70_0),
inference(resolution,[status(thm)],[c_29983,c_20462]) ).
cnf(c_29991,plain,
cast_as_carrier_subset(sk2_esk70_0) = the_carrier(sk2_esk70_0),
inference(rewriting,[status(thm)],[c_29990]) ).
cnf(c_281,plain,
( subset(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p',c_0_2904_1) ).
cnf(c_20551,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(copy,[status(esa)],[c_281]) ).
cnf(c_30008,plain,
subset(cast_as_carrier_subset(sk2_esk70_0),the_carrier(sk2_esk70_0)),
inference(resolution,[status(thm)],[c_29991,c_20551]) ).
cnf(c_30009,plain,
subset(cast_as_carrier_subset(sk2_esk70_0),the_carrier(sk2_esk70_0)),
inference(rewriting,[status(thm)],[c_30008]) ).
cnf(c_760,plain,
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p',c_0_2722_2) ).
cnf(c_21509,plain,
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(copy,[status(esa)],[c_760]) ).
cnf(c_21510,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X1 = X0 ),
inference(rewriting,[status(thm)],[c_21509]) ).
cnf(c_30453,plain,
( ~ subset(the_carrier(sk2_esk70_0),cast_as_carrier_subset(sk2_esk70_0))
| the_carrier(sk2_esk70_0) = cast_as_carrier_subset(sk2_esk70_0) ),
inference(resolution,[status(thm)],[c_30009,c_21510]) ).
cnf(c_30458,plain,
( ~ subset(the_carrier(sk2_esk70_0),cast_as_carrier_subset(sk2_esk70_0))
| the_carrier(sk2_esk70_0) = cast_as_carrier_subset(sk2_esk70_0) ),
inference(rewriting,[status(thm)],[c_30453]) ).
cnf(c_5219,negated_conjecture,
the_carrier(sk2_esk70_0) != cast_as_carrier_subset(sk2_esk70_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p',c_0_2102) ).
cnf(c_8544,negated_conjecture,
the_carrier(sk2_esk70_0) != cast_as_carrier_subset(sk2_esk70_0),
inference(copy,[status(esa)],[c_5219]) ).
cnf(c_9145,negated_conjecture,
the_carrier(sk2_esk70_0) != cast_as_carrier_subset(sk2_esk70_0),
inference(copy,[status(esa)],[c_8544]) ).
cnf(c_9464,negated_conjecture,
the_carrier(sk2_esk70_0) != cast_as_carrier_subset(sk2_esk70_0),
inference(copy,[status(esa)],[c_9145]) ).
cnf(c_14972,negated_conjecture,
the_carrier(sk2_esk70_0) != cast_as_carrier_subset(sk2_esk70_0),
inference(copy,[status(esa)],[c_9464]) ).
cnf(c_29929,plain,
the_carrier(sk2_esk70_0) != cast_as_carrier_subset(sk2_esk70_0),
inference(copy,[status(esa)],[c_14972]) ).
cnf(c_279,plain,
( subset(X0,X1)
| X1 != X0 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p',c_0_2905_1) ).
cnf(c_20547,plain,
( subset(X0,X1)
| X1 != X0 ),
inference(copy,[status(esa)],[c_279]) ).
cnf(c_30011,plain,
subset(the_carrier(sk2_esk70_0),cast_as_carrier_subset(sk2_esk70_0)),
inference(resolution,[status(thm)],[c_29991,c_20547]) ).
cnf(c_30012,plain,
subset(the_carrier(sk2_esk70_0),cast_as_carrier_subset(sk2_esk70_0)),
inference(rewriting,[status(thm)],[c_30011]) ).
cnf(c_56178,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_30458,c_29929,c_30012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU306+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.07 % Command : iprover_modulo %s %d
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Sun Jun 19 21:17:48 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % Running in mono-core mode
% 0.11/0.50 % Orienting using strategy Equiv(ClausalAll)
% 0.11/0.50 % FOF problem with conjecture
% 0.11/0.50 % 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/sandbox2/tmp/iprover_proof_62dfa7.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_f19def | grep -v "SZS"
% 0.11/0.53
% 0.11/0.53 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.11/0.53
% 0.11/0.53 %
% 0.11/0.53 % ------ iProver source info
% 0.11/0.53
% 0.11/0.53 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.11/0.53 % git: non_committed_changes: true
% 0.11/0.53 % git: last_make_outside_of_git: true
% 0.11/0.53
% 0.11/0.53 %
% 0.11/0.53 % ------ Input Options
% 0.11/0.53
% 0.11/0.53 % --out_options all
% 0.11/0.53 % --tptp_safe_out true
% 0.11/0.53 % --problem_path ""
% 0.11/0.53 % --include_path ""
% 0.11/0.53 % --clausifier .//eprover
% 0.11/0.53 % --clausifier_options --tstp-format
% 0.11/0.53 % --stdin false
% 0.11/0.53 % --dbg_backtrace false
% 0.11/0.53 % --dbg_dump_prop_clauses false
% 0.11/0.53 % --dbg_dump_prop_clauses_file -
% 0.11/0.53 % --dbg_out_stat false
% 0.11/0.53
% 0.11/0.53 % ------ General Options
% 0.11/0.53
% 0.11/0.53 % --fof false
% 0.11/0.53 % --time_out_real 150.
% 0.11/0.53 % --time_out_prep_mult 0.2
% 0.11/0.53 % --time_out_virtual -1.
% 0.11/0.53 % --schedule none
% 0.11/0.53 % --ground_splitting input
% 0.11/0.53 % --splitting_nvd 16
% 0.11/0.53 % --non_eq_to_eq false
% 0.11/0.53 % --prep_gs_sim true
% 0.11/0.53 % --prep_unflatten false
% 0.11/0.53 % --prep_res_sim true
% 0.11/0.53 % --prep_upred true
% 0.11/0.53 % --res_sim_input true
% 0.11/0.53 % --clause_weak_htbl true
% 0.11/0.53 % --gc_record_bc_elim false
% 0.11/0.53 % --symbol_type_check false
% 0.11/0.53 % --clausify_out false
% 0.11/0.53 % --large_theory_mode false
% 0.11/0.53 % --prep_sem_filter none
% 0.11/0.53 % --prep_sem_filter_out false
% 0.11/0.53 % --preprocessed_out false
% 0.11/0.53 % --sub_typing false
% 0.11/0.53 % --brand_transform false
% 0.11/0.53 % --pure_diseq_elim true
% 0.11/0.53 % --min_unsat_core false
% 0.11/0.53 % --pred_elim true
% 0.11/0.53 % --add_important_lit false
% 0.11/0.53 % --soft_assumptions false
% 0.11/0.53 % --reset_solvers false
% 0.11/0.53 % --bc_imp_inh []
% 0.11/0.53 % --conj_cone_tolerance 1.5
% 0.11/0.53 % --prolific_symb_bound 500
% 0.11/0.53 % --lt_threshold 2000
% 0.11/0.53
% 0.11/0.53 % ------ SAT Options
% 0.11/0.53
% 0.11/0.53 % --sat_mode false
% 0.11/0.53 % --sat_fm_restart_options ""
% 0.11/0.53 % --sat_gr_def false
% 0.11/0.53 % --sat_epr_types true
% 0.11/0.53 % --sat_non_cyclic_types false
% 0.11/0.53 % --sat_finite_models false
% 0.11/0.53 % --sat_fm_lemmas false
% 0.11/0.53 % --sat_fm_prep false
% 0.11/0.53 % --sat_fm_uc_incr true
% 0.11/0.53 % --sat_out_model small
% 0.11/0.53 % --sat_out_clauses false
% 0.11/0.53
% 0.11/0.53 % ------ QBF Options
% 0.11/0.53
% 0.11/0.53 % --qbf_mode false
% 0.11/0.53 % --qbf_elim_univ true
% 0.11/0.53 % --qbf_sk_in true
% 0.11/0.53 % --qbf_pred_elim true
% 0.11/0.53 % --qbf_split 32
% 0.11/0.53
% 0.11/0.53 % ------ BMC1 Options
% 0.11/0.53
% 0.11/0.53 % --bmc1_incremental false
% 0.11/0.53 % --bmc1_axioms reachable_all
% 0.11/0.53 % --bmc1_min_bound 0
% 0.11/0.53 % --bmc1_max_bound -1
% 0.11/0.53 % --bmc1_max_bound_default -1
% 0.11/0.53 % --bmc1_symbol_reachability true
% 0.11/0.53 % --bmc1_property_lemmas false
% 0.11/0.53 % --bmc1_k_induction false
% 0.11/0.53 % --bmc1_non_equiv_states false
% 0.11/0.53 % --bmc1_deadlock false
% 0.11/0.53 % --bmc1_ucm false
% 0.11/0.53 % --bmc1_add_unsat_core none
% 0.11/0.53 % --bmc1_unsat_core_children false
% 0.11/0.53 % --bmc1_unsat_core_extrapolate_axioms false
% 0.11/0.53 % --bmc1_out_stat full
% 0.11/0.53 % --bmc1_ground_init false
% 0.11/0.53 % --bmc1_pre_inst_next_state false
% 0.11/0.53 % --bmc1_pre_inst_state false
% 0.11/0.53 % --bmc1_pre_inst_reach_state false
% 0.11/0.53 % --bmc1_out_unsat_core false
% 0.11/0.53 % --bmc1_aig_witness_out false
% 0.11/0.53 % --bmc1_verbose false
% 0.11/0.53 % --bmc1_dump_clauses_tptp false
% 0.46/0.67 % --bmc1_dump_unsat_core_tptp false
% 0.46/0.67 % --bmc1_dump_file -
% 0.46/0.67 % --bmc1_ucm_expand_uc_limit 128
% 0.46/0.67 % --bmc1_ucm_n_expand_iterations 6
% 0.46/0.67 % --bmc1_ucm_extend_mode 1
% 0.46/0.67 % --bmc1_ucm_init_mode 2
% 0.46/0.67 % --bmc1_ucm_cone_mode none
% 0.46/0.67 % --bmc1_ucm_reduced_relation_type 0
% 0.46/0.67 % --bmc1_ucm_relax_model 4
% 0.46/0.67 % --bmc1_ucm_full_tr_after_sat true
% 0.46/0.67 % --bmc1_ucm_expand_neg_assumptions false
% 0.46/0.67 % --bmc1_ucm_layered_model none
% 0.46/0.67 % --bmc1_ucm_max_lemma_size 10
% 0.46/0.67
% 0.46/0.67 % ------ AIG Options
% 0.46/0.67
% 0.46/0.67 % --aig_mode false
% 0.46/0.67
% 0.46/0.67 % ------ Instantiation Options
% 0.46/0.67
% 0.46/0.67 % --instantiation_flag true
% 0.46/0.67 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.46/0.67 % --inst_solver_per_active 750
% 0.46/0.67 % --inst_solver_calls_frac 0.5
% 0.46/0.67 % --inst_passive_queue_type priority_queues
% 0.46/0.67 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.46/0.67 % --inst_passive_queues_freq [25;2]
% 0.46/0.67 % --inst_dismatching true
% 0.46/0.67 % --inst_eager_unprocessed_to_passive true
% 0.46/0.67 % --inst_prop_sim_given true
% 0.46/0.67 % --inst_prop_sim_new false
% 0.46/0.67 % --inst_orphan_elimination true
% 0.46/0.67 % --inst_learning_loop_flag true
% 0.46/0.67 % --inst_learning_start 3000
% 0.46/0.67 % --inst_learning_factor 2
% 0.46/0.67 % --inst_start_prop_sim_after_learn 3
% 0.46/0.67 % --inst_sel_renew solver
% 0.46/0.67 % --inst_lit_activity_flag true
% 0.46/0.67 % --inst_out_proof true
% 0.46/0.67
% 0.46/0.67 % ------ Resolution Options
% 0.46/0.67
% 0.46/0.67 % --resolution_flag true
% 0.46/0.67 % --res_lit_sel kbo_max
% 0.46/0.67 % --res_to_prop_solver none
% 0.46/0.67 % --res_prop_simpl_new false
% 0.46/0.67 % --res_prop_simpl_given false
% 0.46/0.67 % --res_passive_queue_type priority_queues
% 0.46/0.67 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.46/0.67 % --res_passive_queues_freq [15;5]
% 0.46/0.67 % --res_forward_subs full
% 0.46/0.67 % --res_backward_subs full
% 0.46/0.67 % --res_forward_subs_resolution true
% 0.46/0.67 % --res_backward_subs_resolution true
% 0.46/0.67 % --res_orphan_elimination false
% 0.46/0.67 % --res_time_limit 1000.
% 0.46/0.67 % --res_out_proof true
% 0.46/0.67 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_62dfa7.s
% 0.46/0.67 % --modulo true
% 0.46/0.67
% 0.46/0.67 % ------ Combination Options
% 0.46/0.67
% 0.46/0.67 % --comb_res_mult 1000
% 0.46/0.67 % --comb_inst_mult 300
% 0.46/0.67 % ------
% 0.46/0.67
% 0.46/0.67 % ------ Parsing...%
% 0.46/0.67
% 0.46/0.67
% 0.46/0.67 % ------ Statistics
% 0.46/0.67
% 0.46/0.67 % ------ General
% 0.46/0.67
% 0.46/0.67 % num_of_input_clauses: 2822
% 0.46/0.67 % num_of_input_neg_conjectures: 0
% 0.46/0.67 % num_of_splits: 0
% 0.46/0.67 % num_of_split_atoms: 0
% 0.46/0.67 % num_of_sem_filtered_clauses: 0
% 0.46/0.67 % num_of_subtypes: 0
% 0.46/0.67 % monotx_restored_types: 0
% 0.46/0.67 % sat_num_of_epr_types: 0
% 0.46/0.67 % sat_num_of_non_cyclic_types: 0
% 0.46/0.67 % sat_guarded_non_collapsed_types: 0
% 0.46/0.67 % is_epr: 0
% 0.46/0.67 % is_horn: 0
% 0.46/0.67 % has_eq: 0
% 0.46/0.67 % num_pure_diseq_elim: 0
% 0.46/0.67 % simp_replaced_by: 0
% 0.46/0.67 % res_preprocessed: 0
% 0.46/0.67 % prep_upred: 0
% 0.46/0.67 % prep_unflattend: 0
% 0.46/0.67 % pred_elim_cands: 0
% 0.46/0.67 % pred_elim: 0
% 0.46/0.67 % pred_elim_cl: 0
% 0.46/0.67 % pred_elim_cycles: 0
% 0.46/0.67 % forced_gc_time: 0
% 0.46/0.67 % gc_basic_clause_elim: 0
% 0.46/0.67 % parsing_time: 0.
% 0.46/0.67 % sem_filter_time: 0.
% 0.46/0.67 % pred_elim_time: 0.
% 0.46/0.67 % out_proof_time: 0.
% 0.46/0.67 % monotx_time: 0.
% 0.46/0.67 % subtype_inf_time: 0.
% 0.46/0.67 % unif_index_cands_time: 0.
% 0.46/0.67 %Fatal error: exception Failure("Parse error in: /export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p line: 2825 near token: '!='")
% 0.46/0.67 unif_index_add_time: 0.
% 0.46/0.67 % total_time: 0.164
% 0.46/0.67 % num_of_symbols: 271
% 0.46/0.67 % num_of_terms: 2700
% 0.46/0.67
% 0.46/0.67 % ------ Propositional Solver
% 0.46/0.67
% 0.46/0.67 % prop_solver_calls: 0
% 0.46/0.67 % prop_fast_solver_calls: 0
% 0.46/0.67 % prop_num_of_clauses: 0
% 0.46/0.67 % prop_preprocess_simplified: 0
% 0.46/0.67 % prop_fo_subsumed: 0
% 0.46/0.67 % prop_solver_time: 0.
% 0.46/0.67 % prop_fast_solver_time: 0.
% 0.46/0.67 % prop_unsat_core_time: 0.
% 0.46/0.67
% 0.46/0.67 % ------ QBF
% 0.46/0.67
% 0.46/0.67 % qbf_q_res: 0
% 0.46/0.67 % qbf_num_tautologies: 0
% 0.46/0.67 % qbf_prep_cycles: 0
% 0.46/0.67
% 0.46/0.67 % ------ BMC1
% 0.46/0.67
% 0.46/0.67 % bmc1_current_bound: -1
% 0.46/0.67 % bmc1_last_solved_bound: -1
% 0.46/0.67 % bmc1_unsat_core_size: -1
% 0.46/0.67 % bmc1_unsat_core_parents_size: -1
% 0.46/0.67 % bmc1_merge_next_fun: 0
% 0.46/0.67 % bmc1_unsat_core_clauses_time: 0.
% 0.46/0.67
% 0.46/0.67 % ------ Instantiation
% 0.46/0.67
% 0.46/0.67 % inst_num_of_clauses: undef
% 0.46/0.67 % inst_num_in_passive: undef
% 0.46/0.67 % inst_num_in_active: 0
% 0.46/0.67 % inst_num_in_unprocessed: 0
% 0.46/0.67 % inst_num_of_loops: 0
% 0.46/0.67 % inst_num_of_learning_restarts: 0
% 0.46/0.67 % inst_num_moves_active_passive: 0
% 0.46/0.67 % inst_lit_activity: 0
% 0.46/0.67 % inst_lit_activity_moves: 0
% 0.46/0.67 % inst_num_tautologies: 0
% 0.46/0.67 % inst_num_prop_implied: 0
% 0.46/0.67 % inst_num_existing_simplified: 0
% 0.46/0.67 % inst_num_eq_res_simplified: 0
% 0.46/0.67 % inst_num_child_elim: 0
% 0.46/0.67 % inst_num_of_dismatching_blockings: 0
% 0.46/0.67 % inst_num_of_non_proper_insts: 0
% 0.46/0.67 % inst_num_of_duplicates: 0
% 0.46/0.67 % inst_inst_num_from_inst_to_res: 0
% 0.46/0.67 % inst_dismatching_checking_time: 0.
% 0.46/0.67
% 0.46/0.67 % ------ Resolution
% 0.46/0.67
% 0.46/0.67 % res_num_of_clauses: undef
% 0.46/0.67 % res_num_in_passive: undef
% 0.46/0.67 % res_num_in_active: 0
% 0.46/0.67 % res_num_of_loops: 0
% 0.46/0.67 % res_forward_subset_subsumed: 0
% 0.46/0.67 % res_backward_subset_subsumed: 0
% 0.46/0.67 % res_forward_subsumed: 0
% 0.46/0.67 % res_backward_subsumed: 0
% 0.46/0.67 % res_forward_subsumption_resolution: 0
% 0.46/0.67 % res_backward_subsumption_resolution: 0
% 0.46/0.67 % res_clause_to_clause_subsumption: 0
% 0.46/0.67 % res_orphan_elimination: 0
% 0.46/0.67 % res_tautology_del: 0
% 0.46/0.67 % res_num_eq_res_simplified: 0
% 0.46/0.67 % res_num_sel_changes: 0
% 0.46/0.67 % res_moves_from_active_to_pass: 0
% 0.46/0.67
% 0.46/0.67 % Status Unknown
% 0.52/0.90 % Orienting using strategy ClausalAll
% 0.52/0.90 % FOF problem with conjecture
% 0.52/0.90 % 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/sandbox2/tmp/iprover_proof_62dfa7.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_4cb22d | grep -v "SZS"
% 0.76/0.92
% 0.76/0.92 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.76/0.92
% 0.76/0.92 %
% 0.76/0.92 % ------ iProver source info
% 0.76/0.92
% 0.76/0.92 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.76/0.92 % git: non_committed_changes: true
% 0.76/0.92 % git: last_make_outside_of_git: true
% 0.76/0.92
% 0.76/0.92 %
% 0.76/0.92 % ------ Input Options
% 0.76/0.92
% 0.76/0.92 % --out_options all
% 0.76/0.92 % --tptp_safe_out true
% 0.76/0.92 % --problem_path ""
% 0.76/0.92 % --include_path ""
% 0.76/0.92 % --clausifier .//eprover
% 0.76/0.92 % --clausifier_options --tstp-format
% 0.76/0.92 % --stdin false
% 0.76/0.92 % --dbg_backtrace false
% 0.76/0.92 % --dbg_dump_prop_clauses false
% 0.76/0.92 % --dbg_dump_prop_clauses_file -
% 0.76/0.92 % --dbg_out_stat false
% 0.76/0.92
% 0.76/0.92 % ------ General Options
% 0.76/0.92
% 0.76/0.92 % --fof false
% 0.76/0.92 % --time_out_real 150.
% 0.76/0.92 % --time_out_prep_mult 0.2
% 0.76/0.92 % --time_out_virtual -1.
% 0.76/0.92 % --schedule none
% 0.76/0.92 % --ground_splitting input
% 0.76/0.92 % --splitting_nvd 16
% 0.76/0.92 % --non_eq_to_eq false
% 0.76/0.92 % --prep_gs_sim true
% 0.76/0.92 % --prep_unflatten false
% 0.76/0.92 % --prep_res_sim true
% 0.76/0.92 % --prep_upred true
% 0.76/0.92 % --res_sim_input true
% 0.76/0.92 % --clause_weak_htbl true
% 0.76/0.92 % --gc_record_bc_elim false
% 0.76/0.92 % --symbol_type_check false
% 0.76/0.92 % --clausify_out false
% 0.76/0.92 % --large_theory_mode false
% 0.76/0.92 % --prep_sem_filter none
% 0.76/0.92 % --prep_sem_filter_out false
% 0.76/0.92 % --preprocessed_out false
% 0.76/0.92 % --sub_typing false
% 0.76/0.92 % --brand_transform false
% 0.76/0.92 % --pure_diseq_elim true
% 0.76/0.92 % --min_unsat_core false
% 0.76/0.92 % --pred_elim true
% 0.76/0.92 % --add_important_lit false
% 0.76/0.92 % --soft_assumptions false
% 0.76/0.92 % --reset_solvers false
% 0.76/0.92 % --bc_imp_inh []
% 0.76/0.92 % --conj_cone_tolerance 1.5
% 0.76/0.92 % --prolific_symb_bound 500
% 0.76/0.92 % --lt_threshold 2000
% 0.76/0.92
% 0.76/0.92 % ------ SAT Options
% 0.76/0.92
% 0.76/0.92 % --sat_mode false
% 0.76/0.92 % --sat_fm_restart_options ""
% 0.76/0.92 % --sat_gr_def false
% 0.76/0.92 % --sat_epr_types true
% 0.76/0.92 % --sat_non_cyclic_types false
% 0.76/0.92 % --sat_finite_models false
% 0.76/0.92 % --sat_fm_lemmas false
% 0.76/0.92 % --sat_fm_prep false
% 0.76/0.92 % --sat_fm_uc_incr true
% 0.76/0.92 % --sat_out_model small
% 0.76/0.92 % --sat_out_clauses false
% 0.76/0.92
% 0.76/0.92 % ------ QBF Options
% 0.76/0.92
% 0.76/0.92 % --qbf_mode false
% 0.76/0.92 % --qbf_elim_univ true
% 0.76/0.92 % --qbf_sk_in true
% 0.76/0.92 % --qbf_pred_elim true
% 0.76/0.92 % --qbf_split 32
% 0.76/0.92
% 0.76/0.92 % ------ BMC1 Options
% 0.76/0.92
% 0.76/0.92 % --bmc1_incremental false
% 0.76/0.92 % --bmc1_axioms reachable_all
% 0.76/0.92 % --bmc1_min_bound 0
% 0.76/0.92 % --bmc1_max_bound -1
% 0.76/0.92 % --bmc1_max_bound_default -1
% 0.76/0.92 % --bmc1_symbol_reachability true
% 0.76/0.92 % --bmc1_property_lemmas false
% 0.76/0.92 % --bmc1_k_induction false
% 0.76/0.92 % --bmc1_non_equiv_states false
% 0.76/0.92 % --bmc1_deadlock false
% 0.76/0.92 % --bmc1_ucm false
% 0.76/0.92 % --bmc1_add_unsat_core none
% 0.76/0.92 % --bmc1_unsat_core_children false
% 0.76/0.92 % --bmc1_unsat_core_extrapolate_axioms false
% 0.76/0.92 % --bmc1_out_stat full
% 0.76/0.92 % --bmc1_ground_init false
% 0.76/0.92 % --bmc1_pre_inst_next_state false
% 0.76/0.92 % --bmc1_pre_inst_state false
% 0.76/0.92 % --bmc1_pre_inst_reach_state false
% 0.76/0.92 % --bmc1_out_unsat_core false
% 0.76/0.92 % --bmc1_aig_witness_out false
% 0.76/0.92 % --bmc1_verbose false
% 0.76/0.92 % --bmc1_dump_clauses_tptp false
% 1.61/1.97 % --bmc1_dump_unsat_core_tptp false
% 1.61/1.97 % --bmc1_dump_file -
% 1.61/1.97 % --bmc1_ucm_expand_uc_limit 128
% 1.61/1.97 % --bmc1_ucm_n_expand_iterations 6
% 1.61/1.97 % --bmc1_ucm_extend_mode 1
% 1.61/1.97 % --bmc1_ucm_init_mode 2
% 1.61/1.97 % --bmc1_ucm_cone_mode none
% 1.61/1.97 % --bmc1_ucm_reduced_relation_type 0
% 1.61/1.97 % --bmc1_ucm_relax_model 4
% 1.61/1.97 % --bmc1_ucm_full_tr_after_sat true
% 1.61/1.97 % --bmc1_ucm_expand_neg_assumptions false
% 1.61/1.97 % --bmc1_ucm_layered_model none
% 1.61/1.97 % --bmc1_ucm_max_lemma_size 10
% 1.61/1.97
% 1.61/1.97 % ------ AIG Options
% 1.61/1.97
% 1.61/1.97 % --aig_mode false
% 1.61/1.97
% 1.61/1.97 % ------ Instantiation Options
% 1.61/1.97
% 1.61/1.97 % --instantiation_flag true
% 1.61/1.97 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.61/1.97 % --inst_solver_per_active 750
% 1.61/1.97 % --inst_solver_calls_frac 0.5
% 1.61/1.97 % --inst_passive_queue_type priority_queues
% 1.61/1.97 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.61/1.98 % --inst_passive_queues_freq [25;2]
% 1.61/1.98 % --inst_dismatching true
% 1.61/1.98 % --inst_eager_unprocessed_to_passive true
% 1.61/1.98 % --inst_prop_sim_given true
% 1.61/1.98 % --inst_prop_sim_new false
% 1.61/1.98 % --inst_orphan_elimination true
% 1.61/1.98 % --inst_learning_loop_flag true
% 1.61/1.98 % --inst_learning_start 3000
% 1.61/1.98 % --inst_learning_factor 2
% 1.61/1.98 % --inst_start_prop_sim_after_learn 3
% 1.61/1.98 % --inst_sel_renew solver
% 1.61/1.98 % --inst_lit_activity_flag true
% 1.61/1.98 % --inst_out_proof true
% 1.61/1.98
% 1.61/1.98 % ------ Resolution Options
% 1.61/1.98
% 1.61/1.98 % --resolution_flag true
% 1.61/1.98 % --res_lit_sel kbo_max
% 1.61/1.98 % --res_to_prop_solver none
% 1.61/1.98 % --res_prop_simpl_new false
% 1.61/1.98 % --res_prop_simpl_given false
% 1.61/1.98 % --res_passive_queue_type priority_queues
% 1.61/1.98 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.61/1.98 % --res_passive_queues_freq [15;5]
% 1.61/1.98 % --res_forward_subs full
% 1.61/1.98 % --res_backward_subs full
% 1.61/1.98 % --res_forward_subs_resolution true
% 1.61/1.98 % --res_backward_subs_resolution true
% 1.61/1.98 % --res_orphan_elimination false
% 1.61/1.98 % --res_time_limit 1000.
% 1.61/1.98 % --res_out_proof true
% 1.61/1.98 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_62dfa7.s
% 1.61/1.98 % --modulo true
% 1.61/1.98
% 1.61/1.98 % ------ Combination Options
% 1.61/1.98
% 1.61/1.98 % --comb_res_mult 1000
% 1.61/1.98 % --comb_inst_mult 300
% 1.61/1.98 % ------
% 1.61/1.98
% 1.61/1.98 % ------ Parsing...% successful
% 1.61/1.98
% 1.61/1.98 % ------ Preprocessing... gs_s sp: 138 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.98
% 1.61/1.98 % ------ Proving...
% 1.61/1.98 % ------ Problem Properties
% 1.61/1.98
% 1.61/1.98 %
% 1.61/1.98 % EPR false
% 1.61/1.98 % Horn false
% 1.61/1.98 % Has equality true
% 1.61/1.98
% 1.61/1.98 % % ------ Input Options Time Limit: Unbounded
% 1.61/1.98
% 1.61/1.98
% 1.61/1.98 % warning: Clause {~(relation(X0));~(function(X0));finite(relation_image(X0,X1));~(finite(X1))} has no selected literals
% 1.61/1.98 cnf(c_5048,plain,
% 1.61/1.98 ( ~ relation(X0)
% 1.61/1.98 | ~ function(X0)
% 1.61/1.98 | finite(relation_image(X0,X1))
% 1.61/1.98 | ~ finite(X1) ),
% 1.61/1.98 file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p', c_0_1919) ).
% 1.61/1.98
% 1.61/1.98 % warning: Clause {finite(set_intersection2(X0,X1));~(finite(X0))} has no selected literals
% 1.61/1.98 cnf(c_5134,plain,
% 1.61/1.98 ( finite(set_intersection2(X0,X1)) | ~ finite(X0) ),
% 1.61/1.98 file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p', c_0_2008) ).
% 1.61/1.98
% 1.61/1.98 Compiling...
% 1.61/1.98 Loading plugin: done.
% 1.61/1.98 Compiling...
% 1.61/1.98 Loading plugin: done.
% 1.61/1.98 Compiling...
% 1.61/1.98 Loading plugin: done.
% 1.61/1.98 Compiling...
% 1.61/1.98 Loading plugin: done.
% 1.61/1.98 Compiling...
% 1.61/1.98 Loading plugin: done.
% 1.61/1.98 % warning: Clause {~(relation(X0));~(function(X0));finite(relation_image(X0,X1));~(finite(X1))} has no selected literals
% 1.61/1.98 cnf(c_5048,plain,
% 1.61/1.98 ( ~ relation(X0)
% 1.61/1.98 | ~ function(X0)
% 1.61/1.98 | finite(relation_image(X0,X1))
% 1.61/1.98 | ~ finite(X1) ),
% 1.61/1.98 file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p', c_0_1919) ).
% 1.76/1.98
% 1.76/1.98 % warning: Clause {finite(set_intersection2(X0,X1));~(finite(X0))} has no selected literals
% 1.76/1.98 cnf(c_5134,plain,
% 1.76/1.98 ( finite(set_intersection2(X0,X1)) | ~ finite(X0) ),
% 1.76/1.98 file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p', c_0_2008) ).
% 1.76/1.98
% 1.76/1.98 % 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
% 1.76/1.98 cnf(c_14738,plain,
% 1.76/1.98 ( ~ relation(X0)
% 1.76/1.98 | ~ function(X0)
% 1.76/1.98 | in(ordered_pair(X1,X2),X0)
% 1.76/1.98 | ~ in(X1,relation_dom(X0))
% 1.76/1.98 | X2 != apply(X0,X1) ),
% 1.76/1.98 inference(copy,[status(esa)],[c_9731]) ).
% 1.76/1.98
% 1.76/1.98 cnf(c_9731,plain,
% 1.76/1.98 ( ~ relation(X0)
% 1.76/1.98 | ~ function(X0)
% 1.76/1.98 | in(ordered_pair(X1,X2),X0)
% 1.76/1.98 | ~ in(X1,relation_dom(X0))
% 1.76/1.98 | X2 != apply(X0,X1) ),
% 1.76/1.98 inference(copy,[status(esa)],[c_8878]) ).
% 1.76/1.98
% 1.76/1.98 cnf(c_8878,plain,
% 1.76/1.98 ( ~ relation(X0)
% 1.76/1.98 | ~ function(X0)
% 1.76/1.98 | in(ordered_pair(X1,X2),X0)
% 1.76/1.98 | ~ in(X1,relation_dom(X0))
% 1.76/1.98 | X2 != apply(X0,X1) ),
% 1.76/1.98 inference(copy,[status(esa)],[c_7706]) ).
% 1.76/1.98
% 1.76/1.98 cnf(c_7706,plain,
% 1.76/1.98 ( ~ relation(X0)
% 1.76/1.98 | ~ function(X0)
% 1.76/1.98 | in(ordered_pair(X1,X2),X0)
% 1.76/1.98 | ~ in(X1,relation_dom(X0))
% 1.76/1.98 | X2 != apply(X0,X1) ),
% 1.76/1.98 inference(copy,[status(esa)],[c_4879]) ).
% 1.76/1.98
% 1.76/1.98 cnf(c_4879,plain,
% 1.76/1.98 ( ~ relation(X0)
% 1.76/1.98 | ~ function(X0)
% 1.76/1.98 | in(ordered_pair(X1,X2),X0)
% 1.76/1.98 | ~ in(X1,relation_dom(X0))
% 1.76/1.98 | X2 != apply(X0,X1) ),
% 1.76/1.98 file('/export/starexec/sandbox2/tmp/iprover_modulo_bb2010.p', c_0_1747) ).
% 1.76/1.98
% 1.76/1.98 % % ------ Current options:
% 1.76/1.98
% 1.76/1.98 % ------ Input Options
% 1.76/1.98
% 1.76/1.98 % --out_options all
% 1.76/1.98 % --tptp_safe_out true
% 1.76/1.98 % --problem_path ""
% 1.76/1.98 % --include_path ""
% 1.76/1.98 % --clausifier .//eprover
% 1.76/1.98 % --clausifier_options --tstp-format
% 1.76/1.98 % --stdin false
% 1.76/1.98 % --dbg_backtrace false
% 1.76/1.98 % --dbg_dump_prop_clauses false
% 1.76/1.98 % --dbg_dump_prop_clauses_file -
% 1.76/1.98 % --dbg_out_stat false
% 1.76/1.98
% 1.76/1.98 % ------ General Options
% 1.76/1.98
% 1.76/1.98 % --fof false
% 1.76/1.98 % --time_out_real 150.
% 1.76/1.98 % --time_out_prep_mult 0.2
% 1.76/1.98 % --time_out_virtual -1.
% 1.76/1.98 % --schedule none
% 1.76/1.98 % --ground_splitting input
% 1.76/1.98 % --splitting_nvd 16
% 1.76/1.98 % --non_eq_to_eq false
% 1.76/1.98 % --prep_gs_sim true
% 1.76/1.98 % --prep_unflatten false
% 1.76/1.98 % --prep_res_sim true
% 1.76/1.98 % --prep_upred true
% 1.76/1.98 % --res_sim_input true
% 1.76/1.98 % --clause_weak_htbl true
% 1.76/1.98 % --gc_record_bc_elim false
% 1.76/1.98 % --symbol_type_check false
% 1.76/1.98 % --clausify_out false
% 1.76/1.98 % --large_theory_mode false
% 1.76/1.98 % --prep_sem_filter none
% 1.76/1.98 % --prep_sem_filter_out false
% 1.76/1.98 % --preprocessed_out false
% 1.76/1.98 % --sub_typing false
% 1.76/1.98 % --brand_transform false
% 1.76/1.98 % --pure_diseq_elim true
% 1.76/1.98 % --min_unsat_core false
% 1.76/1.98 % --pred_elim true
% 1.76/1.98 % --add_important_lit false
% 1.76/1.98 % --soft_assumptions false
% 1.76/1.98 % --reset_solvers false
% 1.76/1.98 % --bc_imp_inh []
% 1.76/1.98 % --conj_cone_tolerance 1.5
% 1.76/1.98 % --prolific_symb_bound 500
% 1.76/1.98 % --lt_threshold 2000
% 1.76/1.98
% 1.76/1.98 % ------ SAT Options
% 1.76/1.98
% 1.76/1.98 % --sat_mode false
% 1.76/1.98 % --sat_fm_restart_options ""
% 1.76/1.98 % --sat_gr_def false
% 1.76/1.98 % --sat_epr_types true
% 1.76/1.98 % --sat_non_cyclic_types false
% 1.76/1.98 % --sat_finite_models false
% 1.76/1.98 % --sat_fm_lemmas false
% 1.76/1.98 % --sat_fm_prep false
% 1.76/1.98 % --sat_fm_uc_incr true
% 1.76/1.98 % --sat_out_model small
% 1.76/1.98 % --sat_out_clauses false
% 2.68/2.97
% 2.68/2.97 % ------ QBF Options
% 2.68/2.97
% 2.68/2.97 % --qbf_mode false
% 2.68/2.97 % --qbf_elim_univ true
% 2.68/2.97 % --qbf_sk_in true
% 2.68/2.97 % --qbf_pred_elim true
% 2.68/2.97 % --qbf_split 32
% 2.68/2.97
% 2.68/2.97 % ------ BMC1 Options
% 2.68/2.97
% 2.68/2.97 % --bmc1_incremental false
% 2.68/2.97 % --bmc1_axioms reachable_all
% 2.68/2.97 % --bmc1_min_bound 0
% 2.68/2.97 % --bmc1_max_bound -1
% 2.68/2.97 % --bmc1_max_bound_default -1
% 2.68/2.97 % --bmc1_symbol_reachability true
% 2.68/2.97 % --bmc1_property_lemmas false
% 2.68/2.97 % --bmc1_k_induction false
% 2.68/2.97 % --bmc1_non_equiv_states false
% 2.68/2.97 % --bmc1_deadlock false
% 2.68/2.97 % --bmc1_ucm false
% 2.68/2.97 % --bmc1_add_unsat_core none
% 2.68/2.97 % --bmc1_unsat_core_children false
% 2.68/2.97 % --bmc1_unsat_core_extrapolate_axioms false
% 2.68/2.97 % --bmc1_out_stat full
% 2.68/2.97 % --bmc1_ground_init false
% 2.68/2.97 % --bmc1_pre_inst_next_state false
% 2.68/2.97 % --bmc1_pre_inst_state false
% 2.68/2.97 % --bmc1_pre_inst_reach_state false
% 2.68/2.97 % --bmc1_out_unsat_core false
% 2.68/2.97 % --bmc1_aig_witness_out false
% 2.68/2.97 % --bmc1_verbose false
% 2.68/2.97 % --bmc1_dump_clauses_tptp false
% 2.68/2.97 % --bmc1_dump_unsat_core_tptp false
% 2.68/2.97 % --bmc1_dump_file -
% 2.68/2.97 % --bmc1_ucm_expand_uc_limit 128
% 2.68/2.97 % --bmc1_ucm_n_expand_iterations 6
% 2.68/2.97 % --bmc1_ucm_extend_mode 1
% 2.68/2.97 % --bmc1_ucm_init_mode 2
% 2.68/2.97 % --bmc1_ucm_cone_mode none
% 2.68/2.97 % --bmc1_ucm_reduced_relation_type 0
% 2.68/2.97 % --bmc1_ucm_relax_model 4
% 2.68/2.97 % --bmc1_ucm_full_tr_after_sat true
% 2.68/2.97 % --bmc1_ucm_expand_neg_assumptions false
% 2.68/2.97 % --bmc1_ucm_layered_model none
% 2.68/2.97 % --bmc1_ucm_max_lemma_size 10
% 2.68/2.97
% 2.68/2.97 % ------ AIG Options
% 2.68/2.97
% 2.68/2.97 % --aig_mode false
% 2.68/2.97
% 2.68/2.97 % ------ Instantiation Options
% 2.68/2.97
% 2.68/2.97 % --instantiation_flag true
% 2.68/2.97 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 2.68/2.97 % --inst_solver_per_active 750
% 2.68/2.97 % --inst_solver_calls_frac 0.5
% 2.68/2.97 % --inst_passive_queue_type priority_queues
% 2.68/2.97 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.68/2.97 % --inst_passive_queues_freq [25;2]
% 2.68/2.97 % --inst_dismatching true
% 2.68/2.97 % --inst_eager_unprocessed_to_passive true
% 2.68/2.97 % --inst_prop_sim_given true
% 2.68/2.97 % --inst_prop_sim_new false
% 2.68/2.97 % --inst_orphan_elimination true
% 2.68/2.97 % --inst_learning_loop_flag true
% 2.68/2.97 % --inst_learning_start 3000
% 2.68/2.97 % --inst_learning_factor 2
% 2.68/2.97 % --inst_start_prop_sim_after_learn 3
% 2.68/2.97 % --inst_sel_renew solver
% 2.68/2.97 % --inst_lit_activity_flag true
% 2.68/2.97 % --inst_out_proof true
% 2.68/2.97
% 2.68/2.97 % ------ Resolution Options
% 2.68/2.97
% 2.68/2.97 % --resolution_flag true
% 2.68/2.97 % --res_lit_sel kbo_max
% 2.68/2.97 % --res_to_prop_solver none
% 2.68/2.97 % --res_prop_simpl_new false
% 2.68/2.97 % --res_prop_simpl_given false
% 2.68/2.97 % --res_passive_queue_type priority_queues
% 2.68/2.97 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.68/2.97 % --res_passive_queues_freq [15;5]
% 2.68/2.97 % --res_forward_subs full
% 2.68/2.97 % --res_backward_subs full
% 2.68/2.97 % --res_forward_subs_resolution true
% 2.68/2.97 % --res_backward_subs_resolution true
% 2.68/2.97 % --res_orphan_elimination false
% 2.68/2.97 % --res_time_limit 1000.
% 2.68/2.97 % --res_out_proof true
% 2.68/2.97 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_62dfa7.s
% 2.68/2.97 % --modulo true
% 2.68/2.97
% 2.68/2.97 % ------ Combination Options
% 2.68/2.97
% 2.68/2.97 % --comb_res_mult 1000
% 2.68/2.97 % --comb_inst_mult 300
% 2.68/2.97 % ------
% 2.68/2.97
% 2.68/2.97
% 2.68/2.97
% 2.68/2.97 % ------ Proving...
% 2.68/2.97 %
% 2.68/2.97
% 2.68/2.97
% 2.68/2.97 % Resolution empty clause
% 2.68/2.97
% 2.68/2.97 % ------ Statistics
% 2.68/2.97
% 2.68/2.97 % ------ General
% 2.68/2.97
% 2.68/2.97 % num_of_input_clauses: 5248
% 2.68/2.97 % num_of_input_neg_conjectures: 2
% 2.68/2.97 % num_of_splits: 138
% 2.68/2.97 % num_of_split_atoms: 22
% 2.68/2.97 % num_of_sem_filtered_clauses: 0
% 2.68/2.97 % num_of_subtypes: 0
% 2.68/2.97 % monotx_restored_types: 0
% 2.68/2.97 % sat_num_of_epr_types: 0
% 2.68/2.97 % sat_num_of_non_cyclic_types: 0
% 2.68/2.97 % sat_guarded_non_collapsed_types: 0
% 2.68/2.97 % is_epr: 0
% 2.68/2.97 % is_horn: 0
% 2.68/2.97 % has_eq: 1
% 2.68/2.97 % num_pure_diseq_elim: 0
% 2.68/2.97 % simp_replaced_by: 0
% 2.68/2.97 % res_preprocessed: 909
% 2.68/2.97 % prep_upred: 0
% 2.68/2.97 % prep_unflattend: 54
% 2.68/2.97 % pred_elim_cands: 58
% 2.68/2.97 % pred_elim: 14
% 2.68/2.97 % pred_elim_cl: 232
% 2.68/2.97 % pred_elim_cycles: 40
% 2.68/2.97 % forced_gc_time: 0
% 2.68/2.97 % gc_basic_clause_elim: 0
% 2.68/2.97 % parsing_time: 0.243
% 2.68/2.97 % sem_filter_time: 0.
% 2.68/2.97 % pred_elim_time: 0.103
% 2.68/2.97 % out_proof_time: 0.
% 2.68/2.97 % monotx_time: 0.
% 2.68/2.97 % subtype_inf_time: 0.
% 2.68/2.97 % unif_index_cands_time: 0.
% 2.68/2.97 % unif_index_add_time: 0.001
% 2.68/2.97 % total_time: 2.064
% 2.68/2.97 % num_of_symbols: 477
% 2.68/2.97 % num_of_terms: 31446
% 2.68/2.97
% 2.68/2.97 % ------ Propositional Solver
% 2.68/2.97
% 2.68/2.97 % prop_solver_calls: 1
% 2.68/2.97 % prop_fast_solver_calls: 8540
% 2.68/2.97 % prop_num_of_clauses: 4221
% 2.68/2.97 % prop_preprocess_simplified: 24670
% 2.68/2.97 % prop_fo_subsumed: 48
% 2.68/2.97 % prop_solver_time: 0.
% 2.68/2.97 % prop_fast_solver_time: 0.01
% 2.68/2.97 % prop_unsat_core_time: 0.
% 2.68/2.97
% 2.68/2.97 % ------ QBF
% 2.68/2.97
% 2.68/2.97 % qbf_q_res: 0
% 2.68/2.97 % qbf_num_tautologies: 0
% 2.68/2.97 % qbf_prep_cycles: 0
% 2.68/2.97
% 2.68/2.97 % ------ BMC1
% 2.68/2.97
% 2.68/2.97 % bmc1_current_bound: -1
% 2.68/2.97 % bmc1_last_solved_bound: -1
% 2.68/2.97 % bmc1_unsat_core_size: -1
% 2.68/2.97 % bmc1_unsat_core_parents_size: -1
% 2.68/2.97 % bmc1_merge_next_fun: 0
% 2.68/2.97 % bmc1_unsat_core_clauses_time: 0.
% 2.68/2.97
% 2.68/2.97 % ------ Instantiation
% 2.68/2.97
% 2.68/2.97 % inst_num_of_clauses: 4820
% 2.68/2.97 % inst_num_in_passive: 0
% 2.68/2.97 % inst_num_in_active: 0
% 2.68/2.97 % inst_num_in_unprocessed: 4998
% 2.68/2.97 % inst_num_of_loops: 0
% 2.68/2.97 % inst_num_of_learning_restarts: 0
% 2.68/2.97 % inst_num_moves_active_passive: 0
% 2.68/2.97 % inst_lit_activity: 0
% 2.68/2.97 % inst_lit_activity_moves: 0
% 2.68/2.97 % inst_num_tautologies: 0
% 2.68/2.97 % inst_num_prop_implied: 0
% 2.68/2.97 % inst_num_existing_simplified: 0
% 2.68/2.97 % inst_num_eq_res_simplified: 0
% 2.68/2.97 % inst_num_child_elim: 0
% 2.68/2.97 % inst_num_of_dismatching_blockings: 0
% 2.68/2.97 % inst_num_of_non_proper_insts: 0
% 2.68/2.97 % inst_num_of_duplicates: 0
% 2.68/2.97 % inst_inst_num_from_inst_to_res: 0
% 2.68/2.97 % inst_dismatching_checking_time: 0.
% 2.68/2.97
% 2.68/2.97 % ------ Resolution
% 2.68/2.97
% 2.68/2.97 % res_num_of_clauses: 17360
% 2.68/2.97 % res_num_in_passive: 11869
% 2.68/2.97 % res_num_in_active: 1615
% 2.68/2.97 % res_num_of_loops: 310
% 2.68/2.97 % res_forward_subset_subsumed: 3309
% 2.68/2.97 % res_backward_subset_subsumed: 2
% 2.68/2.97 % res_forward_subsumed: 67
% 2.68/2.97 % res_backward_subsumed: 0
% 2.68/2.97 % res_forward_subsumption_resolution: 47
% 2.68/2.97 % res_backward_subsumption_resolution: 0
% 2.68/2.97 % res_clause_to_clause_subsumption: 2363
% 2.68/2.97 % res_orphan_elimination: 0
% 2.68/2.97 % res_tautology_del: 39
% 2.68/2.97 % res_num_eq_res_simplified: 2
% 2.68/2.97 % res_num_sel_changes: 0
% 2.68/2.97 % res_moves_from_active_to_pass: 0
% 2.68/2.97
% 2.68/2.97 % Status Unsatisfiable
% 2.68/2.97 % SZS status Theorem
% 2.68/2.97 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------